Align Judge data with paper J1 and J2; remove J3
Browse filesKeep Apply unchanged; retain J1 full 300 and separate filtered 261; replace error detection with J2 strategy identification 80.
- DATASET_VERSION_ZH.md +61 -0
- README.md +79 -35
- data/judge_j2.json +0 -0
- data/judge_j3.json +0 -1154
- data/manifest.json +59 -0
- data/subsets/judge_j1_paper_filtered_261.json +0 -0
DATASET_VERSION_ZH.md
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# 论文数据版本与使用口径
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当前数据版本为 `paper-aligned-v1`。Judge 只包含论文定义的两个任务：
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| 任务 | 数据文件（相对数据目录） | 数量 | 答案形式 |
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|---|---|---:|---|
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| Apply | `sensemath_v2_d2.json`、`sensemath_v2_d4.json`、`sensemath_v2_d8.json`、`sensemath_v2_d16.json` | 每个文件 400 组、1200 题；共 4800 题 | 原题答案 |
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| J1：捷径适用性判断 | `judge_j1.json` | 300 题 | YES / NO |
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| J2：策略识别 | `judge_j2.json` | 80 题 | SHORTCUT / COMPUTATION |
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| J1 论文筛选子集 | `subsets/judge_j1_paper_filtered_261.json` | 261 题，为全量 J1 的子集 | YES / NO |
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GitHub 数据目录是 `benchmark/`，HF 数据目录是 `data/`；目录内使用相同的文件名、任务定义和 `manifest.json`。题目、提示词、选项、答案与原来源一致，本次只统一版本和入口。
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## J1 两种口径不能混合
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J1 默认采用 300 题全量版本。论文部分结果使用 261 题筛选集，两者单独报告；不能把 261 题结果写成 300 题成绩，也不能把子集再次加入总题量。筛选集的题目 ID 和内容均与全量中的对应记录相同。
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旧 GitHub 默认文件曾为 261 题，现保留在明确命名的 `subsets/` 路径。两者差异为 39 道 OE 题，原有题目没有重写。
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## J2 按论文定义
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J2 给出题目及已有解法，判断该解法使用的是捷径还是逐步计算。80 题中有 54 个 SHORTCUT 标签和 26 个 COMPUTATION 标签。不能把其他任务的历史输出改名后作为这 80 题的结果。
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Apply 与 Generate 仍属于论文整体评测设置。当前清单管理发布的 Apply 和 Judge 数据，不代表新增了 Generate 任务文件或模型结果。
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## 校验和运行
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在 GitHub 仓库根目录执行无模型调用的校验：
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```bash
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python code/run_judge_tasks.py --step validate --task all
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python code/run_judge_tasks.py --step validate --task j1 --j1-profile paper-filtered
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```
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默认 J1 为 300 题；复现筛选集结果时显式指定 `--j1-profile paper-filtered`。读取 HF 本地副本时可用 `--data-dir /path/to/hf/data`，该目录必须包含对应的清单文件。
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推理示例（这些命令会调用模型并产生费用，此次版本同步没有执行）：
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```bash
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python code/run_judge_tasks.py --step inference --task j1 --api --api-model gpt-4.1-mini
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python code/run_judge_tasks.py --step inference --task j1 --j1-profile paper-filtered --api --api-model gpt-4.1-mini
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python code/run_judge_tasks.py --step inference --task j2 --api --api-model gpt-4.1-mini
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```
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新输出放入 `results/paper-aligned-v1/`，J1 文件名区分 `full` 与 `paper-filtered`。每条结果记录任务名、数据哈希和预期题量；续跑会拒绝不同版本、子集、提示词或答案的记录。旧 `results/` 输出保持原状，不自动迁移或改写。
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分析时也应选择相同的 J1 profile。现有答案提取和评分规则未在本次重构；版本校验不等于评分器或所有策略标签已通过有效性验证。
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## 精确读取原始 JSON
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对大整数题，建议使用 Python 的 JSON 读取以保留整数精度，不要先把数值转换为浮点数：
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```python
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import json
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from pathlib import Path
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data_dir = Path("benchmark") # HF 本地副本则为 data/
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families = json.loads((data_dir / "sensemath_v2_d16.json").read_bytes())
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```
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文件哈希和任务数量见数据目录中的 `manifest.json`。本次同步不修改历史 Git 提交，也不把内部审计快照或试改题库作为额外数据发布。
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README.md
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- math
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- number-sense
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- benchmark
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- shortcuts
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- numerical-reasoning
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size_categories:
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- 1K<n<10K
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---
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# SenseMath:
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##
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| `data/sensemath_v2_d16.json` | 400 families, 16-digit operands |
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| `data/judge_j1.json` | J1 task: shortcut recognition (251 items) |
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| `data/judge_j2.json` | J2 task: strategy identification (80 items) |
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| `data/judge_j3.json` | J3 task items |
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## Usage
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from datasets import load_dataset
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ds = load_dataset("DaydreamerMZM/SenseMath", split="train")
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import json
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```
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## Citation
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```bibtex
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@article{
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title={SenseMath:
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author={Zhuang, Haomin and Wang, Xiangqi and Shen, Yili and Cheng, Ying and Zhang, Xiangliang},
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journal={arXiv preprint arXiv:
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year={
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}
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```
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- **Code**: [GitHub](https://github.com/zhmzm/SenseMath)
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- **Project Page**: [zhmzm.github.io/SenseMath](https://zhmzm.github.io/SenseMath/)
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- math
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- number-sense
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- benchmark
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size_categories:
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- 1K<n<10K
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configs:
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- config_name: apply_d2
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data_files:
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- split: train
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path: data/sensemath_v2_d2.json
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- config_name: apply_d4
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data_files:
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- split: train
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path: data/sensemath_v2_d4.json
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- config_name: apply_d8
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data_files:
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- split: train
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path: data/sensemath_v2_d8.json
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- config_name: apply_d16
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data_files:
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- split: train
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path: data/sensemath_v2_d16.json
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- config_name: judge_j1
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data_files:
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- split: train
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path: data/judge_j1.json
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- config_name: judge_j1_paper_filtered_261
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data_files:
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- split: train
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path: data/subsets/judge_j1_paper_filtered_261.json
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- config_name: judge_j2
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data_files:
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- split: train
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path: data/judge_j2.json
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---
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# SenseMath: Do LLMs Have Number Sense? Evaluating Shortcut Use, Judgment, and Generation
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SenseMath contains 4,800 Apply items across eight number-sense categories and four
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nominal digit-scale conditions, with strong, weak, and control variants. The
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paper's Judge setting contains exactly J1 shortcut appropriateness and J2 strategy
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identification. Current data version: `paper-aligned-v1`.
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## Files and Task Definitions
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| File | Task | Records |
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|------|------|--------:|
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| `data/sensemath_v2_d2.json` | Apply, d2 | 400 families / 1,200 items |
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| `data/sensemath_v2_d4.json` | Apply, d4 | 400 families / 1,200 items |
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| `data/sensemath_v2_d8.json` | Apply, d8 | 400 families / 1,200 items |
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| `data/sensemath_v2_d16.json` | Apply, d16 | 400 families / 1,200 items |
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| `data/judge_j1.json` | J1: is a shortcut appropriate? YES / NO | 300 items |
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| `data/judge_j2.json` | J2: classify a supplied solution as SHORTCUT / COMPUTATION | 80 items |
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| `data/subsets/judge_j1_paper_filtered_261.json` | Separate J1 reporting subset | 261 of the 300 J1 items |
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The full J1 and filtered J1 profiles are reported separately in the paper. Do not
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pool their scores or add the subset to the total item count. J2 has 54 SHORTCUT
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and 26 COMPUTATION labels. Task identity must be determined from the manifest and
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`task_type`, not from a filename in an earlier revision.
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`data/manifest.json` records task identities, counts, and SHA256 hashes. The GitHub
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repository uses the same data filenames under `benchmark/` rather than `data/`.
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Questions, options, prompts and reference labels are retained from their source
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sets; this version alignment is not a new model evaluation or a semantic
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revalidation of every strategy label.
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## Usage
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Read original JSON with Python to preserve large integer values exactly:
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```python
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import json
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from pathlib import Path
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families = json.loads(Path("data/sensemath_v2_d4.json").read_bytes())
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j1 = json.loads(Path("data/judge_j1.json").read_bytes())
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j2 = json.loads(Path("data/judge_j2.json").read_bytes())
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```
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The named configurations above separate the different schemas; do not combine
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all JSON files into a single task. For exact arithmetic, original JSON integers
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are authoritative rather than any floating-point conversion by downstream tools.
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Use the GitHub Judge runner with `--step validate` to verify hashes and task types.
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J1 defaults to the 300-item profile; select `--j1-profile paper-filtered` for the
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261-item subset. The runner accepts an HF checkout via `--data-dir /path/to/data`.
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## 中文说明
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本版本严格对应论文的 J1、J2：J1 判断捷径是否适用，J2 判断给定解法属于捷径还是逐步计算。J1 全量 300 题与论文筛选 261 题分别使用，不能混算。完整说明见 [数据版本与使用口径](DATASET_VERSION_ZH.md)。
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## Citation
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```bibtex
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@article{zhuang2026sensemath,
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title={SenseMath: Do LLMs Have Number Sense? Evaluating Shortcut Use, Judgment, and Generation},
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author={Zhuang, Haomin and Wang, Xiangqi and Shen, Yili and Cheng, Ying and Zhang, Xiangliang},
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journal={arXiv preprint arXiv:2604.01988},
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year={2026}
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}
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```
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- [Paper](https://arxiv.org/abs/2604.01988)
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- [Code](https://github.com/zhmzm/SenseMath)
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- [Project page](https://zhmzm.github.io/SenseMath/)
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data/judge_j2.json
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The diff for this file is too large to render.
See raw diff
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data/judge_j3.json
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[
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{
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"task_id": "J3_compatible_numbers_000642",
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"task_type": "J3_pairwise_efficiency",
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"category": "compatible_numbers",
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"problem": "Estimate 5082 × 1800.",
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"solution_a": "Algorithmic approach (4 steps): Compute step by step → 9147600",
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"solution_b": "NS approach (2 steps): Round to 5000×2000 for easy mental computation. → 9147600",
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"correct_answer": "B",
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"ns_steps": 2,
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"algo_steps": 4,
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"prompt": "Both solutions below are correct. Which one uses fewer reasoning steps? Answer A or B.\n\nProblem: Estimate 5082 × 1800.\n\nSolution A: Algorithmic approach (4 steps): Compute step by step → 9147600\n\nSolution B: NS approach (2 steps): Round to 5000×2000 for easy mental computation. → 9147600"
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},
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{
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"task_id": "J3_cancellation_identity_000568",
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"task_type": "J3_pairwise_efficiency",
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"category": "cancellation_identity",
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"problem": "Evaluate: 9227 + 8064 - 8063",
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"solution_a": "NS approach (2 steps): Near-cancellation: 8064 - 8063 = 1, so answer ≈ 9227 + 1. → 9228",
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"solution_b": "Algorithmic approach (3 steps): Compute step by step → 9228",
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"correct_answer": "A",
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"ns_steps": 2,
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"algo_steps": 3,
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"prompt": "Both solutions below are correct. Which one uses fewer reasoning steps? Answer A or B.\n\nProblem: Evaluate: 9227 + 8064 - 8063\n\nSolution A: NS approach (2 steps): Near-cancellation: 8064 - 8063 = 1, so answer ≈ 9227 + 1. → 9228\n\nSolution B: Algorithmic approach (3 steps): Compute step by step → 9228"
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},
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{
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"task_id": "J3_equation_reasoning_000709",
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"task_type": "J3_pairwise_efficiency",
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"category": "equation_reasoning",
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"problem": "What value fills the blank? 3459 × 5559 × 2959 = ___ × 2959 × 3459",
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"solution_a": "NS approach (1 steps): Recognize commutativity/distributive law — matching terms cancel. → 5559",
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"solution_b": "Algorithmic approach (3 steps): Compute step by step → 5559",
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"correct_answer": "A",
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"ns_steps": 1,
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"algo_steps": 3,
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"prompt": "Both solutions below are correct. Which one uses fewer reasoning steps? Answer A or B.\n\nProblem: What value fills the blank? 3459 × 5559 × 2959 = ___ × 2959 × 3459\n\nSolution A: NS approach (1 steps): Recognize commutativity/distributive law — matching terms cancel. → 5559\n\nSolution B: Algorithmic approach (3 steps): Compute step by step → 5559"
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-
},
|
| 38 |
-
{
|
| 39 |
-
"task_id": "J3_option_elimination_000798",
|
| 40 |
-
"task_type": "J3_pairwise_efficiency",
|
| 41 |
-
"category": "option_elimination",
|
| 42 |
-
"problem": "What is 1760 × 7480?",
|
| 43 |
-
"solution_a": "NS approach (2 steps): Check trailing digit / parity / magnitude — only one option matches. → 13164800",
|
| 44 |
-
"solution_b": "Algorithmic approach (4 steps): Compute step by step → 13164800",
|
| 45 |
-
"correct_answer": "A",
|
| 46 |
-
"ns_steps": 2,
|
| 47 |
-
"algo_steps": 4,
|
| 48 |
-
"prompt": "Both solutions below are correct. Which one uses fewer reasoning steps? Answer A or B.\n\nProblem: What is 1760 × 7480?\n\nSolution A: NS approach (2 steps): Check trailing digit / parity / magnitude — only one option matches. → 13164800\n\nSolution B: Algorithmic approach (4 steps): Compute step by step → 13164800"
|
| 49 |
-
},
|
| 50 |
-
{
|
| 51 |
-
"task_id": "J3_magnitude_estimation_000415",
|
| 52 |
-
"task_type": "J3_pairwise_efficiency",
|
| 53 |
-
"category": "magnitude_estimation",
|
| 54 |
-
"problem": "Which of the following is the best estimate for 9900 * 9900?",
|
| 55 |
-
"solution_a": "Algorithmic approach (4 steps): Compute step by step → 98010000",
|
| 56 |
-
"solution_b": "NS approach (2 steps): Round both to 10000 and multiply. → 98010000",
|
| 57 |
-
"correct_answer": "B",
|
| 58 |
-
"ns_steps": 2,
|
| 59 |
-
"algo_steps": 4,
|
| 60 |
-
"prompt": "Both solutions below are correct. Which one uses fewer reasoning steps? Answer A or B.\n\nProblem: Which of the following is the best estimate for 9900 * 9900?\n\nSolution A: Algorithmic approach (4 steps): Compute step by step → 98010000\n\nSolution B: NS approach (2 steps): Round both to 10000 and multiply. → 98010000"
|
| 61 |
-
},
|
| 62 |
-
{
|
| 63 |
-
"task_id": "J3_relative_distance_000547",
|
| 64 |
-
"task_type": "J3_pairwise_efficiency",
|
| 65 |
-
"category": "relative_distance",
|
| 66 |
-
"problem": "Which is larger: 1518/3038 or 3432/6744?",
|
| 67 |
-
"solution_a": "NS approach (2 steps): One is below 1/2, the other above; no computation needed. → 3432/6744",
|
| 68 |
-
"solution_b": "Algorithmic approach (3 steps): Compute step by step → 3432/6744",
|
| 69 |
-
"correct_answer": "A",
|
| 70 |
-
"ns_steps": 2,
|
| 71 |
-
"algo_steps": 3,
|
| 72 |
-
"prompt": "Both solutions below are correct. Which one uses fewer reasoning steps? Answer A or B.\n\nProblem: Which is larger: 1518/3038 or 3432/6744?\n\nSolution A: NS approach (2 steps): One is below 1/2, the other above; no computation needed. → 3432/6744\n\nSolution B: Algorithmic approach (3 steps): Compute step by step → 3432/6744"
|
| 73 |
-
},
|
| 74 |
-
{
|
| 75 |
-
"task_id": "J3_cancellation_identity_000579",
|
| 76 |
-
"task_type": "J3_pairwise_efficiency",
|
| 77 |
-
"category": "cancellation_identity",
|
| 78 |
-
"problem": "Evaluate: 1817 + 5124 - 5125",
|
| 79 |
-
"solution_a": "NS approach (2 steps): Near-cancellation: 5124 - 5125 = -1, so answer ≈ 1817 + -1. → 1816",
|
| 80 |
-
"solution_b": "Algorithmic approach (3 steps): Compute step by step → 1816",
|
| 81 |
-
"correct_answer": "A",
|
| 82 |
-
"ns_steps": 2,
|
| 83 |
-
"algo_steps": 3,
|
| 84 |
-
"prompt": "Both solutions below are correct. Which one uses fewer reasoning steps? Answer A or B.\n\nProblem: Evaluate: 1817 + 5124 - 5125\n\nSolution A: NS approach (2 steps): Near-cancellation: 5124 - 5125 = -1, so answer ≈ 1817 + -1. → 1816\n\nSolution B: Algorithmic approach (3 steps): Compute step by step → 1816"
|
| 85 |
-
},
|
| 86 |
-
{
|
| 87 |
-
"task_id": "J3_compatible_numbers_000648",
|
| 88 |
-
"task_type": "J3_pairwise_efficiency",
|
| 89 |
-
"category": "compatible_numbers",
|
| 90 |
-
"problem": "Estimate 2520 × 3623.",
|
| 91 |
-
"solution_a": "NS approach (2 steps): Round to 2500×4000 for easy mental computation. → 9129960",
|
| 92 |
-
"solution_b": "Algorithmic approach (4 steps): Compute step by step → 9129960",
|
| 93 |
-
"correct_answer": "A",
|
| 94 |
-
"ns_steps": 2,
|
| 95 |
-
"algo_steps": 4,
|
| 96 |
-
"prompt": "Both solutions below are correct. Which one uses fewer reasoning steps? Answer A or B.\n\nProblem: Estimate 2520 × 3623.\n\nSolution A: NS approach (2 steps): Round to 2500×4000 for easy mental computation. → 9129960\n\nSolution B: Algorithmic approach (4 steps): Compute step by step → 9129960"
|
| 97 |
-
},
|
| 98 |
-
{
|
| 99 |
-
"task_id": "J3_option_elimination_000788",
|
| 100 |
-
"task_type": "J3_pairwise_efficiency",
|
| 101 |
-
"category": "option_elimination",
|
| 102 |
-
"problem": "What is 2243 × 8255?",
|
| 103 |
-
"solution_a": "Algorithmic approach (4 steps): Compute step by step → 18515965",
|
| 104 |
-
"solution_b": "NS approach (2 steps): Check trailing digit / parity / magnitude — only one option matches. → 18515965",
|
| 105 |
-
"correct_answer": "B",
|
| 106 |
-
"ns_steps": 2,
|
| 107 |
-
"algo_steps": 4,
|
| 108 |
-
"prompt": "Both solutions below are correct. Which one uses fewer reasoning steps? Answer A or B.\n\nProblem: What is 2243 × 8255?\n\nSolution A: Algorithmic approach (4 steps): Compute step by step → 18515965\n\nSolution B: NS approach (2 steps): Check trailing digit / parity / magnitude — only one option matches. → 18515965"
|
| 109 |
-
},
|
| 110 |
-
{
|
| 111 |
-
"task_id": "J3_cancellation_identity_000559",
|
| 112 |
-
"task_type": "J3_pairwise_efficiency",
|
| 113 |
-
"category": "cancellation_identity",
|
| 114 |
-
"problem": "Evaluate: 5670 + 1297 - 1299",
|
| 115 |
-
"solution_a": "Algorithmic approach (3 steps): Compute step by step → 5668",
|
| 116 |
-
"solution_b": "NS approach (2 steps): Near-cancellation: 1297 - 1299 = -2, so answer ≈ 5670 + -2. → 5668",
|
| 117 |
-
"correct_answer": "B",
|
| 118 |
-
"ns_steps": 2,
|
| 119 |
-
"algo_steps": 3,
|
| 120 |
-
"prompt": "Both solutions below are correct. Which one uses fewer reasoning steps? Answer A or B.\n\nProblem: Evaluate: 5670 + 1297 - 1299\n\nSolution A: Algorithmic approach (3 steps): Compute step by step → 5668\n\nSolution B: NS approach (2 steps): Near-cancellation: 1297 - 1299 = -2, so answer ≈ 5670 + -2. → 5668"
|
| 121 |
-
},
|
| 122 |
-
{
|
| 123 |
-
"task_id": "J3_landmark_comparison_000664",
|
| 124 |
-
"task_type": "J3_pairwise_efficiency",
|
| 125 |
-
"category": "landmark_comparison",
|
| 126 |
-
"problem": "Is 24% of 44600 greater than 13866?",
|
| 127 |
-
"solution_a": "NS approach (2 steps): Use 25% as landmark: 25% of 44600 = 11150. → No",
|
| 128 |
-
"solution_b": "Algorithmic approach (3 steps): Compute step by step → No",
|
| 129 |
-
"correct_answer": "A",
|
| 130 |
-
"ns_steps": 2,
|
| 131 |
-
"algo_steps": 3,
|
| 132 |
-
"prompt": "Both solutions below are correct. Which one uses fewer reasoning steps? Answer A or B.\n\nProblem: Is 24% of 44600 greater than 13866?\n\nSolution A: NS approach (2 steps): Use 25% as landmark: 25% of 44600 = 11150. → No\n\nSolution B: Algorithmic approach (3 steps): Compute step by step → No"
|
| 133 |
-
},
|
| 134 |
-
{
|
| 135 |
-
"task_id": "J3_structural_shortcuts_000484",
|
| 136 |
-
"task_type": "J3_pairwise_efficiency",
|
| 137 |
-
"category": "structural_shortcuts",
|
| 138 |
-
"problem": "What is 10001 * 4007?",
|
| 139 |
-
"solution_a": "NS approach (3 steps): Use (10000+1)*m = 10000*m + 1*m. → 40074007",
|
| 140 |
-
"solution_b": "Algorithmic approach (4 steps): Compute step by step → 40074007",
|
| 141 |
-
"correct_answer": "A",
|
| 142 |
-
"ns_steps": 3,
|
| 143 |
-
"algo_steps": 4,
|
| 144 |
-
"prompt": "Both solutions below are correct. Which one uses fewer reasoning steps? Answer A or B.\n\nProblem: What is 10001 * 4007?\n\nSolution A: NS approach (3 steps): Use (10000+1)*m = 10000*m + 1*m. → 40074007\n\nSolution B: Algorithmic approach (4 steps): Compute step by step → 40074007"
|
| 145 |
-
},
|
| 146 |
-
{
|
| 147 |
-
"task_id": "J3_compatible_numbers_000606",
|
| 148 |
-
"task_type": "J3_pairwise_efficiency",
|
| 149 |
-
"category": "compatible_numbers",
|
| 150 |
-
"problem": "Estimate 5081 × 2047.",
|
| 151 |
-
"solution_a": "Algorithmic approach (4 steps): Compute step by step → 10400807",
|
| 152 |
-
"solution_b": "NS approach (2 steps): Round to 5000×2000 for easy mental computation. → 10400807",
|
| 153 |
-
"correct_answer": "B",
|
| 154 |
-
"ns_steps": 2,
|
| 155 |
-
"algo_steps": 4,
|
| 156 |
-
"prompt": "Both solutions below are correct. Which one uses fewer reasoning steps? Answer A or B.\n\nProblem: Estimate 5081 × 2047.\n\nSolution A: Algorithmic approach (4 steps): Compute step by step → 10400807\n\nSolution B: NS approach (2 steps): Round to 5000×2000 for easy mental computation. → 10400807"
|
| 157 |
-
},
|
| 158 |
-
{
|
| 159 |
-
"task_id": "J3_structural_shortcuts_000454",
|
| 160 |
-
"task_type": "J3_pairwise_efficiency",
|
| 161 |
-
"category": "structural_shortcuts",
|
| 162 |
-
"problem": "What is 9998 * 5588?",
|
| 163 |
-
"solution_a": "NS approach (3 steps): Use (10000-2)*m = 10000*m - 2*m. → 55868824",
|
| 164 |
-
"solution_b": "Algorithmic approach (4 steps): Compute step by step → 55868824",
|
| 165 |
-
"correct_answer": "A",
|
| 166 |
-
"ns_steps": 3,
|
| 167 |
-
"algo_steps": 4,
|
| 168 |
-
"prompt": "Both solutions below are correct. Which one uses fewer reasoning steps? Answer A or B.\n\nProblem: What is 9998 * 5588?\n\nSolution A: NS approach (3 steps): Use (10000-2)*m = 10000*m - 2*m. → 55868824\n\nSolution B: Algorithmic approach (4 steps): Compute step by step → 55868824"
|
| 169 |
-
},
|
| 170 |
-
{
|
| 171 |
-
"task_id": "J3_equation_reasoning_000729",
|
| 172 |
-
"task_type": "J3_pairwise_efficiency",
|
| 173 |
-
"category": "equation_reasoning",
|
| 174 |
-
"problem": "What value fills the blank? 9604 + 3781 = ___ + 3591",
|
| 175 |
-
"solution_a": "Algorithmic approach (3 steps): Compute step by step → 9794",
|
| 176 |
-
"solution_b": "NS approach (1 steps): Recognize commutativity/distributive law — matching terms cancel. → 9794",
|
| 177 |
-
"correct_answer": "B",
|
| 178 |
-
"ns_steps": 1,
|
| 179 |
-
"algo_steps": 3,
|
| 180 |
-
"prompt": "Both solutions below are correct. Which one uses fewer reasoning steps? Answer A or B.\n\nProblem: What value fills the blank? 9604 + 3781 = ___ + 3591\n\nSolution A: Algorithmic approach (3 steps): Compute step by step → 9794\n\nSolution B: NS approach (1 steps): Recognize commutativity/distributive law — matching terms cancel. → 9794"
|
| 181 |
-
},
|
| 182 |
-
{
|
| 183 |
-
"task_id": "J3_cancellation_identity_000576",
|
| 184 |
-
"task_type": "J3_pairwise_efficiency",
|
| 185 |
-
"category": "cancellation_identity",
|
| 186 |
-
"problem": "Evaluate: 5487 + 9932 - 9930",
|
| 187 |
-
"solution_a": "Algorithmic approach (3 steps): Compute step by step → 5489",
|
| 188 |
-
"solution_b": "NS approach (2 steps): Near-cancellation: 9932 - 9930 = 2, so answer ≈ 5487 + 2. → 5489",
|
| 189 |
-
"correct_answer": "B",
|
| 190 |
-
"ns_steps": 2,
|
| 191 |
-
"algo_steps": 3,
|
| 192 |
-
"prompt": "Both solutions below are correct. Which one uses fewer reasoning steps? Answer A or B.\n\nProblem: Evaluate: 5487 + 9932 - 9930\n\nSolution A: Algorithmic approach (3 steps): Compute step by step → 5489\n\nSolution B: NS approach (2 steps): Near-cancellation: 9932 - 9930 = 2, so answer ≈ 5487 + 2. → 5489"
|
| 193 |
-
},
|
| 194 |
-
{
|
| 195 |
-
"task_id": "J3_structural_shortcuts_000471",
|
| 196 |
-
"task_type": "J3_pairwise_efficiency",
|
| 197 |
-
"category": "structural_shortcuts",
|
| 198 |
-
"problem": "What is 9998 * 7041?",
|
| 199 |
-
"solution_a": "Algorithmic approach (4 steps): Compute step by step → 70395918",
|
| 200 |
-
"solution_b": "NS approach (3 steps): Use (10000-2)*m = 10000*m - 2*m. → 70395918",
|
| 201 |
-
"correct_answer": "B",
|
| 202 |
-
"ns_steps": 3,
|
| 203 |
-
"algo_steps": 4,
|
| 204 |
-
"prompt": "Both solutions below are correct. Which one uses fewer reasoning steps? Answer A or B.\n\nProblem: What is 9998 * 7041?\n\nSolution A: Algorithmic approach (4 steps): Compute step by step → 70395918\n\nSolution B: NS approach (3 steps): Use (10000-2)*m = 10000*m - 2*m. → 70395918"
|
| 205 |
-
},
|
| 206 |
-
{
|
| 207 |
-
"task_id": "J3_equation_reasoning_000713",
|
| 208 |
-
"task_type": "J3_pairwise_efficiency",
|
| 209 |
-
"category": "equation_reasoning",
|
| 210 |
-
"problem": "What value fills the blank? 5328 × (9719 + 5079) = 5328 × ___ + 5328 × 5079",
|
| 211 |
-
"solution_a": "Algorithmic approach (3 steps): Compute step by step → 9719",
|
| 212 |
-
"solution_b": "NS approach (1 steps): Recognize commutativity/distributive law — matching terms cancel. → 9719",
|
| 213 |
-
"correct_answer": "B",
|
| 214 |
-
"ns_steps": 1,
|
| 215 |
-
"algo_steps": 3,
|
| 216 |
-
"prompt": "Both solutions below are correct. Which one uses fewer reasoning steps? Answer A or B.\n\nProblem: What value fills the blank? 5328 × (9719 + 5079) = 5328 × ___ + 5328 × 5079\n\nSolution A: Algorithmic approach (3 steps): Compute step by step → 9719\n\nSolution B: NS approach (1 steps): Recognize commutativity/distributive law — matching terms cancel. → 9719"
|
| 217 |
-
},
|
| 218 |
-
{
|
| 219 |
-
"task_id": "J3_landmark_comparison_000654",
|
| 220 |
-
"task_type": "J3_pairwise_efficiency",
|
| 221 |
-
"category": "landmark_comparison",
|
| 222 |
-
"problem": "Is 10% of 95860 greater than 25675?",
|
| 223 |
-
"solution_a": "Algorithmic approach (3 steps): Compute step by step → No",
|
| 224 |
-
"solution_b": "NS approach (2 steps): Use 10% as landmark: 10% of 95860 = 9586. → No",
|
| 225 |
-
"correct_answer": "B",
|
| 226 |
-
"ns_steps": 2,
|
| 227 |
-
"algo_steps": 3,
|
| 228 |
-
"prompt": "Both solutions below are correct. Which one uses fewer reasoning steps? Answer A or B.\n\nProblem: Is 10% of 95860 greater than 25675?\n\nSolution A: Algorithmic approach (3 steps): Compute step by step → No\n\nSolution B: NS approach (2 steps): Use 10% as landmark: 10% of 95860 = 9586. → No"
|
| 229 |
-
},
|
| 230 |
-
{
|
| 231 |
-
"task_id": "J3_structural_shortcuts_000491",
|
| 232 |
-
"task_type": "J3_pairwise_efficiency",
|
| 233 |
-
"category": "structural_shortcuts",
|
| 234 |
-
"problem": "What is 9999 * 8827?",
|
| 235 |
-
"solution_a": "NS approach (3 steps): Use (10000-1)*m = 10000*m - 1*m. → 88261173",
|
| 236 |
-
"solution_b": "Algorithmic approach (4 steps): Compute step by step → 88261173",
|
| 237 |
-
"correct_answer": "A",
|
| 238 |
-
"ns_steps": 3,
|
| 239 |
-
"algo_steps": 4,
|
| 240 |
-
"prompt": "Both solutions below are correct. Which one uses fewer reasoning steps? Answer A or B.\n\nProblem: What is 9999 * 8827?\n\nSolution A: NS approach (3 steps): Use (10000-1)*m = 10000*m - 1*m. → 88261173\n\nSolution B: Algorithmic approach (4 steps): Compute step by step → 88261173"
|
| 241 |
-
},
|
| 242 |
-
{
|
| 243 |
-
"task_id": "J3_magnitude_estimation_000440",
|
| 244 |
-
"task_type": "J3_pairwise_efficiency",
|
| 245 |
-
"category": "magnitude_estimation",
|
| 246 |
-
"problem": "Which of the following is the best estimate for 9900 * 9900?",
|
| 247 |
-
"solution_a": "Algorithmic approach (4 steps): Compute step by step → 98010000",
|
| 248 |
-
"solution_b": "NS approach (2 steps): Round both to 10000 and multiply. → 98010000",
|
| 249 |
-
"correct_answer": "B",
|
| 250 |
-
"ns_steps": 2,
|
| 251 |
-
"algo_steps": 4,
|
| 252 |
-
"prompt": "Both solutions below are correct. Which one uses fewer reasoning steps? Answer A or B.\n\nProblem: Which of the following is the best estimate for 9900 * 9900?\n\nSolution A: Algorithmic approach (4 steps): Compute step by step → 98010000\n\nSolution B: NS approach (2 steps): Round both to 10000 and multiply. → 98010000"
|
| 253 |
-
},
|
| 254 |
-
{
|
| 255 |
-
"task_id": "J3_compatible_numbers_000628",
|
| 256 |
-
"task_type": "J3_pairwise_efficiency",
|
| 257 |
-
"category": "compatible_numbers",
|
| 258 |
-
"problem": "Estimate 1248 × 7302.",
|
| 259 |
-
"solution_a": "NS approach (2 steps): Round to 1250×8000 for easy mental computation. → 9112896",
|
| 260 |
-
"solution_b": "Algorithmic approach (4 steps): Compute step by step → 9112896",
|
| 261 |
-
"correct_answer": "A",
|
| 262 |
-
"ns_steps": 2,
|
| 263 |
-
"algo_steps": 4,
|
| 264 |
-
"prompt": "Both solutions below are correct. Which one uses fewer reasoning steps? Answer A or B.\n\nProblem: Estimate 1248 × 7302.\n\nSolution A: NS approach (2 steps): Round to 1250×8000 for easy mental computation. → 9112896\n\nSolution B: Algorithmic approach (4 steps): Compute step by step → 9112896"
|
| 265 |
-
},
|
| 266 |
-
{
|
| 267 |
-
"task_id": "J3_structural_shortcuts_000485",
|
| 268 |
-
"task_type": "J3_pairwise_efficiency",
|
| 269 |
-
"category": "structural_shortcuts",
|
| 270 |
-
"problem": "What is 9999 * 9992?",
|
| 271 |
-
"solution_a": "Algorithmic approach (4 steps): Compute step by step → 99910008",
|
| 272 |
-
"solution_b": "NS approach (3 steps): Use (10000-1)*m = 10000*m - 1*m. → 99910008",
|
| 273 |
-
"correct_answer": "B",
|
| 274 |
-
"ns_steps": 3,
|
| 275 |
-
"algo_steps": 4,
|
| 276 |
-
"prompt": "Both solutions below are correct. Which one uses fewer reasoning steps? Answer A or B.\n\nProblem: What is 9999 * 9992?\n\nSolution A: Algorithmic approach (4 steps): Compute step by step → 99910008\n\nSolution B: NS approach (3 steps): Use (10000-1)*m = 10000*m - 1*m. → 99910008"
|
| 277 |
-
},
|
| 278 |
-
{
|
| 279 |
-
"task_id": "J3_structural_shortcuts_000477",
|
| 280 |
-
"task_type": "J3_pairwise_efficiency",
|
| 281 |
-
"category": "structural_shortcuts",
|
| 282 |
-
"problem": "What is 9999 * 3736?",
|
| 283 |
-
"solution_a": "NS approach (3 steps): Use (10000-1)*m = 10000*m - 1*m. → 37356264",
|
| 284 |
-
"solution_b": "Algorithmic approach (4 steps): Compute step by step → 37356264",
|
| 285 |
-
"correct_answer": "A",
|
| 286 |
-
"ns_steps": 3,
|
| 287 |
-
"algo_steps": 4,
|
| 288 |
-
"prompt": "Both solutions below are correct. Which one uses fewer reasoning steps? Answer A or B.\n\nProblem: What is 9999 * 3736?\n\nSolution A: NS approach (3 steps): Use (10000-1)*m = 10000*m - 1*m. → 37356264\n\nSolution B: Algorithmic approach (4 steps): Compute step by step → 37356264"
|
| 289 |
-
},
|
| 290 |
-
{
|
| 291 |
-
"task_id": "J3_option_elimination_000778",
|
| 292 |
-
"task_type": "J3_pairwise_efficiency",
|
| 293 |
-
"category": "option_elimination",
|
| 294 |
-
"problem": "What is 1220 × 5134?",
|
| 295 |
-
"solution_a": "Algorithmic approach (4 steps): Compute step by step → 6263480",
|
| 296 |
-
"solution_b": "NS approach (2 steps): Check trailing digit / parity / magnitude — only one option matches. → 6263480",
|
| 297 |
-
"correct_answer": "B",
|
| 298 |
-
"ns_steps": 2,
|
| 299 |
-
"algo_steps": 4,
|
| 300 |
-
"prompt": "Both solutions below are correct. Which one uses fewer reasoning steps? Answer A or B.\n\nProblem: What is 1220 × 5134?\n\nSolution A: Algorithmic approach (4 steps): Compute step by step → 6263480\n\nSolution B: NS approach (2 steps): Check trailing digit / parity / magnitude — only one option matches. → 6263480"
|
| 301 |
-
},
|
| 302 |
-
{
|
| 303 |
-
"task_id": "J3_compatible_numbers_000638",
|
| 304 |
-
"task_type": "J3_pairwise_efficiency",
|
| 305 |
-
"category": "compatible_numbers",
|
| 306 |
-
"problem": "Estimate 2548 × 3929.",
|
| 307 |
-
"solution_a": "NS approach (2 steps): Round to 2500×4000 for easy mental computation. → 10011092",
|
| 308 |
-
"solution_b": "Algorithmic approach (4 steps): Compute step by step → 10011092",
|
| 309 |
-
"correct_answer": "A",
|
| 310 |
-
"ns_steps": 2,
|
| 311 |
-
"algo_steps": 4,
|
| 312 |
-
"prompt": "Both solutions below are correct. Which one uses fewer reasoning steps? Answer A or B.\n\nProblem: Estimate 2548 × 3929.\n\nSolution A: NS approach (2 steps): Round to 2500×4000 for easy mental computation. → 10011092\n\nSolution B: Algorithmic approach (4 steps): Compute step by step → 10011092"
|
| 313 |
-
},
|
| 314 |
-
{
|
| 315 |
-
"task_id": "J3_relative_distance_000515",
|
| 316 |
-
"task_type": "J3_pairwise_efficiency",
|
| 317 |
-
"category": "relative_distance",
|
| 318 |
-
"problem": "Which is larger: 4405/8858 or 4666/9156?",
|
| 319 |
-
"solution_a": "NS approach (2 steps): One is below 1/2, the other above; no computation needed. → 4666/9156",
|
| 320 |
-
"solution_b": "Algorithmic approach (3 steps): Compute step by step → 4666/9156",
|
| 321 |
-
"correct_answer": "A",
|
| 322 |
-
"ns_steps": 2,
|
| 323 |
-
"algo_steps": 3,
|
| 324 |
-
"prompt": "Both solutions below are correct. Which one uses fewer reasoning steps? Answer A or B.\n\nProblem: Which is larger: 4405/8858 or 4666/9156?\n\nSolution A: NS approach (2 steps): One is below 1/2, the other above; no computation needed. → 4666/9156\n\nSolution B: Algorithmic approach (3 steps): Compute step by step → 4666/9156"
|
| 325 |
-
},
|
| 326 |
-
{
|
| 327 |
-
"task_id": "J3_landmark_comparison_000680",
|
| 328 |
-
"task_type": "J3_pairwise_efficiency",
|
| 329 |
-
"category": "landmark_comparison",
|
| 330 |
-
"problem": "Is 23% of 72010 greater than 15760?",
|
| 331 |
-
"solution_a": "NS approach (2 steps): Use 25% as landmark: 25% of 72010 = 18002. → Yes",
|
| 332 |
-
"solution_b": "Algorithmic approach (3 steps): Compute step by step → Yes",
|
| 333 |
-
"correct_answer": "A",
|
| 334 |
-
"ns_steps": 2,
|
| 335 |
-
"algo_steps": 3,
|
| 336 |
-
"prompt": "Both solutions below are correct. Which one uses fewer reasoning steps? Answer A or B.\n\nProblem: Is 23% of 72010 greater than 15760?\n\nSolution A: NS approach (2 steps): Use 25% as landmark: 25% of 72010 = 18002. → Yes\n\nSolution B: Algorithmic approach (3 steps): Compute step by step → Yes"
|
| 337 |
-
},
|
| 338 |
-
{
|
| 339 |
-
"task_id": "J3_landmark_comparison_000688",
|
| 340 |
-
"task_type": "J3_pairwise_efficiency",
|
| 341 |
-
"category": "landmark_comparison",
|
| 342 |
-
"problem": "Is 27% of 63860 greater than 30514?",
|
| 343 |
-
"solution_a": "Algorithmic approach (3 steps): Compute step by step → No",
|
| 344 |
-
"solution_b": "NS approach (2 steps): Use 25% as landmark: 25% of 63860 = 15965. → No",
|
| 345 |
-
"correct_answer": "B",
|
| 346 |
-
"ns_steps": 2,
|
| 347 |
-
"algo_steps": 3,
|
| 348 |
-
"prompt": "Both solutions below are correct. Which one uses fewer reasoning steps? Answer A or B.\n\nProblem: Is 27% of 63860 greater than 30514?\n\nSolution A: Algorithmic approach (3 steps): Compute step by step → No\n\nSolution B: NS approach (2 steps): Use 25% as landmark: 25% of 63860 = 15965. → No"
|
| 349 |
-
},
|
| 350 |
-
{
|
| 351 |
-
"task_id": "J3_equation_reasoning_000748",
|
| 352 |
-
"task_type": "J3_pairwise_efficiency",
|
| 353 |
-
"category": "equation_reasoning",
|
| 354 |
-
"problem": "What value fills the blank? 3807 + 1362 + ___ = 1362 + 8347 + 3807",
|
| 355 |
-
"solution_a": "Algorithmic approach (3 steps): Compute step by step → 8347",
|
| 356 |
-
"solution_b": "NS approach (1 steps): Recognize commutativity/distributive law — matching terms cancel. → 8347",
|
| 357 |
-
"correct_answer": "B",
|
| 358 |
-
"ns_steps": 1,
|
| 359 |
-
"algo_steps": 3,
|
| 360 |
-
"prompt": "Both solutions below are correct. Which one uses fewer reasoning steps? Answer A or B.\n\nProblem: What value fills the blank? 3807 + 1362 + ___ = 1362 + 8347 + 3807\n\nSolution A: Algorithmic approach (3 steps): Compute step by step → 8347\n\nSolution B: NS approach (1 steps): Recognize commutativity/distributive law — matching terms cancel. → 8347"
|
| 361 |
-
},
|
| 362 |
-
{
|
| 363 |
-
"task_id": "J3_cancellation_identity_000556",
|
| 364 |
-
"task_type": "J3_pairwise_efficiency",
|
| 365 |
-
"category": "cancellation_identity",
|
| 366 |
-
"problem": "Evaluate: 6861 + 5024 - 5026",
|
| 367 |
-
"solution_a": "Algorithmic approach (3 steps): Compute step by step → 6859",
|
| 368 |
-
"solution_b": "NS approach (2 steps): Near-cancellation: 5024 - 5026 = -2, so answer ≈ 6861 + -2. → 6859",
|
| 369 |
-
"correct_answer": "B",
|
| 370 |
-
"ns_steps": 2,
|
| 371 |
-
"algo_steps": 3,
|
| 372 |
-
"prompt": "Both solutions below are correct. Which one uses fewer reasoning steps? Answer A or B.\n\nProblem: Evaluate: 6861 + 5024 - 5026\n\nSolution A: Algorithmic approach (3 steps): Compute step by step → 6859\n\nSolution B: NS approach (2 steps): Near-cancellation: 5024 - 5026 = -2, so answer ≈ 6861 + -2. → 6859"
|
| 373 |
-
},
|
| 374 |
-
{
|
| 375 |
-
"task_id": "J3_relative_distance_000504",
|
| 376 |
-
"task_type": "J3_pairwise_efficiency",
|
| 377 |
-
"category": "relative_distance",
|
| 378 |
-
"problem": "Which is larger: 570/1150 or 4951/9819?",
|
| 379 |
-
"solution_a": "NS approach (2 steps): One is below 1/2, the other above; no computation needed. → 4951/9819",
|
| 380 |
-
"solution_b": "Algorithmic approach (3 steps): Compute step by step → 4951/9819",
|
| 381 |
-
"correct_answer": "A",
|
| 382 |
-
"ns_steps": 2,
|
| 383 |
-
"algo_steps": 3,
|
| 384 |
-
"prompt": "Both solutions below are correct. Which one uses fewer reasoning steps? Answer A or B.\n\nProblem: Which is larger: 570/1150 or 4951/9819?\n\nSolution A: NS approach (2 steps): One is below 1/2, the other above; no computation needed. → 4951/9819\n\nSolution B: Algorithmic approach (3 steps): Compute step by step → 4951/9819"
|
| 385 |
-
},
|
| 386 |
-
{
|
| 387 |
-
"task_id": "J3_compatible_numbers_000609",
|
| 388 |
-
"task_type": "J3_pairwise_efficiency",
|
| 389 |
-
"category": "compatible_numbers",
|
| 390 |
-
"problem": "Estimate 5009 × 1968.",
|
| 391 |
-
"solution_a": "Algorithmic approach (4 steps): Compute step by step → 9857712",
|
| 392 |
-
"solution_b": "NS approach (2 steps): Round to 5000×2000 for easy mental computation. → 9857712",
|
| 393 |
-
"correct_answer": "B",
|
| 394 |
-
"ns_steps": 2,
|
| 395 |
-
"algo_steps": 4,
|
| 396 |
-
"prompt": "Both solutions below are correct. Which one uses fewer reasoning steps? Answer A or B.\n\nProblem: Estimate 5009 × 1968.\n\nSolution A: Algorithmic approach (4 steps): Compute step by step → 9857712\n\nSolution B: NS approach (2 steps): Round to 5000×2000 for easy mental computation. → 9857712"
|
| 397 |
-
},
|
| 398 |
-
{
|
| 399 |
-
"task_id": "J3_compatible_numbers_000646",
|
| 400 |
-
"task_type": "J3_pairwise_efficiency",
|
| 401 |
-
"category": "compatible_numbers",
|
| 402 |
-
"problem": "Estimate 2473 × 4227.",
|
| 403 |
-
"solution_a": "NS approach (2 steps): Round to 2500×4000 for easy mental computation. → 10453371",
|
| 404 |
-
"solution_b": "Algorithmic approach (4 steps): Compute step by step → 10453371",
|
| 405 |
-
"correct_answer": "A",
|
| 406 |
-
"ns_steps": 2,
|
| 407 |
-
"algo_steps": 4,
|
| 408 |
-
"prompt": "Both solutions below are correct. Which one uses fewer reasoning steps? Answer A or B.\n\nProblem: Estimate 2473 × 4227.\n\nSolution A: NS approach (2 steps): Round to 2500×4000 for easy mental computation. → 10453371\n\nSolution B: Algorithmic approach (4 steps): Compute step by step → 10453371"
|
| 409 |
-
},
|
| 410 |
-
{
|
| 411 |
-
"task_id": "J3_relative_distance_000524",
|
| 412 |
-
"task_type": "J3_pairwise_efficiency",
|
| 413 |
-
"category": "relative_distance",
|
| 414 |
-
"problem": "Which is larger: 1837/3735 or 2765/5491?",
|
| 415 |
-
"solution_a": "NS approach (2 steps): One is below 1/2, the other above; no computation needed. → 2765/5491",
|
| 416 |
-
"solution_b": "Algorithmic approach (3 steps): Compute step by step → 2765/5491",
|
| 417 |
-
"correct_answer": "A",
|
| 418 |
-
"ns_steps": 2,
|
| 419 |
-
"algo_steps": 3,
|
| 420 |
-
"prompt": "Both solutions below are correct. Which one uses fewer reasoning steps? Answer A or B.\n\nProblem: Which is larger: 1837/3735 or 2765/5491?\n\nSolution A: NS approach (2 steps): One is below 1/2, the other above; no computation needed. → 2765/5491\n\nSolution B: Algorithmic approach (3 steps): Compute step by step → 2765/5491"
|
| 421 |
-
},
|
| 422 |
-
{
|
| 423 |
-
"task_id": "J3_cancellation_identity_000595",
|
| 424 |
-
"task_type": "J3_pairwise_efficiency",
|
| 425 |
-
"category": "cancellation_identity",
|
| 426 |
-
"problem": "Evaluate: 2576 + 4339 - 4341",
|
| 427 |
-
"solution_a": "NS approach (2 steps): Near-cancellation: 4339 - 4341 = -2, so answer ≈ 2576 + -2. → 2574",
|
| 428 |
-
"solution_b": "Algorithmic approach (3 steps): Compute step by step → 2574",
|
| 429 |
-
"correct_answer": "A",
|
| 430 |
-
"ns_steps": 2,
|
| 431 |
-
"algo_steps": 3,
|
| 432 |
-
"prompt": "Both solutions below are correct. Which one uses fewer reasoning steps? Answer A or B.\n\nProblem: Evaluate: 2576 + 4339 - 4341\n\nSolution A: NS approach (2 steps): Near-cancellation: 4339 - 4341 = -2, so answer ≈ 2576 + -2. → 2574\n\nSolution B: Algorithmic approach (3 steps): Compute step by step → 2574"
|
| 433 |
-
},
|
| 434 |
-
{
|
| 435 |
-
"task_id": "J3_structural_shortcuts_000492",
|
| 436 |
-
"task_type": "J3_pairwise_efficiency",
|
| 437 |
-
"category": "structural_shortcuts",
|
| 438 |
-
"problem": "What is 9998 * 2912?",
|
| 439 |
-
"solution_a": "NS approach (3 steps): Use (10000-2)*m = 10000*m - 2*m. → 29114176",
|
| 440 |
-
"solution_b": "Algorithmic approach (4 steps): Compute step by step → 29114176",
|
| 441 |
-
"correct_answer": "A",
|
| 442 |
-
"ns_steps": 3,
|
| 443 |
-
"algo_steps": 4,
|
| 444 |
-
"prompt": "Both solutions below are correct. Which one uses fewer reasoning steps? Answer A or B.\n\nProblem: What is 9998 * 2912?\n\nSolution A: NS approach (3 steps): Use (10000-2)*m = 10000*m - 2*m. → 29114176\n\nSolution B: Algorithmic approach (4 steps): Compute step by step → 29114176"
|
| 445 |
-
},
|
| 446 |
-
{
|
| 447 |
-
"task_id": "J3_option_elimination_000753",
|
| 448 |
-
"task_type": "J3_pairwise_efficiency",
|
| 449 |
-
"category": "option_elimination",
|
| 450 |
-
"problem": "What is 6918 × 8652?",
|
| 451 |
-
"solution_a": "Algorithmic approach (4 steps): Compute step by step → 59854536",
|
| 452 |
-
"solution_b": "NS approach (2 steps): Check trailing digit / parity / magnitude — only one option matches. → 59854536",
|
| 453 |
-
"correct_answer": "B",
|
| 454 |
-
"ns_steps": 2,
|
| 455 |
-
"algo_steps": 4,
|
| 456 |
-
"prompt": "Both solutions below are correct. Which one uses fewer reasoning steps? Answer A or B.\n\nProblem: What is 6918 × 8652?\n\nSolution A: Algorithmic approach (4 steps): Compute step by step → 59854536\n\nSolution B: NS approach (2 steps): Check trailing digit / parity / magnitude — only one option matches. → 59854536"
|
| 457 |
-
},
|
| 458 |
-
{
|
| 459 |
-
"task_id": "J3_magnitude_estimation_000441",
|
| 460 |
-
"task_type": "J3_pairwise_efficiency",
|
| 461 |
-
"category": "magnitude_estimation",
|
| 462 |
-
"problem": "Which of the following is the best estimate for 9800 * 10200?",
|
| 463 |
-
"solution_a": "Algorithmic approach (4 steps): Compute step by step → 99960000",
|
| 464 |
-
"solution_b": "NS approach (2 steps): Round both to 10000 and multiply. → 99960000",
|
| 465 |
-
"correct_answer": "B",
|
| 466 |
-
"ns_steps": 2,
|
| 467 |
-
"algo_steps": 4,
|
| 468 |
-
"prompt": "Both solutions below are correct. Which one uses fewer reasoning steps? Answer A or B.\n\nProblem: Which of the following is the best estimate for 9800 * 10200?\n\nSolution A: Algorithmic approach (4 steps): Compute step by step → 99960000\n\nSolution B: NS approach (2 steps): Round both to 10000 and multiply. → 99960000"
|
| 469 |
-
},
|
| 470 |
-
{
|
| 471 |
-
"task_id": "J3_magnitude_estimation_000422",
|
| 472 |
-
"task_type": "J3_pairwise_efficiency",
|
| 473 |
-
"category": "magnitude_estimation",
|
| 474 |
-
"problem": "Which of the following is the best estimate for 9800 * 10200?",
|
| 475 |
-
"solution_a": "Algorithmic approach (4 steps): Compute step by step → 99960000",
|
| 476 |
-
"solution_b": "NS approach (2 steps): Round both to 10000 and multiply. → 99960000",
|
| 477 |
-
"correct_answer": "B",
|
| 478 |
-
"ns_steps": 2,
|
| 479 |
-
"algo_steps": 4,
|
| 480 |
-
"prompt": "Both solutions below are correct. Which one uses fewer reasoning steps? Answer A or B.\n\nProblem: Which of the following is the best estimate for 9800 * 10200?\n\nSolution A: Algorithmic approach (4 steps): Compute step by step → 99960000\n\nSolution B: NS approach (2 steps): Round both to 10000 and multiply. → 99960000"
|
| 481 |
-
},
|
| 482 |
-
{
|
| 483 |
-
"task_id": "J3_cancellation_identity_000573",
|
| 484 |
-
"task_type": "J3_pairwise_efficiency",
|
| 485 |
-
"category": "cancellation_identity",
|
| 486 |
-
"problem": "Evaluate: 9000 + 5060 - 5058",
|
| 487 |
-
"solution_a": "Algorithmic approach (3 steps): Compute step by step → 9002",
|
| 488 |
-
"solution_b": "NS approach (2 steps): Near-cancellation: 5060 - 5058 = 2, so answer ≈ 9000 + 2. → 9002",
|
| 489 |
-
"correct_answer": "B",
|
| 490 |
-
"ns_steps": 2,
|
| 491 |
-
"algo_steps": 3,
|
| 492 |
-
"prompt": "Both solutions below are correct. Which one uses fewer reasoning steps? Answer A or B.\n\nProblem: Evaluate: 9000 + 5060 - 5058\n\nSolution A: Algorithmic approach (3 steps): Compute step by step → 9002\n\nSolution B: NS approach (2 steps): Near-cancellation: 5060 - 5058 = 2, so answer ≈ 9000 + 2. → 9002"
|
| 493 |
-
},
|
| 494 |
-
{
|
| 495 |
-
"task_id": "J3_structural_shortcuts_000457",
|
| 496 |
-
"task_type": "J3_pairwise_efficiency",
|
| 497 |
-
"category": "structural_shortcuts",
|
| 498 |
-
"problem": "What is 9999 * 2376?",
|
| 499 |
-
"solution_a": "NS approach (3 steps): Use (10000-1)*m = 10000*m - 1*m. → 23757624",
|
| 500 |
-
"solution_b": "Algorithmic approach (4 steps): Compute step by step → 23757624",
|
| 501 |
-
"correct_answer": "A",
|
| 502 |
-
"ns_steps": 3,
|
| 503 |
-
"algo_steps": 4,
|
| 504 |
-
"prompt": "Both solutions below are correct. Which one uses fewer reasoning steps? Answer A or B.\n\nProblem: What is 9999 * 2376?\n\nSolution A: NS approach (3 steps): Use (10000-1)*m = 10000*m - 1*m. → 23757624\n\nSolution B: Algorithmic approach (4 steps): Compute step by step → 23757624"
|
| 505 |
-
},
|
| 506 |
-
{
|
| 507 |
-
"task_id": "J3_magnitude_estimation_000423",
|
| 508 |
-
"task_type": "J3_pairwise_efficiency",
|
| 509 |
-
"category": "magnitude_estimation",
|
| 510 |
-
"problem": "Which of the following is the best estimate for 10100 * 9800?",
|
| 511 |
-
"solution_a": "Algorithmic approach (4 steps): Compute step by step → 98980000",
|
| 512 |
-
"solution_b": "NS approach (2 steps): Round both to 10000 and multiply. → 98980000",
|
| 513 |
-
"correct_answer": "B",
|
| 514 |
-
"ns_steps": 2,
|
| 515 |
-
"algo_steps": 4,
|
| 516 |
-
"prompt": "Both solutions below are correct. Which one uses fewer reasoning steps? Answer A or B.\n\nProblem: Which of the following is the best estimate for 10100 * 9800?\n\nSolution A: Algorithmic approach (4 steps): Compute step by step → 98980000\n\nSolution B: NS approach (2 steps): Round both to 10000 and multiply. → 98980000"
|
| 517 |
-
},
|
| 518 |
-
{
|
| 519 |
-
"task_id": "J3_structural_shortcuts_000451",
|
| 520 |
-
"task_type": "J3_pairwise_efficiency",
|
| 521 |
-
"category": "structural_shortcuts",
|
| 522 |
-
"problem": "What is 10001 * 5029?",
|
| 523 |
-
"solution_a": "Algorithmic approach (4 steps): Compute step by step → 50295029",
|
| 524 |
-
"solution_b": "NS approach (3 steps): Use (10000+1)*m = 10000*m + 1*m. → 50295029",
|
| 525 |
-
"correct_answer": "B",
|
| 526 |
-
"ns_steps": 3,
|
| 527 |
-
"algo_steps": 4,
|
| 528 |
-
"prompt": "Both solutions below are correct. Which one uses fewer reasoning steps? Answer A or B.\n\nProblem: What is 10001 * 5029?\n\nSolution A: Algorithmic approach (4 steps): Compute step by step → 50295029\n\nSolution B: NS approach (3 steps): Use (10000+1)*m = 10000*m + 1*m. → 50295029"
|
| 529 |
-
},
|
| 530 |
-
{
|
| 531 |
-
"task_id": "J3_option_elimination_000780",
|
| 532 |
-
"task_type": "J3_pairwise_efficiency",
|
| 533 |
-
"category": "option_elimination",
|
| 534 |
-
"problem": "What is 8020 × 2628?",
|
| 535 |
-
"solution_a": "NS approach (2 steps): Check trailing digit / parity / magnitude — only one option matches. → 21076560",
|
| 536 |
-
"solution_b": "Algorithmic approach (4 steps): Compute step by step → 21076560",
|
| 537 |
-
"correct_answer": "A",
|
| 538 |
-
"ns_steps": 2,
|
| 539 |
-
"algo_steps": 4,
|
| 540 |
-
"prompt": "Both solutions below are correct. Which one uses fewer reasoning steps? Answer A or B.\n\nProblem: What is 8020 × 2628?\n\nSolution A: NS approach (2 steps): Check trailing digit / parity / magnitude — only one option matches. → 21076560\n\nSolution B: Algorithmic approach (4 steps): Compute step by step → 21076560"
|
| 541 |
-
},
|
| 542 |
-
{
|
| 543 |
-
"task_id": "J3_magnitude_estimation_000430",
|
| 544 |
-
"task_type": "J3_pairwise_efficiency",
|
| 545 |
-
"category": "magnitude_estimation",
|
| 546 |
-
"problem": "Which of the following is the best estimate for 10100 * 9900?",
|
| 547 |
-
"solution_a": "Algorithmic approach (4 steps): Compute step by step → 99990000",
|
| 548 |
-
"solution_b": "NS approach (2 steps): Round both to 10000 and multiply. → 99990000",
|
| 549 |
-
"correct_answer": "B",
|
| 550 |
-
"ns_steps": 2,
|
| 551 |
-
"algo_steps": 4,
|
| 552 |
-
"prompt": "Both solutions below are correct. Which one uses fewer reasoning steps? Answer A or B.\n\nProblem: Which of the following is the best estimate for 10100 * 9900?\n\nSolution A: Algorithmic approach (4 steps): Compute step by step → 99990000\n\nSolution B: NS approach (2 steps): Round both to 10000 and multiply. → 99990000"
|
| 553 |
-
},
|
| 554 |
-
{
|
| 555 |
-
"task_id": "J3_equation_reasoning_000721",
|
| 556 |
-
"task_type": "J3_pairwise_efficiency",
|
| 557 |
-
"category": "equation_reasoning",
|
| 558 |
-
"problem": "What value fills the blank? 6468 × (2099 + 2237) = 6468 × ___ + 6468 × 2237",
|
| 559 |
-
"solution_a": "Algorithmic approach (3 steps): Compute step by step → 2099",
|
| 560 |
-
"solution_b": "NS approach (1 steps): Recognize commutativity/distributive law — matching terms cancel. → 2099",
|
| 561 |
-
"correct_answer": "B",
|
| 562 |
-
"ns_steps": 1,
|
| 563 |
-
"algo_steps": 3,
|
| 564 |
-
"prompt": "Both solutions below are correct. Which one uses fewer reasoning steps? Answer A or B.\n\nProblem: What value fills the blank? 6468 × (2099 + 2237) = 6468 × ___ + 6468 × 2237\n\nSolution A: Algorithmic approach (3 steps): Compute step by step → 2099\n\nSolution B: NS approach (1 steps): Recognize commutativity/distributive law — matching terms cancel. → 2099"
|
| 565 |
-
},
|
| 566 |
-
{
|
| 567 |
-
"task_id": "J3_cancellation_identity_000578",
|
| 568 |
-
"task_type": "J3_pairwise_efficiency",
|
| 569 |
-
"category": "cancellation_identity",
|
| 570 |
-
"problem": "Evaluate: 5722 + 2063 - 2062",
|
| 571 |
-
"solution_a": "Algorithmic approach (3 steps): Compute step by step → 5723",
|
| 572 |
-
"solution_b": "NS approach (2 steps): Near-cancellation: 2063 - 2062 = 1, so answer ≈ 5722 + 1. → 5723",
|
| 573 |
-
"correct_answer": "B",
|
| 574 |
-
"ns_steps": 2,
|
| 575 |
-
"algo_steps": 3,
|
| 576 |
-
"prompt": "Both solutions below are correct. Which one uses fewer reasoning steps? Answer A or B.\n\nProblem: Evaluate: 5722 + 2063 - 2062\n\nSolution A: Algorithmic approach (3 steps): Compute step by step → 5723\n\nSolution B: NS approach (2 steps): Near-cancellation: 2063 - 2062 = 1, so answer ≈ 5722 + 1. → 5723"
|
| 577 |
-
},
|
| 578 |
-
{
|
| 579 |
-
"task_id": "J3_compatible_numbers_000616",
|
| 580 |
-
"task_type": "J3_pairwise_efficiency",
|
| 581 |
-
"category": "compatible_numbers",
|
| 582 |
-
"problem": "Estimate 1233 × 7868.",
|
| 583 |
-
"solution_a": "Algorithmic approach (4 steps): Compute step by step → 9701244",
|
| 584 |
-
"solution_b": "NS approach (2 steps): Round to 1250×8000 for easy mental computation. → 9701244",
|
| 585 |
-
"correct_answer": "B",
|
| 586 |
-
"ns_steps": 2,
|
| 587 |
-
"algo_steps": 4,
|
| 588 |
-
"prompt": "Both solutions below are correct. Which one uses fewer reasoning steps? Answer A or B.\n\nProblem: Estimate 1233 × 7868.\n\nSolution A: Algorithmic approach (4 steps): Compute step by step → 9701244\n\nSolution B: NS approach (2 steps): Round to 1250×8000 for easy mental computation. → 9701244"
|
| 589 |
-
},
|
| 590 |
-
{
|
| 591 |
-
"task_id": "J3_relative_distance_000512",
|
| 592 |
-
"task_type": "J3_pairwise_efficiency",
|
| 593 |
-
"category": "relative_distance",
|
| 594 |
-
"problem": "Which is larger: 1039/2080 or 3210/6396?",
|
| 595 |
-
"solution_a": "NS approach (2 steps): One is below 1/2, the other above; no computation needed. → 3210/6396",
|
| 596 |
-
"solution_b": "Algorithmic approach (3 steps): Compute step by step → 3210/6396",
|
| 597 |
-
"correct_answer": "A",
|
| 598 |
-
"ns_steps": 2,
|
| 599 |
-
"algo_steps": 3,
|
| 600 |
-
"prompt": "Both solutions below are correct. Which one uses fewer reasoning steps? Answer A or B.\n\nProblem: Which is larger: 1039/2080 or 3210/6396?\n\nSolution A: NS approach (2 steps): One is below 1/2, the other above; no computation needed. → 3210/6396\n\nSolution B: Algorithmic approach (3 steps): Compute step by step → 3210/6396"
|
| 601 |
-
},
|
| 602 |
-
{
|
| 603 |
-
"task_id": "J3_landmark_comparison_000652",
|
| 604 |
-
"task_type": "J3_pairwise_efficiency",
|
| 605 |
-
"category": "landmark_comparison",
|
| 606 |
-
"problem": "Is 9% of 48380 greater than 22179?",
|
| 607 |
-
"solution_a": "Algorithmic approach (3 steps): Compute step by step → No",
|
| 608 |
-
"solution_b": "NS approach (2 steps): Use 10% as landmark: 10% of 48380 = 4838. → No",
|
| 609 |
-
"correct_answer": "B",
|
| 610 |
-
"ns_steps": 2,
|
| 611 |
-
"algo_steps": 3,
|
| 612 |
-
"prompt": "Both solutions below are correct. Which one uses fewer reasoning steps? Answer A or B.\n\nProblem: Is 9% of 48380 greater than 22179?\n\nSolution A: Algorithmic approach (3 steps): Compute step by step → No\n\nSolution B: NS approach (2 steps): Use 10% as landmark: 10% of 48380 = 4838. → No"
|
| 613 |
-
},
|
| 614 |
-
{
|
| 615 |
-
"task_id": "J3_cancellation_identity_000588",
|
| 616 |
-
"task_type": "J3_pairwise_efficiency",
|
| 617 |
-
"category": "cancellation_identity",
|
| 618 |
-
"problem": "Evaluate: 9092 + 3990 - 3991",
|
| 619 |
-
"solution_a": "NS approach (2 steps): Near-cancellation: 3990 - 3991 = -1, so answer ≈ 9092 + -1. → 9091",
|
| 620 |
-
"solution_b": "Algorithmic approach (3 steps): Compute step by step → 9091",
|
| 621 |
-
"correct_answer": "A",
|
| 622 |
-
"ns_steps": 2,
|
| 623 |
-
"algo_steps": 3,
|
| 624 |
-
"prompt": "Both solutions below are correct. Which one uses fewer reasoning steps? Answer A or B.\n\nProblem: Evaluate: 9092 + 3990 - 3991\n\nSolution A: NS approach (2 steps): Near-cancellation: 3990 - 3991 = -1, so answer ≈ 9092 + -1. → 9091\n\nSolution B: Algorithmic approach (3 steps): Compute step by step → 9091"
|
| 625 |
-
},
|
| 626 |
-
{
|
| 627 |
-
"task_id": "J3_equation_reasoning_000727",
|
| 628 |
-
"task_type": "J3_pairwise_efficiency",
|
| 629 |
-
"category": "equation_reasoning",
|
| 630 |
-
"problem": "What value fills the blank? 3305 + 5079 + ___ = 5079 + 3905 + 3305",
|
| 631 |
-
"solution_a": "NS approach (1 steps): Recognize commutativity/distributive law — matching terms cancel. → 3905",
|
| 632 |
-
"solution_b": "Algorithmic approach (3 steps): Compute step by step → 3905",
|
| 633 |
-
"correct_answer": "A",
|
| 634 |
-
"ns_steps": 1,
|
| 635 |
-
"algo_steps": 3,
|
| 636 |
-
"prompt": "Both solutions below are correct. Which one uses fewer reasoning steps? Answer A or B.\n\nProblem: What value fills the blank? 3305 + 5079 + ___ = 5079 + 3905 + 3305\n\nSolution A: NS approach (1 steps): Recognize commutativity/distributive law — matching terms cancel. → 3905\n\nSolution B: Algorithmic approach (3 steps): Compute step by step → 3905"
|
| 637 |
-
},
|
| 638 |
-
{
|
| 639 |
-
"task_id": "J3_equation_reasoning_000704",
|
| 640 |
-
"task_type": "J3_pairwise_efficiency",
|
| 641 |
-
"category": "equation_reasoning",
|
| 642 |
-
"problem": "What value fills the blank? 9515 + 8703 = ___ + 7313",
|
| 643 |
-
"solution_a": "Algorithmic approach (3 steps): Compute step by step → 10905",
|
| 644 |
-
"solution_b": "NS approach (1 steps): Recognize commutativity/distributive law — matching terms cancel. → 10905",
|
| 645 |
-
"correct_answer": "B",
|
| 646 |
-
"ns_steps": 1,
|
| 647 |
-
"algo_steps": 3,
|
| 648 |
-
"prompt": "Both solutions below are correct. Which one uses fewer reasoning steps? Answer A or B.\n\nProblem: What value fills the blank? 9515 + 8703 = ___ + 7313\n\nSolution A: Algorithmic approach (3 steps): Compute step by step → 10905\n\nSolution B: NS approach (1 steps): Recognize commutativity/distributive law — matching terms cancel. → 10905"
|
| 649 |
-
},
|
| 650 |
-
{
|
| 651 |
-
"task_id": "J3_option_elimination_000800",
|
| 652 |
-
"task_type": "J3_pairwise_efficiency",
|
| 653 |
-
"category": "option_elimination",
|
| 654 |
-
"problem": "What is 6809 × 9143?",
|
| 655 |
-
"solution_a": "NS approach (2 steps): Check trailing digit / parity / magnitude — only one option matches. → 62254687",
|
| 656 |
-
"solution_b": "Algorithmic approach (4 steps): Compute step by step → 62254687",
|
| 657 |
-
"correct_answer": "A",
|
| 658 |
-
"ns_steps": 2,
|
| 659 |
-
"algo_steps": 4,
|
| 660 |
-
"prompt": "Both solutions below are correct. Which one uses fewer reasoning steps? Answer A or B.\n\nProblem: What is 6809 × 9143?\n\nSolution A: NS approach (2 steps): Check trailing digit / parity / magnitude — only one option matches. → 62254687\n\nSolution B: Algorithmic approach (4 steps): Compute step by step → 62254687"
|
| 661 |
-
},
|
| 662 |
-
{
|
| 663 |
-
"task_id": "J3_magnitude_estimation_000420",
|
| 664 |
-
"task_type": "J3_pairwise_efficiency",
|
| 665 |
-
"category": "magnitude_estimation",
|
| 666 |
-
"problem": "Which of the following is the best estimate for 10200 * 9800?",
|
| 667 |
-
"solution_a": "NS approach (2 steps): Round both to 10000 and multiply. → 99960000",
|
| 668 |
-
"solution_b": "Algorithmic approach (4 steps): Compute step by step → 99960000",
|
| 669 |
-
"correct_answer": "A",
|
| 670 |
-
"ns_steps": 2,
|
| 671 |
-
"algo_steps": 4,
|
| 672 |
-
"prompt": "Both solutions below are correct. Which one uses fewer reasoning steps? Answer A or B.\n\nProblem: Which of the following is the best estimate for 10200 * 9800?\n\nSolution A: NS approach (2 steps): Round both to 10000 and multiply. → 99960000\n\nSolution B: Algorithmic approach (4 steps): Compute step by step → 99960000"
|
| 673 |
-
},
|
| 674 |
-
{
|
| 675 |
-
"task_id": "J3_relative_distance_000509",
|
| 676 |
-
"task_type": "J3_pairwise_efficiency",
|
| 677 |
-
"category": "relative_distance",
|
| 678 |
-
"problem": "Which is larger: 2166/4399 or 1489/2922?",
|
| 679 |
-
"solution_a": "NS approach (2 steps): One is below 1/2, the other above; no computation needed. → 1489/2922",
|
| 680 |
-
"solution_b": "Algorithmic approach (3 steps): Compute step by step → 1489/2922",
|
| 681 |
-
"correct_answer": "A",
|
| 682 |
-
"ns_steps": 2,
|
| 683 |
-
"algo_steps": 3,
|
| 684 |
-
"prompt": "Both solutions below are correct. Which one uses fewer reasoning steps? Answer A or B.\n\nProblem: Which is larger: 2166/4399 or 1489/2922?\n\nSolution A: NS approach (2 steps): One is below 1/2, the other above; no computation needed. → 1489/2922\n\nSolution B: Algorithmic approach (3 steps): Compute step by step → 1489/2922"
|
| 685 |
-
},
|
| 686 |
-
{
|
| 687 |
-
"task_id": "J3_magnitude_estimation_000407",
|
| 688 |
-
"task_type": "J3_pairwise_efficiency",
|
| 689 |
-
"category": "magnitude_estimation",
|
| 690 |
-
"problem": "Which of the following is the best estimate for 9900 * 10100?",
|
| 691 |
-
"solution_a": "Algorithmic approach (4 steps): Compute step by step → 99990000",
|
| 692 |
-
"solution_b": "NS approach (2 steps): Round both to 10000 and multiply. → 99990000",
|
| 693 |
-
"correct_answer": "B",
|
| 694 |
-
"ns_steps": 2,
|
| 695 |
-
"algo_steps": 4,
|
| 696 |
-
"prompt": "Both solutions below are correct. Which one uses fewer reasoning steps? Answer A or B.\n\nProblem: Which of the following is the best estimate for 9900 * 10100?\n\nSolution A: Algorithmic approach (4 steps): Compute step by step → 99990000\n\nSolution B: NS approach (2 steps): Round both to 10000 and multiply. → 99990000"
|
| 697 |
-
},
|
| 698 |
-
{
|
| 699 |
-
"task_id": "J3_compatible_numbers_000605",
|
| 700 |
-
"task_type": "J3_pairwise_efficiency",
|
| 701 |
-
"category": "compatible_numbers",
|
| 702 |
-
"problem": "Estimate 1274 × 8785.",
|
| 703 |
-
"solution_a": "Algorithmic approach (4 steps): Compute step by step → 11192090",
|
| 704 |
-
"solution_b": "NS approach (2 steps): Round to 1250×8000 for easy mental computation. → 11192090",
|
| 705 |
-
"correct_answer": "B",
|
| 706 |
-
"ns_steps": 2,
|
| 707 |
-
"algo_steps": 4,
|
| 708 |
-
"prompt": "Both solutions below are correct. Which one uses fewer reasoning steps? Answer A or B.\n\nProblem: Estimate 1274 × 8785.\n\nSolution A: Algorithmic approach (4 steps): Compute step by step → 11192090\n\nSolution B: NS approach (2 steps): Round to 1250×8000 for easy mental computation. → 11192090"
|
| 709 |
-
},
|
| 710 |
-
{
|
| 711 |
-
"task_id": "J3_relative_distance_000543",
|
| 712 |
-
"task_type": "J3_pairwise_efficiency",
|
| 713 |
-
"category": "relative_distance",
|
| 714 |
-
"problem": "Which is larger: 1162/2369 or 1679/3322?",
|
| 715 |
-
"solution_a": "Algorithmic approach (3 steps): Compute step by step → 1679/3322",
|
| 716 |
-
"solution_b": "NS approach (2 steps): One is below 1/2, the other above; no computation needed. → 1679/3322",
|
| 717 |
-
"correct_answer": "B",
|
| 718 |
-
"ns_steps": 2,
|
| 719 |
-
"algo_steps": 3,
|
| 720 |
-
"prompt": "Both solutions below are correct. Which one uses fewer reasoning steps? Answer A or B.\n\nProblem: Which is larger: 1162/2369 or 1679/3322?\n\nSolution A: Algorithmic approach (3 steps): Compute step by step → 1679/3322\n\nSolution B: NS approach (2 steps): One is below 1/2, the other above; no computation needed. → 1679/3322"
|
| 721 |
-
},
|
| 722 |
-
{
|
| 723 |
-
"task_id": "J3_relative_distance_000527",
|
| 724 |
-
"task_type": "J3_pairwise_efficiency",
|
| 725 |
-
"category": "relative_distance",
|
| 726 |
-
"problem": "Which is larger: 1753/3550 or 4210/8308?",
|
| 727 |
-
"solution_a": "NS approach (2 steps): One is below 1/2, the other above; no computation needed. → 4210/8308",
|
| 728 |
-
"solution_b": "Algorithmic approach (3 steps): Compute step by step → 4210/8308",
|
| 729 |
-
"correct_answer": "A",
|
| 730 |
-
"ns_steps": 2,
|
| 731 |
-
"algo_steps": 3,
|
| 732 |
-
"prompt": "Both solutions below are correct. Which one uses fewer reasoning steps? Answer A or B.\n\nProblem: Which is larger: 1753/3550 or 4210/8308?\n\nSolution A: NS approach (2 steps): One is below 1/2, the other above; no computation needed. → 4210/8308\n\nSolution B: Algorithmic approach (3 steps): Compute step by step → 4210/8308"
|
| 733 |
-
},
|
| 734 |
-
{
|
| 735 |
-
"task_id": "J3_equation_reasoning_000726",
|
| 736 |
-
"task_type": "J3_pairwise_efficiency",
|
| 737 |
-
"category": "equation_reasoning",
|
| 738 |
-
"problem": "What value fills the blank? 1264 + 1118 = ___ + 7226",
|
| 739 |
-
"solution_a": "NS approach (1 steps): Recognize commutativity/distributive law — matching terms cancel. → -4844",
|
| 740 |
-
"solution_b": "Algorithmic approach (3 steps): Compute step by step → -4844",
|
| 741 |
-
"correct_answer": "A",
|
| 742 |
-
"ns_steps": 1,
|
| 743 |
-
"algo_steps": 3,
|
| 744 |
-
"prompt": "Both solutions below are correct. Which one uses fewer reasoning steps? Answer A or B.\n\nProblem: What value fills the blank? 1264 + 1118 = ___ + 7226\n\nSolution A: NS approach (1 steps): Recognize commutativity/distributive law — matching terms cancel. → -4844\n\nSolution B: Algorithmic approach (3 steps): Compute step by step → -4844"
|
| 745 |
-
},
|
| 746 |
-
{
|
| 747 |
-
"task_id": "J3_magnitude_estimation_000443",
|
| 748 |
-
"task_type": "J3_pairwise_efficiency",
|
| 749 |
-
"category": "magnitude_estimation",
|
| 750 |
-
"problem": "Which of the following is the best estimate for 9800 * 9800?",
|
| 751 |
-
"solution_a": "Algorithmic approach (4 steps): Compute step by step → 96040000",
|
| 752 |
-
"solution_b": "NS approach (2 steps): Round both to 10000 and multiply. → 96040000",
|
| 753 |
-
"correct_answer": "B",
|
| 754 |
-
"ns_steps": 2,
|
| 755 |
-
"algo_steps": 4,
|
| 756 |
-
"prompt": "Both solutions below are correct. Which one uses fewer reasoning steps? Answer A or B.\n\nProblem: Which of the following is the best estimate for 9800 * 9800?\n\nSolution A: Algorithmic approach (4 steps): Compute step by step → 96040000\n\nSolution B: NS approach (2 steps): Round both to 10000 and multiply. → 96040000"
|
| 757 |
-
},
|
| 758 |
-
{
|
| 759 |
-
"task_id": "J3_landmark_comparison_000653",
|
| 760 |
-
"task_type": "J3_pairwise_efficiency",
|
| 761 |
-
"category": "landmark_comparison",
|
| 762 |
-
"problem": "Is 48% of 75650 greater than 34563?",
|
| 763 |
-
"solution_a": "Algorithmic approach (3 steps): Compute step by step → Yes",
|
| 764 |
-
"solution_b": "NS approach (2 steps): Use 50% as landmark: 50% of 75650 = 37825. → Yes",
|
| 765 |
-
"correct_answer": "B",
|
| 766 |
-
"ns_steps": 2,
|
| 767 |
-
"algo_steps": 3,
|
| 768 |
-
"prompt": "Both solutions below are correct. Which one uses fewer reasoning steps? Answer A or B.\n\nProblem: Is 48% of 75650 greater than 34563?\n\nSolution A: Algorithmic approach (3 steps): Compute step by step → Yes\n\nSolution B: NS approach (2 steps): Use 50% as landmark: 50% of 75650 = 37825. → Yes"
|
| 769 |
-
},
|
| 770 |
-
{
|
| 771 |
-
"task_id": "J3_relative_distance_000534",
|
| 772 |
-
"task_type": "J3_pairwise_efficiency",
|
| 773 |
-
"category": "relative_distance",
|
| 774 |
-
"problem": "Which is larger: 4320/8812 or 1806/3591?",
|
| 775 |
-
"solution_a": "Algorithmic approach (3 steps): Compute step by step → 1806/3591",
|
| 776 |
-
"solution_b": "NS approach (2 steps): One is below 1/2, the other above; no computation needed. → 1806/3591",
|
| 777 |
-
"correct_answer": "B",
|
| 778 |
-
"ns_steps": 2,
|
| 779 |
-
"algo_steps": 3,
|
| 780 |
-
"prompt": "Both solutions below are correct. Which one uses fewer reasoning steps? Answer A or B.\n\nProblem: Which is larger: 4320/8812 or 1806/3591?\n\nSolution A: Algorithmic approach (3 steps): Compute step by step → 1806/3591\n\nSolution B: NS approach (2 steps): One is below 1/2, the other above; no computation needed. → 1806/3591"
|
| 781 |
-
},
|
| 782 |
-
{
|
| 783 |
-
"task_id": "J3_option_elimination_000782",
|
| 784 |
-
"task_type": "J3_pairwise_efficiency",
|
| 785 |
-
"category": "option_elimination",
|
| 786 |
-
"problem": "What is 1133 × 1067?",
|
| 787 |
-
"solution_a": "NS approach (2 steps): Check trailing digit / parity / magnitude — only one option matches. → 1208911",
|
| 788 |
-
"solution_b": "Algorithmic approach (4 steps): Compute step by step → 1208911",
|
| 789 |
-
"correct_answer": "A",
|
| 790 |
-
"ns_steps": 2,
|
| 791 |
-
"algo_steps": 4,
|
| 792 |
-
"prompt": "Both solutions below are correct. Which one uses fewer reasoning steps? Answer A or B.\n\nProblem: What is 1133 × 1067?\n\nSolution A: NS approach (2 steps): Check trailing digit / parity / magnitude — only one option matches. → 1208911\n\nSolution B: Algorithmic approach (4 steps): Compute step by step → 1208911"
|
| 793 |
-
},
|
| 794 |
-
{
|
| 795 |
-
"task_id": "J3_compatible_numbers_000608",
|
| 796 |
-
"task_type": "J3_pairwise_efficiency",
|
| 797 |
-
"category": "compatible_numbers",
|
| 798 |
-
"problem": "Estimate 5009 × 1968.",
|
| 799 |
-
"solution_a": "NS approach (2 steps): Round to 5000×2000 for easy mental computation. → 9857712",
|
| 800 |
-
"solution_b": "Algorithmic approach (4 steps): Compute step by step → 9857712",
|
| 801 |
-
"correct_answer": "A",
|
| 802 |
-
"ns_steps": 2,
|
| 803 |
-
"algo_steps": 4,
|
| 804 |
-
"prompt": "Both solutions below are correct. Which one uses fewer reasoning steps? Answer A or B.\n\nProblem: Estimate 5009 × 1968.\n\nSolution A: NS approach (2 steps): Round to 5000×2000 for easy mental computation. → 9857712\n\nSolution B: Algorithmic approach (4 steps): Compute step by step → 9857712"
|
| 805 |
-
},
|
| 806 |
-
{
|
| 807 |
-
"task_id": "J3_landmark_comparison_000699",
|
| 808 |
-
"task_type": "J3_pairwise_efficiency",
|
| 809 |
-
"category": "landmark_comparison",
|
| 810 |
-
"problem": "Is 11% of 57250 greater than 11559?",
|
| 811 |
-
"solution_a": "NS approach (2 steps): Use 10% as landmark: 10% of 57250 = 5725. → No",
|
| 812 |
-
"solution_b": "Algorithmic approach (3 steps): Compute step by step → No",
|
| 813 |
-
"correct_answer": "A",
|
| 814 |
-
"ns_steps": 2,
|
| 815 |
-
"algo_steps": 3,
|
| 816 |
-
"prompt": "Both solutions below are correct. Which one uses fewer reasoning steps? Answer A or B.\n\nProblem: Is 11% of 57250 greater than 11559?\n\nSolution A: NS approach (2 steps): Use 10% as landmark: 10% of 57250 = 5725. → No\n\nSolution B: Algorithmic approach (3 steps): Compute step by step → No"
|
| 817 |
-
},
|
| 818 |
-
{
|
| 819 |
-
"task_id": "J3_cancellation_identity_000599",
|
| 820 |
-
"task_type": "J3_pairwise_efficiency",
|
| 821 |
-
"category": "cancellation_identity",
|
| 822 |
-
"problem": "Evaluate: 2021 + 4865 - 4863",
|
| 823 |
-
"solution_a": "Algorithmic approach (3 steps): Compute step by step → 2023",
|
| 824 |
-
"solution_b": "NS approach (2 steps): Near-cancellation: 4865 - 4863 = 2, so answer ≈ 2021 + 2. → 2023",
|
| 825 |
-
"correct_answer": "B",
|
| 826 |
-
"ns_steps": 2,
|
| 827 |
-
"algo_steps": 3,
|
| 828 |
-
"prompt": "Both solutions below are correct. Which one uses fewer reasoning steps? Answer A or B.\n\nProblem: Evaluate: 2021 + 4865 - 4863\n\nSolution A: Algorithmic approach (3 steps): Compute step by step → 2023\n\nSolution B: NS approach (2 steps): Near-cancellation: 4865 - 4863 = 2, so answer ≈ 2021 + 2. → 2023"
|
| 829 |
-
},
|
| 830 |
-
{
|
| 831 |
-
"task_id": "J3_structural_shortcuts_000460",
|
| 832 |
-
"task_type": "J3_pairwise_efficiency",
|
| 833 |
-
"category": "structural_shortcuts",
|
| 834 |
-
"problem": "What is 10001 * 4123?",
|
| 835 |
-
"solution_a": "Algorithmic approach (4 steps): Compute step by step → 41234123",
|
| 836 |
-
"solution_b": "NS approach (3 steps): Use (10000+1)*m = 10000*m + 1*m. → 41234123",
|
| 837 |
-
"correct_answer": "B",
|
| 838 |
-
"ns_steps": 3,
|
| 839 |
-
"algo_steps": 4,
|
| 840 |
-
"prompt": "Both solutions below are correct. Which one uses fewer reasoning steps? Answer A or B.\n\nProblem: What is 10001 * 4123?\n\nSolution A: Algorithmic approach (4 steps): Compute step by step → 41234123\n\nSolution B: NS approach (3 steps): Use (10000+1)*m = 10000*m + 1*m. → 41234123"
|
| 841 |
-
},
|
| 842 |
-
{
|
| 843 |
-
"task_id": "J3_structural_shortcuts_000478",
|
| 844 |
-
"task_type": "J3_pairwise_efficiency",
|
| 845 |
-
"category": "structural_shortcuts",
|
| 846 |
-
"problem": "What is 9999 * 2734?",
|
| 847 |
-
"solution_a": "NS approach (3 steps): Use (10000-1)*m = 10000*m - 1*m. → 27337266",
|
| 848 |
-
"solution_b": "Algorithmic approach (4 steps): Compute step by step → 27337266",
|
| 849 |
-
"correct_answer": "A",
|
| 850 |
-
"ns_steps": 3,
|
| 851 |
-
"algo_steps": 4,
|
| 852 |
-
"prompt": "Both solutions below are correct. Which one uses fewer reasoning steps? Answer A or B.\n\nProblem: What is 9999 * 2734?\n\nSolution A: NS approach (3 steps): Use (10000-1)*m = 10000*m - 1*m. → 27337266\n\nSolution B: Algorithmic approach (4 steps): Compute step by step → 27337266"
|
| 853 |
-
},
|
| 854 |
-
{
|
| 855 |
-
"task_id": "J3_option_elimination_000758",
|
| 856 |
-
"task_type": "J3_pairwise_efficiency",
|
| 857 |
-
"category": "option_elimination",
|
| 858 |
-
"problem": "What is 7525 × 5474?",
|
| 859 |
-
"solution_a": "NS approach (2 steps): Check trailing digit / parity / magnitude — only one option matches. → 41191850",
|
| 860 |
-
"solution_b": "Algorithmic approach (4 steps): Compute step by step → 41191850",
|
| 861 |
-
"correct_answer": "A",
|
| 862 |
-
"ns_steps": 2,
|
| 863 |
-
"algo_steps": 4,
|
| 864 |
-
"prompt": "Both solutions below are correct. Which one uses fewer reasoning steps? Answer A or B.\n\nProblem: What is 7525 × 5474?\n\nSolution A: NS approach (2 steps): Check trailing digit / parity / magnitude — only one option matches. → 41191850\n\nSolution B: Algorithmic approach (4 steps): Compute step by step → 41191850"
|
| 865 |
-
},
|
| 866 |
-
{
|
| 867 |
-
"task_id": "J3_relative_distance_000541",
|
| 868 |
-
"task_type": "J3_pairwise_efficiency",
|
| 869 |
-
"category": "relative_distance",
|
| 870 |
-
"problem": "Which is larger: 1748/3532 or 1376/2725?",
|
| 871 |
-
"solution_a": "Algorithmic approach (3 steps): Compute step by step → 1376/2725",
|
| 872 |
-
"solution_b": "NS approach (2 steps): One is below 1/2, the other above; no computation needed. → 1376/2725",
|
| 873 |
-
"correct_answer": "B",
|
| 874 |
-
"ns_steps": 2,
|
| 875 |
-
"algo_steps": 3,
|
| 876 |
-
"prompt": "Both solutions below are correct. Which one uses fewer reasoning steps? Answer A or B.\n\nProblem: Which is larger: 1748/3532 or 1376/2725?\n\nSolution A: Algorithmic approach (3 steps): Compute step by step → 1376/2725\n\nSolution B: NS approach (2 steps): One is below 1/2, the other above; no computation needed. → 1376/2725"
|
| 877 |
-
},
|
| 878 |
-
{
|
| 879 |
-
"task_id": "J3_landmark_comparison_000695",
|
| 880 |
-
"task_type": "J3_pairwise_efficiency",
|
| 881 |
-
"category": "landmark_comparison",
|
| 882 |
-
"problem": "Is 50% of 45760 greater than 12614?",
|
| 883 |
-
"solution_a": "NS approach (2 steps): Use 50% as landmark: 50% of 45760 = 22880. → Yes",
|
| 884 |
-
"solution_b": "Algorithmic approach (3 steps): Compute step by step → Yes",
|
| 885 |
-
"correct_answer": "A",
|
| 886 |
-
"ns_steps": 2,
|
| 887 |
-
"algo_steps": 3,
|
| 888 |
-
"prompt": "Both solutions below are correct. Which one uses fewer reasoning steps? Answer A or B.\n\nProblem: Is 50% of 45760 greater than 12614?\n\nSolution A: NS approach (2 steps): Use 50% as landmark: 50% of 45760 = 22880. → Yes\n\nSolution B: Algorithmic approach (3 steps): Compute step by step → Yes"
|
| 889 |
-
},
|
| 890 |
-
{
|
| 891 |
-
"task_id": "J3_option_elimination_000776",
|
| 892 |
-
"task_type": "J3_pairwise_efficiency",
|
| 893 |
-
"category": "option_elimination",
|
| 894 |
-
"problem": "What is 6135 × 7717?",
|
| 895 |
-
"solution_a": "Algorithmic approach (4 steps): Compute step by step → 47343795",
|
| 896 |
-
"solution_b": "NS approach (2 steps): Check trailing digit / parity / magnitude — only one option matches. → 47343795",
|
| 897 |
-
"correct_answer": "B",
|
| 898 |
-
"ns_steps": 2,
|
| 899 |
-
"algo_steps": 4,
|
| 900 |
-
"prompt": "Both solutions below are correct. Which one uses fewer reasoning steps? Answer A or B.\n\nProblem: What is 6135 × 7717?\n\nSolution A: Algorithmic approach (4 steps): Compute step by step → 47343795\n\nSolution B: NS approach (2 steps): Check trailing digit / parity / magnitude — only one option matches. → 47343795"
|
| 901 |
-
},
|
| 902 |
-
{
|
| 903 |
-
"task_id": "J3_magnitude_estimation_000402",
|
| 904 |
-
"task_type": "J3_pairwise_efficiency",
|
| 905 |
-
"category": "magnitude_estimation",
|
| 906 |
-
"problem": "Which of the following is the best estimate for 10100 * 9900?",
|
| 907 |
-
"solution_a": "NS approach (2 steps): Round both to 10000 and multiply. → 99990000",
|
| 908 |
-
"solution_b": "Algorithmic approach (4 steps): Compute step by step → 99990000",
|
| 909 |
-
"correct_answer": "A",
|
| 910 |
-
"ns_steps": 2,
|
| 911 |
-
"algo_steps": 4,
|
| 912 |
-
"prompt": "Both solutions below are correct. Which one uses fewer reasoning steps? Answer A or B.\n\nProblem: Which of the following is the best estimate for 10100 * 9900?\n\nSolution A: NS approach (2 steps): Round both to 10000 and multiply. → 99990000\n\nSolution B: Algorithmic approach (4 steps): Compute step by step → 99990000"
|
| 913 |
-
},
|
| 914 |
-
{
|
| 915 |
-
"task_id": "J3_structural_shortcuts_000496",
|
| 916 |
-
"task_type": "J3_pairwise_efficiency",
|
| 917 |
-
"category": "structural_shortcuts",
|
| 918 |
-
"problem": "What is 9998 * 3721?",
|
| 919 |
-
"solution_a": "Algorithmic approach (4 steps): Compute step by step → 37202558",
|
| 920 |
-
"solution_b": "NS approach (3 steps): Use (10000-2)*m = 10000*m - 2*m. → 37202558",
|
| 921 |
-
"correct_answer": "B",
|
| 922 |
-
"ns_steps": 3,
|
| 923 |
-
"algo_steps": 4,
|
| 924 |
-
"prompt": "Both solutions below are correct. Which one uses fewer reasoning steps? Answer A or B.\n\nProblem: What is 9998 * 3721?\n\nSolution A: Algorithmic approach (4 steps): Compute step by step → 37202558\n\nSolution B: NS approach (3 steps): Use (10000-2)*m = 10000*m - 2*m. → 37202558"
|
| 925 |
-
},
|
| 926 |
-
{
|
| 927 |
-
"task_id": "J3_equation_reasoning_000734",
|
| 928 |
-
"task_type": "J3_pairwise_efficiency",
|
| 929 |
-
"category": "equation_reasoning",
|
| 930 |
-
"problem": "What value fills the blank? 5844 + 3069 + ___ = 3069 + 6695 + 5844",
|
| 931 |
-
"solution_a": "NS approach (1 steps): Recognize commutativity/distributive law — matching terms cancel. → 6695",
|
| 932 |
-
"solution_b": "Algorithmic approach (3 steps): Compute step by step → 6695",
|
| 933 |
-
"correct_answer": "A",
|
| 934 |
-
"ns_steps": 1,
|
| 935 |
-
"algo_steps": 3,
|
| 936 |
-
"prompt": "Both solutions below are correct. Which one uses fewer reasoning steps? Answer A or B.\n\nProblem: What value fills the blank? 5844 + 3069 + ___ = 3069 + 6695 + 5844\n\nSolution A: NS approach (1 steps): Recognize commutativity/distributive law — matching terms cancel. → 6695\n\nSolution B: Algorithmic approach (3 steps): Compute step by step → 6695"
|
| 937 |
-
},
|
| 938 |
-
{
|
| 939 |
-
"task_id": "J3_magnitude_estimation_000414",
|
| 940 |
-
"task_type": "J3_pairwise_efficiency",
|
| 941 |
-
"category": "magnitude_estimation",
|
| 942 |
-
"problem": "Which of the following is the best estimate for 10200 * 9800?",
|
| 943 |
-
"solution_a": "NS approach (2 steps): Round both to 10000 and multiply. → 99960000",
|
| 944 |
-
"solution_b": "Algorithmic approach (4 steps): Compute step by step → 99960000",
|
| 945 |
-
"correct_answer": "A",
|
| 946 |
-
"ns_steps": 2,
|
| 947 |
-
"algo_steps": 4,
|
| 948 |
-
"prompt": "Both solutions below are correct. Which one uses fewer reasoning steps? Answer A or B.\n\nProblem: Which of the following is the best estimate for 10200 * 9800?\n\nSolution A: NS approach (2 steps): Round both to 10000 and multiply. → 99960000\n\nSolution B: Algorithmic approach (4 steps): Compute step by step → 99960000"
|
| 949 |
-
},
|
| 950 |
-
{
|
| 951 |
-
"task_id": "J3_cancellation_identity_000555",
|
| 952 |
-
"task_type": "J3_pairwise_efficiency",
|
| 953 |
-
"category": "cancellation_identity",
|
| 954 |
-
"problem": "Evaluate: 7126 + 2057 - 2055",
|
| 955 |
-
"solution_a": "NS approach (2 steps): Near-cancellation: 2057 - 2055 = 2, so answer ≈ 7126 + 2. → 7128",
|
| 956 |
-
"solution_b": "Algorithmic approach (3 steps): Compute step by step → 7128",
|
| 957 |
-
"correct_answer": "A",
|
| 958 |
-
"ns_steps": 2,
|
| 959 |
-
"algo_steps": 3,
|
| 960 |
-
"prompt": "Both solutions below are correct. Which one uses fewer reasoning steps? Answer A or B.\n\nProblem: Evaluate: 7126 + 2057 - 2055\n\nSolution A: NS approach (2 steps): Near-cancellation: 2057 - 2055 = 2, so answer ≈ 7126 + 2. → 7128\n\nSolution B: Algorithmic approach (3 steps): Compute step by step → 7128"
|
| 961 |
-
},
|
| 962 |
-
{
|
| 963 |
-
"task_id": "J3_equation_reasoning_000703",
|
| 964 |
-
"task_type": "J3_pairwise_efficiency",
|
| 965 |
-
"category": "equation_reasoning",
|
| 966 |
-
"problem": "What value fills the blank? 4391 + 8555 + ___ = 8555 + 8523 + 4391",
|
| 967 |
-
"solution_a": "Algorithmic approach (3 steps): Compute step by step → 8523",
|
| 968 |
-
"solution_b": "NS approach (1 steps): Recognize commutativity/distributive law — matching terms cancel. → 8523",
|
| 969 |
-
"correct_answer": "B",
|
| 970 |
-
"ns_steps": 1,
|
| 971 |
-
"algo_steps": 3,
|
| 972 |
-
"prompt": "Both solutions below are correct. Which one uses fewer reasoning steps? Answer A or B.\n\nProblem: What value fills the blank? 4391 + 8555 + ___ = 8555 + 8523 + 4391\n\nSolution A: Algorithmic approach (3 steps): Compute step by step → 8523\n\nSolution B: NS approach (1 steps): Recognize commutativity/distributive law — matching terms cancel. → 8523"
|
| 973 |
-
},
|
| 974 |
-
{
|
| 975 |
-
"task_id": "J3_compatible_numbers_000603",
|
| 976 |
-
"task_type": "J3_pairwise_efficiency",
|
| 977 |
-
"category": "compatible_numbers",
|
| 978 |
-
"problem": "Estimate 2520 × 3783.",
|
| 979 |
-
"solution_a": "Algorithmic approach (4 steps): Compute step by step → 9533160",
|
| 980 |
-
"solution_b": "NS approach (2 steps): Round to 2500×4000 for easy mental computation. → 9533160",
|
| 981 |
-
"correct_answer": "B",
|
| 982 |
-
"ns_steps": 2,
|
| 983 |
-
"algo_steps": 4,
|
| 984 |
-
"prompt": "Both solutions below are correct. Which one uses fewer reasoning steps? Answer A or B.\n\nProblem: Estimate 2520 × 3783.\n\nSolution A: Algorithmic approach (4 steps): Compute step by step → 9533160\n\nSolution B: NS approach (2 steps): Round to 2500×4000 for easy mental computation. → 9533160"
|
| 985 |
-
},
|
| 986 |
-
{
|
| 987 |
-
"task_id": "J3_landmark_comparison_000681",
|
| 988 |
-
"task_type": "J3_pairwise_efficiency",
|
| 989 |
-
"category": "landmark_comparison",
|
| 990 |
-
"problem": "Is 9% of 52080 greater than 22238?",
|
| 991 |
-
"solution_a": "NS approach (2 steps): Use 10% as landmark: 10% of 52080 = 5208. → No",
|
| 992 |
-
"solution_b": "Algorithmic approach (3 steps): Compute step by step → No",
|
| 993 |
-
"correct_answer": "A",
|
| 994 |
-
"ns_steps": 2,
|
| 995 |
-
"algo_steps": 3,
|
| 996 |
-
"prompt": "Both solutions below are correct. Which one uses fewer reasoning steps? Answer A or B.\n\nProblem: Is 9% of 52080 greater than 22238?\n\nSolution A: NS approach (2 steps): Use 10% as landmark: 10% of 52080 = 5208. → No\n\nSolution B: Algorithmic approach (3 steps): Compute step by step → No"
|
| 997 |
-
},
|
| 998 |
-
{
|
| 999 |
-
"task_id": "J3_magnitude_estimation_000434",
|
| 1000 |
-
"task_type": "J3_pairwise_efficiency",
|
| 1001 |
-
"category": "magnitude_estimation",
|
| 1002 |
-
"problem": "Which of the following is the best estimate for 10200 * 9800?",
|
| 1003 |
-
"solution_a": "Algorithmic approach (4 steps): Compute step by step → 99960000",
|
| 1004 |
-
"solution_b": "NS approach (2 steps): Round both to 10000 and multiply. → 99960000",
|
| 1005 |
-
"correct_answer": "B",
|
| 1006 |
-
"ns_steps": 2,
|
| 1007 |
-
"algo_steps": 4,
|
| 1008 |
-
"prompt": "Both solutions below are correct. Which one uses fewer reasoning steps? Answer A or B.\n\nProblem: Which of the following is the best estimate for 10200 * 9800?\n\nSolution A: Algorithmic approach (4 steps): Compute step by step → 99960000\n\nSolution B: NS approach (2 steps): Round both to 10000 and multiply. → 99960000"
|
| 1009 |
-
},
|
| 1010 |
-
{
|
| 1011 |
-
"task_id": "J3_equation_reasoning_000718",
|
| 1012 |
-
"task_type": "J3_pairwise_efficiency",
|
| 1013 |
-
"category": "equation_reasoning",
|
| 1014 |
-
"problem": "What value fills the blank? 2661 + 1919 + ___ = 1919 + 6614 + 2661",
|
| 1015 |
-
"solution_a": "NS approach (1 steps): Recognize commutativity/distributive law — matching terms cancel. → 6614",
|
| 1016 |
-
"solution_b": "Algorithmic approach (3 steps): Compute step by step → 6614",
|
| 1017 |
-
"correct_answer": "A",
|
| 1018 |
-
"ns_steps": 1,
|
| 1019 |
-
"algo_steps": 3,
|
| 1020 |
-
"prompt": "Both solutions below are correct. Which one uses fewer reasoning steps? Answer A or B.\n\nProblem: What value fills the blank? 2661 + 1919 + ___ = 1919 + 6614 + 2661\n\nSolution A: NS approach (1 steps): Recognize commutativity/distributive law — matching terms cancel. → 6614\n\nSolution B: Algorithmic approach (3 steps): Compute step by step → 6614"
|
| 1021 |
-
},
|
| 1022 |
-
{
|
| 1023 |
-
"task_id": "J3_relative_distance_000530",
|
| 1024 |
-
"task_type": "J3_pairwise_efficiency",
|
| 1025 |
-
"category": "relative_distance",
|
| 1026 |
-
"problem": "Which is larger: 3937/7998 or 3703/7314?",
|
| 1027 |
-
"solution_a": "Algorithmic approach (3 steps): Compute step by step → 3703/7314",
|
| 1028 |
-
"solution_b": "NS approach (2 steps): One is below 1/2, the other above; no computation needed. → 3703/7314",
|
| 1029 |
-
"correct_answer": "B",
|
| 1030 |
-
"ns_steps": 2,
|
| 1031 |
-
"algo_steps": 3,
|
| 1032 |
-
"prompt": "Both solutions below are correct. Which one uses fewer reasoning steps? Answer A or B.\n\nProblem: Which is larger: 3937/7998 or 3703/7314?\n\nSolution A: Algorithmic approach (3 steps): Compute step by step → 3703/7314\n\nSolution B: NS approach (2 steps): One is below 1/2, the other above; no computation needed. → 3703/7314"
|
| 1033 |
-
},
|
| 1034 |
-
{
|
| 1035 |
-
"task_id": "J3_relative_distance_000528",
|
| 1036 |
-
"task_type": "J3_pairwise_efficiency",
|
| 1037 |
-
"category": "relative_distance",
|
| 1038 |
-
"problem": "Which is larger: 2499/5018 or 4280/8455?",
|
| 1039 |
-
"solution_a": "Algorithmic approach (3 steps): Compute step by step → 4280/8455",
|
| 1040 |
-
"solution_b": "NS approach (2 steps): One is below 1/2, the other above; no computation needed. → 4280/8455",
|
| 1041 |
-
"correct_answer": "B",
|
| 1042 |
-
"ns_steps": 2,
|
| 1043 |
-
"algo_steps": 3,
|
| 1044 |
-
"prompt": "Both solutions below are correct. Which one uses fewer reasoning steps? Answer A or B.\n\nProblem: Which is larger: 2499/5018 or 4280/8455?\n\nSolution A: Algorithmic approach (3 steps): Compute step by step → 4280/8455\n\nSolution B: NS approach (2 steps): One is below 1/2, the other above; no computation needed. → 4280/8455"
|
| 1045 |
-
},
|
| 1046 |
-
{
|
| 1047 |
-
"task_id": "J3_option_elimination_000771",
|
| 1048 |
-
"task_type": "J3_pairwise_efficiency",
|
| 1049 |
-
"category": "option_elimination",
|
| 1050 |
-
"problem": "What is 5562 × 7803?",
|
| 1051 |
-
"solution_a": "Algorithmic approach (4 steps): Compute step by step → 43400286",
|
| 1052 |
-
"solution_b": "NS approach (2 steps): Check trailing digit / parity / magnitude — only one option matches. → 43400286",
|
| 1053 |
-
"correct_answer": "B",
|
| 1054 |
-
"ns_steps": 2,
|
| 1055 |
-
"algo_steps": 4,
|
| 1056 |
-
"prompt": "Both solutions below are correct. Which one uses fewer reasoning steps? Answer A or B.\n\nProblem: What is 5562 × 7803?\n\nSolution A: Algorithmic approach (4 steps): Compute step by step → 43400286\n\nSolution B: NS approach (2 steps): Check trailing digit / parity / magnitude — only one option matches. → 43400286"
|
| 1057 |
-
},
|
| 1058 |
-
{
|
| 1059 |
-
"task_id": "J3_landmark_comparison_000668",
|
| 1060 |
-
"task_type": "J3_pairwise_efficiency",
|
| 1061 |
-
"category": "landmark_comparison",
|
| 1062 |
-
"problem": "Is 10% of 93060 greater than 31194?",
|
| 1063 |
-
"solution_a": "Algorithmic approach (3 steps): Compute step by step → No",
|
| 1064 |
-
"solution_b": "NS approach (2 steps): Use 10% as landmark: 10% of 93060 = 9306. → No",
|
| 1065 |
-
"correct_answer": "B",
|
| 1066 |
-
"ns_steps": 2,
|
| 1067 |
-
"algo_steps": 3,
|
| 1068 |
-
"prompt": "Both solutions below are correct. Which one uses fewer reasoning steps? Answer A or B.\n\nProblem: Is 10% of 93060 greater than 31194?\n\nSolution A: Algorithmic approach (3 steps): Compute step by step → No\n\nSolution B: NS approach (2 steps): Use 10% as landmark: 10% of 93060 = 9306. → No"
|
| 1069 |
-
},
|
| 1070 |
-
{
|
| 1071 |
-
"task_id": "J3_landmark_comparison_000677",
|
| 1072 |
-
"task_type": "J3_pairwise_efficiency",
|
| 1073 |
-
"category": "landmark_comparison",
|
| 1074 |
-
"problem": "Is 48% of 23770 greater than 9136?",
|
| 1075 |
-
"solution_a": "Algorithmic approach (3 steps): Compute step by step → Yes",
|
| 1076 |
-
"solution_b": "NS approach (2 steps): Use 50% as landmark: 50% of 23770 = 11885. → Yes",
|
| 1077 |
-
"correct_answer": "B",
|
| 1078 |
-
"ns_steps": 2,
|
| 1079 |
-
"algo_steps": 3,
|
| 1080 |
-
"prompt": "Both solutions below are correct. Which one uses fewer reasoning steps? Answer A or B.\n\nProblem: Is 48% of 23770 greater than 9136?\n\nSolution A: Algorithmic approach (3 steps): Compute step by step → Yes\n\nSolution B: NS approach (2 steps): Use 50% as landmark: 50% of 23770 = 11885. → Yes"
|
| 1081 |
-
},
|
| 1082 |
-
{
|
| 1083 |
-
"task_id": "J3_landmark_comparison_000694",
|
| 1084 |
-
"task_type": "J3_pairwise_efficiency",
|
| 1085 |
-
"category": "landmark_comparison",
|
| 1086 |
-
"problem": "Is 24% of 90400 greater than 25771?",
|
| 1087 |
-
"solution_a": "Algorithmic approach (3 steps): Compute step by step → No",
|
| 1088 |
-
"solution_b": "NS approach (2 steps): Use 25% as landmark: 25% of 90400 = 22600. → No",
|
| 1089 |
-
"correct_answer": "B",
|
| 1090 |
-
"ns_steps": 2,
|
| 1091 |
-
"algo_steps": 3,
|
| 1092 |
-
"prompt": "Both solutions below are correct. Which one uses fewer reasoning steps? Answer A or B.\n\nProblem: Is 24% of 90400 greater than 25771?\n\nSolution A: Algorithmic approach (3 steps): Compute step by step → No\n\nSolution B: NS approach (2 steps): Use 25% as landmark: 25% of 90400 = 22600. → No"
|
| 1093 |
-
},
|
| 1094 |
-
{
|
| 1095 |
-
"task_id": "J3_option_elimination_000792",
|
| 1096 |
-
"task_type": "J3_pairwise_efficiency",
|
| 1097 |
-
"category": "option_elimination",
|
| 1098 |
-
"problem": "What is 4893 × 1523?",
|
| 1099 |
-
"solution_a": "NS approach (2 steps): Check trailing digit / parity / magnitude — only one option matches. → 7452039",
|
| 1100 |
-
"solution_b": "Algorithmic approach (4 steps): Compute step by step → 7452039",
|
| 1101 |
-
"correct_answer": "A",
|
| 1102 |
-
"ns_steps": 2,
|
| 1103 |
-
"algo_steps": 4,
|
| 1104 |
-
"prompt": "Both solutions below are correct. Which one uses fewer reasoning steps? Answer A or B.\n\nProblem: What is 4893 × 1523?\n\nSolution A: NS approach (2 steps): Check trailing digit / parity / magnitude — only one option matches. → 7452039\n\nSolution B: Algorithmic approach (4 steps): Compute step by step → 7452039"
|
| 1105 |
-
},
|
| 1106 |
-
{
|
| 1107 |
-
"task_id": "J3_compatible_numbers_000613",
|
| 1108 |
-
"task_type": "J3_pairwise_efficiency",
|
| 1109 |
-
"category": "compatible_numbers",
|
| 1110 |
-
"problem": "Estimate 2540 × 3676.",
|
| 1111 |
-
"solution_a": "Algorithmic approach (4 steps): Compute step by step → 9337040",
|
| 1112 |
-
"solution_b": "NS approach (2 steps): Round to 2500×4000 for easy mental computation. → 9337040",
|
| 1113 |
-
"correct_answer": "B",
|
| 1114 |
-
"ns_steps": 2,
|
| 1115 |
-
"algo_steps": 4,
|
| 1116 |
-
"prompt": "Both solutions below are correct. Which one uses fewer reasoning steps? Answer A or B.\n\nProblem: Estimate 2540 × 3676.\n\nSolution A: Algorithmic approach (4 steps): Compute step by step → 9337040\n\nSolution B: NS approach (2 steps): Round to 2500×4000 for easy mental computation. → 9337040"
|
| 1117 |
-
},
|
| 1118 |
-
{
|
| 1119 |
-
"task_id": "J3_cancellation_identity_000585",
|
| 1120 |
-
"task_type": "J3_pairwise_efficiency",
|
| 1121 |
-
"category": "cancellation_identity",
|
| 1122 |
-
"problem": "Evaluate: 4359 + 9463 - 9464",
|
| 1123 |
-
"solution_a": "Algorithmic approach (3 steps): Compute step by step → 4358",
|
| 1124 |
-
"solution_b": "NS approach (2 steps): Near-cancellation: 9463 - 9464 = -1, so answer ≈ 4359 + -1. → 4358",
|
| 1125 |
-
"correct_answer": "B",
|
| 1126 |
-
"ns_steps": 2,
|
| 1127 |
-
"algo_steps": 3,
|
| 1128 |
-
"prompt": "Both solutions below are correct. Which one uses fewer reasoning steps? Answer A or B.\n\nProblem: Evaluate: 4359 + 9463 - 9464\n\nSolution A: Algorithmic approach (3 steps): Compute step by step → 4358\n\nSolution B: NS approach (2 steps): Near-cancellation: 9463 - 9464 = -1, so answer ≈ 4359 + -1. → 4358"
|
| 1129 |
-
},
|
| 1130 |
-
{
|
| 1131 |
-
"task_id": "J3_equation_reasoning_000743",
|
| 1132 |
-
"task_type": "J3_pairwise_efficiency",
|
| 1133 |
-
"category": "equation_reasoning",
|
| 1134 |
-
"problem": "What value fills the blank? 6010 × (2659 + 2481) = 6010 × ___ + 6010 × 2481",
|
| 1135 |
-
"solution_a": "NS approach (1 steps): Recognize commutativity/distributive law — matching terms cancel. → 2659",
|
| 1136 |
-
"solution_b": "Algorithmic approach (3 steps): Compute step by step → 2659",
|
| 1137 |
-
"correct_answer": "A",
|
| 1138 |
-
"ns_steps": 1,
|
| 1139 |
-
"algo_steps": 3,
|
| 1140 |
-
"prompt": "Both solutions below are correct. Which one uses fewer reasoning steps? Answer A or B.\n\nProblem: What value fills the blank? 6010 × (2659 + 2481) = 6010 × ___ + 6010 × 2481\n\nSolution A: NS approach (1 steps): Recognize commutativity/distributive law — matching terms cancel. → 2659\n\nSolution B: Algorithmic approach (3 steps): Compute step by step → 2659"
|
| 1141 |
-
},
|
| 1142 |
-
{
|
| 1143 |
-
"task_id": "J3_option_elimination_000765",
|
| 1144 |
-
"task_type": "J3_pairwise_efficiency",
|
| 1145 |
-
"category": "option_elimination",
|
| 1146 |
-
"problem": "What is 1104 × 5487?",
|
| 1147 |
-
"solution_a": "NS approach (2 steps): Check trailing digit / parity / magnitude — only one option matches. → 6057648",
|
| 1148 |
-
"solution_b": "Algorithmic approach (4 steps): Compute step by step → 6057648",
|
| 1149 |
-
"correct_answer": "A",
|
| 1150 |
-
"ns_steps": 2,
|
| 1151 |
-
"algo_steps": 4,
|
| 1152 |
-
"prompt": "Both solutions below are correct. Which one uses fewer reasoning steps? Answer A or B.\n\nProblem: What is 1104 × 5487?\n\nSolution A: NS approach (2 steps): Check trailing digit / parity / magnitude — only one option matches. → 6057648\n\nSolution B: Algorithmic approach (4 steps): Compute step by step → 6057648"
|
| 1153 |
-
}
|
| 1154 |
-
]
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|
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|
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|
|
|
data/manifest.json
ADDED
|
@@ -0,0 +1,59 @@
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
| 1 |
+
{
|
| 2 |
+
"schema_version": 1,
|
| 3 |
+
"release_id": "paper-aligned-v1",
|
| 4 |
+
"authority": "paper_task_definitions",
|
| 5 |
+
"tasks": {
|
| 6 |
+
"apply.d2": {
|
| 7 |
+
"path": "sensemath_v2_d2.json",
|
| 8 |
+
"task_type": "Apply_family",
|
| 9 |
+
"record_count": 400,
|
| 10 |
+
"item_count": 1200,
|
| 11 |
+
"sha256": "e035bada7115ee7177e5c4d81c7ea699c73dd555a2acdebe85d48b2152535e5a"
|
| 12 |
+
},
|
| 13 |
+
"apply.d4": {
|
| 14 |
+
"path": "sensemath_v2_d4.json",
|
| 15 |
+
"task_type": "Apply_family",
|
| 16 |
+
"record_count": 400,
|
| 17 |
+
"item_count": 1200,
|
| 18 |
+
"sha256": "fba417d8ec49c5fb6c79e77a43ea9c0514421d12a72f4d17c5bf61fe590e2693"
|
| 19 |
+
},
|
| 20 |
+
"apply.d8": {
|
| 21 |
+
"path": "sensemath_v2_d8.json",
|
| 22 |
+
"task_type": "Apply_family",
|
| 23 |
+
"record_count": 400,
|
| 24 |
+
"item_count": 1200,
|
| 25 |
+
"sha256": "7f008fd7c653263f6e2cce1691f86bf52a53395ddadc41b3e953221b5ddeb6be"
|
| 26 |
+
},
|
| 27 |
+
"apply.d16": {
|
| 28 |
+
"path": "sensemath_v2_d16.json",
|
| 29 |
+
"task_type": "Apply_family",
|
| 30 |
+
"record_count": 400,
|
| 31 |
+
"item_count": 1200,
|
| 32 |
+
"sha256": "4de5f838ca8844f7a5891a84289fa76b26155bf7417fa9e09a27ed43a9db3635"
|
| 33 |
+
},
|
| 34 |
+
"judge.j1.strategy_appropriateness": {
|
| 35 |
+
"path": "judge_j1.json",
|
| 36 |
+
"task_type": "J1_strategy_appropriateness",
|
| 37 |
+
"record_count": 300,
|
| 38 |
+
"item_count": 300,
|
| 39 |
+
"sha256": "bc04363791ae4a520d541a42e345eb86e3e9b1a240926bdc3d49f2e68a7bfa1c"
|
| 40 |
+
},
|
| 41 |
+
"judge.j2.strategy_identification": {
|
| 42 |
+
"path": "judge_j2.json",
|
| 43 |
+
"task_type": "J2_strategy_identification",
|
| 44 |
+
"record_count": 80,
|
| 45 |
+
"item_count": 80,
|
| 46 |
+
"sha256": "cdde7d7ca4212c54782b3dad46cbc881d9f2365548c8259ad401004933b1abcf"
|
| 47 |
+
}
|
| 48 |
+
},
|
| 49 |
+
"subsets": {
|
| 50 |
+
"judge.j1.paper_filtered_261": {
|
| 51 |
+
"path": "subsets/judge_j1_paper_filtered_261.json",
|
| 52 |
+
"task_type": "J1_strategy_appropriateness",
|
| 53 |
+
"record_count": 261,
|
| 54 |
+
"sha256": "673a6c2211707e184bb6ada31c306c9a18eaa17051920e895559399c90a570be",
|
| 55 |
+
"parent_task": "judge.j1.strategy_appropriateness",
|
| 56 |
+
"pool_with_parent": false
|
| 57 |
+
}
|
| 58 |
+
}
|
| 59 |
+
}
|
data/subsets/judge_j1_paper_filtered_261.json
ADDED
|
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