MATH-Perturb: Benchmarking LLMs' Math Reasoning Abilities against Hard Perturbations
Paper • 2502.06453 • Published
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The dataset generation failed
Error code: DatasetGenerationError
Exception: ValueError
Message: Expected object or value
Traceback: Traceback (most recent call last):
File "/usr/local/lib/python3.14/site-packages/datasets/builder.py", line 1827, in _prepare_split_single
for key, table in generator:
^^^^^^^^^
File "/src/services/worker/src/worker/job_runners/config/parquet_and_info.py", line 613, in wrapped
for item in generator(*args, **kwargs):
~~~~~~~~~^^^^^^^^^^^^^^^^^
File "/usr/local/lib/python3.14/site-packages/datasets/packaged_modules/json/json.py", line 281, in _generate_tables
examples = [ujson_loads(line) for line in batch.splitlines()]
~~~~~~~~~~~^^^^^^
File "/usr/local/lib/python3.14/site-packages/datasets/utils/json.py", line 20, in ujson_loads
return pd.io.json.ujson_loads(*args, **kwargs)
~~~~~~~~~~~~~~~~~~~~~~^^^^^^^^^^^^^^^^^
ValueError: Expected object or value
The above exception was the direct cause of the following exception:
Traceback (most recent call last):
File "/src/services/worker/src/worker/job_runners/config/parquet_and_info.py", line 1369, in compute_config_parquet_and_info_response
parquet_operations, partial, estimated_dataset_info = stream_convert_to_parquet(
~~~~~~~~~~~~~~~~~~~~~~~~~^
builder, max_dataset_size_bytes=max_dataset_size_bytes
^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
)
^
File "/src/services/worker/src/worker/job_runners/config/parquet_and_info.py", line 948, in stream_convert_to_parquet
builder._prepare_split(split_generator=splits_generators[split], file_format="parquet")
~~~~~~~~~~~~~~~~~~~~~~^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
File "/usr/local/lib/python3.14/site-packages/datasets/builder.py", line 1694, in _prepare_split
for job_id, done, content in self._prepare_split_single(
~~~~~~~~~~~~~~~~~~~~~~~~~~^
gen_kwargs=gen_kwargs, job_id=job_id, **_prepare_split_args
^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
):
^
File "/usr/local/lib/python3.14/site-packages/datasets/builder.py", line 1880, in _prepare_split_single
raise DatasetGenerationError("An error occurred while generating the dataset") from e
datasets.exceptions.DatasetGenerationError: An error occurred while generating the datasetNeed help to make the dataset viewer work? Make sure to review how to configure the dataset viewer, and open a discussion for direct support.
answer unknown | id string | key_seed float64 | level string | original_split string | problem string | problem_id int64 | source string | source_commit string | source_file string | source_file_sha256 string | source_git string | split string | subject string | type string | variant string |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
"2\\sqrt{39}-2" | 10:hard | 3,734,494,027,891,680,000 | Level 5 | train | Let \[f(n) = \left\{
\begin{array}{cl}
n^2-2 & \text{ if }n<0, \\
2n-20 & \text{ if }n \geq 0.
\end{array}
\right.\]What is the positive difference between the two values of $a$ that satisfy the equation $f(a)+f(-a)+f(2)=0$? | 10 | math-perturb | df4840f680fce405c9449008564574961c7f4df1 | math_perturb/math_perturb_hard.jsonl | 418ca51e02f3b639a919dda72b5201ce35ac6c6d7d31c3231735beb4ea012dd7 | https://github.com/Kaffaljidhmah2/MATH-Perturb | calibration | Algebra | Algebra | hard |
1009 | 16:hard | 8,092,997,021,402,695,000 | Level 5 | test | Find the least positive four-digit solution $r$ of the congruence $r^2 + 4r + 4 \equiv 1 \pmod{55} $. | 16 | math-perturb | df4840f680fce405c9449008564574961c7f4df1 | math_perturb/math_perturb_hard.jsonl | 418ca51e02f3b639a919dda72b5201ce35ac6c6d7d31c3231735beb4ea012dd7 | https://github.com/Kaffaljidhmah2/MATH-Perturb | calibration | Number Theory | Number Theory | hard |
72 | 23:hard | 8,059,494,370,382,587,000 | Level 5 | test | In how many ways can $7$ people sit around a round table if no two of the $3$ people Pierre, Rosa, and Thomas can sit next to each other? (Seating arrangements which are rotations or reflections of each other are treated as the same.) | 23 | math-perturb | df4840f680fce405c9449008564574961c7f4df1 | math_perturb/math_perturb_hard.jsonl | 418ca51e02f3b639a919dda72b5201ce35ac6c6d7d31c3231735beb4ea012dd7 | https://github.com/Kaffaljidhmah2/MATH-Perturb | calibration | Counting & Probability | Counting & Probability | hard |
2 | 260:hard | 3,360,177,859,866,000,400 | Level 5 | test | Find the number of integer values of $k$ in the closed interval $[-500,500]$ for which the equation $\log(kx^2+kx)=2\log(x+2)$ has exactly one real solution. | 260 | math-perturb | df4840f680fce405c9449008564574961c7f4df1 | math_perturb/math_perturb_hard.jsonl | 418ca51e02f3b639a919dda72b5201ce35ac6c6d7d31c3231735beb4ea012dd7 | https://github.com/Kaffaljidhmah2/MATH-Perturb | calibration | Intermediate Algebra | Intermediate Algebra | hard |
1.4 | 726:hard | 1,494,818,847,706,040,300 | Level 5 | test | Bill walks $\frac{1}{2}$ mile south, then $\frac{3}{4}$ mile east, and finally $\frac{1}{2}$ mile southeast. How many miles is he, in a direct line, from his starting point? Express your answer as a decimal to the nearest hundredth. | 726 | math-perturb | df4840f680fce405c9449008564574961c7f4df1 | math_perturb/math_perturb_hard.jsonl | 418ca51e02f3b639a919dda72b5201ce35ac6c6d7d31c3231735beb4ea012dd7 | https://github.com/Kaffaljidhmah2/MATH-Perturb | calibration | Prealgebra | Prealgebra | hard |
20 | 731:hard | 2,269,909,083,535,186,400 | Level 5 | test | A worker receives an annual wage of $\$20{,}000$, which he always deposits into a savings account at the end of the year. Upon deposit, the bank offers an extra $\$200$ bonus credited to his account. By the end of the third year (when he makes the third deposit), he wants to have at least $\$73,528$ in the account to f... | 731 | math-perturb | df4840f680fce405c9449008564574961c7f4df1 | math_perturb/math_perturb_hard.jsonl | 418ca51e02f3b639a919dda72b5201ce35ac6c6d7d31c3231735beb4ea012dd7 | https://github.com/Kaffaljidhmah2/MATH-Perturb | calibration | Algebra | Algebra | hard |
1 | 749:hard | 7,485,627,033,553,465,000 | Level 5 | train | In square $ABCD$, points $E$ and $H$ lie on $\overline{AB}$ and $\overline{DA}$, respectively, so that $AE=AH.$ Points $F$ and $G$ lie on $\overline{BC}$ and $\overline{CD}$, respectively, and points $I$ and $J$ lie on $\overline{EH}$ so that $\overline{FI} \perp \overline{EH}$ and $\overline{GJ} \perp \overline{EH}$. ... | 749 | math-perturb | df4840f680fce405c9449008564574961c7f4df1 | math_perturb/math_perturb_hard.jsonl | 418ca51e02f3b639a919dda72b5201ce35ac6c6d7d31c3231735beb4ea012dd7 | https://github.com/Kaffaljidhmah2/MATH-Perturb | calibration | Geometry | Geometry | hard |
0 | 1958:hard | 5,021,748,509,499,634,000 | Level 5 | test | How many square units are in the region satisfying the inequalities $y \ge |x|$ and $y \le -|x|-3$? Express your answer as a decimal. | 1,958 | math-perturb | df4840f680fce405c9449008564574961c7f4df1 | math_perturb/math_perturb_hard.jsonl | 418ca51e02f3b639a919dda72b5201ce35ac6c6d7d31c3231735beb4ea012dd7 | https://github.com/Kaffaljidhmah2/MATH-Perturb | calibration | Algebra | Algebra | hard |
0 | 1964:hard | 14,548,380,502,442,381,000 | Level 5 | train | Let $A = \{1, 2, 3, 4, 5, 6, 7\}$, and let $N$ be the number of injection $f$ from set $A$ to set $A$ such that $f(f(x))$ is a constant function. Find the remainder when $N$ is divided by $1000$. | 1,964 | math-perturb | df4840f680fce405c9449008564574961c7f4df1 | math_perturb/math_perturb_hard.jsonl | 418ca51e02f3b639a919dda72b5201ce35ac6c6d7d31c3231735beb4ea012dd7 | https://github.com/Kaffaljidhmah2/MATH-Perturb | calibration | Counting & Probability | Counting & Probability | hard |
"(-\\infty, -2\\sqrt{2} + 3 ] \\cup [2\\sqrt{2} + 3, +\\infty)" | 1992:hard | 15,591,971,142,368,092,000 | Level 5 | train | What is the range of the function $y = \frac{x^2 + 3x + 2}{x}$? (Express your answer using interval notation.) | 1,992 | math-perturb | df4840f680fce405c9449008564574961c7f4df1 | math_perturb/math_perturb_hard.jsonl | 418ca51e02f3b639a919dda72b5201ce35ac6c6d7d31c3231735beb4ea012dd7 | https://github.com/Kaffaljidhmah2/MATH-Perturb | calibration | Algebra | Algebra | hard |
"\\frac{5964}{19683}" | 2007:hard | 6,800,384,561,034,016,000 | Level 5 | test | Pat wants to select 9 pieces of fruit to bring in the car for the people he's driving to Montana with. He randomly chooses each piece of fruit to be an orange, an apple, or a banana. What is the probability that either exactly 3 of the pieces of fruit are oranges or exactly 6 of the pieces of fruit are apples? | 2,007 | math-perturb | df4840f680fce405c9449008564574961c7f4df1 | math_perturb/math_perturb_hard.jsonl | 418ca51e02f3b639a919dda72b5201ce35ac6c6d7d31c3231735beb4ea012dd7 | https://github.com/Kaffaljidhmah2/MATH-Perturb | calibration | Counting & Probability | Counting & Probability | hard |
"-\\frac{29}{5}" | 2041:hard | 1,313,500,219,363,065,600 | Level 5 | test | What is the value of $x$ if $-\frac{2}{3}|x-5|=\frac{3}{2}(x+1)$?
| 2,041 | math-perturb | df4840f680fce405c9449008564574961c7f4df1 | math_perturb/math_perturb_hard.jsonl | 418ca51e02f3b639a919dda72b5201ce35ac6c6d7d31c3231735beb4ea012dd7 | https://github.com/Kaffaljidhmah2/MATH-Perturb | calibration | Prealgebra | Prealgebra | hard |
"(6-3x+2y)(6-3x-5y)" | 2099:hard | 18,193,665,660,180,894,000 | Level 5 | train | Factor $36+9x^2-10y^2+9xy-36x-18y$ | 2,099 | math-perturb | df4840f680fce405c9449008564574961c7f4df1 | math_perturb/math_perturb_hard.jsonl | 418ca51e02f3b639a919dda72b5201ce35ac6c6d7d31c3231735beb4ea012dd7 | https://github.com/Kaffaljidhmah2/MATH-Perturb | calibration | Algebra | Algebra | hard |
"\\frac{4 \\sqrt{3}}{3} + \\frac{1}{2}" | 2432:hard | 4,876,785,694,065,177,000 | Level 5 | train | Find the minimum positive value of
\[y = \tan \left( x + \frac{2 \pi}{3} \right) - \tan \left( x + \frac{\pi}{6} \right) + \cos 2\left( x + \frac{\pi}{6} \right)\]for $-\frac{\pi}{3} \le x \le 0.$ | 2,432 | math-perturb | df4840f680fce405c9449008564574961c7f4df1 | math_perturb/math_perturb_hard.jsonl | 418ca51e02f3b639a919dda72b5201ce35ac6c6d7d31c3231735beb4ea012dd7 | https://github.com/Kaffaljidhmah2/MATH-Perturb | calibration | Precalculus | Precalculus | hard |
-3 | 2439:hard | 10,069,421,843,030,727,000 | Level 5 | train | Let $z = \cos \frac{4 \pi}{7} + i \sin \frac{4 \pi}{7}.$ Compute
\[\frac{z^8}{1 + z^{16}} + \frac{z^9}{1 + z^{25}} + \frac{z^{10}}{1 + z^{34}} - 1.\] | 2,439 | math-perturb | df4840f680fce405c9449008564574961c7f4df1 | math_perturb/math_perturb_hard.jsonl | 418ca51e02f3b639a919dda72b5201ce35ac6c6d7d31c3231735beb4ea012dd7 | https://github.com/Kaffaljidhmah2/MATH-Perturb | calibration | Precalculus | Precalculus | hard |
"(-8,1]" | 2680:hard | 299,790,680,928,550,400 | Level 5 | test | Solve
\[\frac{x(x + 2)^2}{x + 8} \le 1.\]Enter your answer using interval notation. | 2,680 | math-perturb | df4840f680fce405c9449008564574961c7f4df1 | math_perturb/math_perturb_hard.jsonl | 418ca51e02f3b639a919dda72b5201ce35ac6c6d7d31c3231735beb4ea012dd7 | https://github.com/Kaffaljidhmah2/MATH-Perturb | calibration | Intermediate Algebra | Intermediate Algebra | hard |
0 | 3165:hard | 1,583,361,149,066,257,400 | Level 5 | test | Determine the smallest non-negative integer $a$ that satisfies the congruences: \begin{align*} &a\equiv 2\pmod 3,\\ &a\equiv 4\pmod 5,\\ &a\equiv 6\pmod 7,\\ &a\equiv 10\pmod 9. \end{align*} Answer 0 if doesn't exist. | 3,165 | math-perturb | df4840f680fce405c9449008564574961c7f4df1 | math_perturb/math_perturb_hard.jsonl | 418ca51e02f3b639a919dda72b5201ce35ac6c6d7d31c3231735beb4ea012dd7 | https://github.com/Kaffaljidhmah2/MATH-Perturb | calibration | Number Theory | Number Theory | hard |
18 | 3188:hard | 12,224,613,548,996,432,000 | Level 5 | train | Let $\omega$ be a complex number such that $\omega^19 = 1$ and $\omega \ne 1.$ Compute the number of possible values of
\[\omega^{16} + \omega^{18} + \omega^{20} + \dots + \omega^{54}.\] | 3,188 | math-perturb | df4840f680fce405c9449008564574961c7f4df1 | math_perturb/math_perturb_hard.jsonl | 418ca51e02f3b639a919dda72b5201ce35ac6c6d7d31c3231735beb4ea012dd7 | https://github.com/Kaffaljidhmah2/MATH-Perturb | calibration | Intermediate Algebra | Intermediate Algebra | hard |
16.5 | 10:simple | 11,731,911,042,518,413,000 | Level 5 | train | Let \[f(n) = \left\{
\begin{array}{cl}
n^2-2 & \text{ if }n<0, \\
2n-20 & \text{ if }n \geq 0.
\end{array}
\right.\]What is the positive difference between the two values of $a$ that satisfy the equation $f(-3)+f(3)+f(a)=0$? | 10 | math-perturb | df4840f680fce405c9449008564574961c7f4df1 | math_perturb/math_perturb_simple.jsonl | 2130821d4235dc1f5d962bee7f84a096651bf98fcb17b6dcfd3d0a48875ba5bb | https://github.com/Kaffaljidhmah2/MATH-Perturb | calibration | Algebra | Algebra | simple |
1011 | 16:simple | 1,452,782,539,351,574,500 | Level 5 | test | Find the least positive four-digit solution $r$ of the congruence $r^2 + 4r + 4 \equiv r^2 + 2r + 1 \pmod{45} $. | 16 | math-perturb | df4840f680fce405c9449008564574961c7f4df1 | math_perturb/math_perturb_simple.jsonl | 2130821d4235dc1f5d962bee7f84a096651bf98fcb17b6dcfd3d0a48875ba5bb | https://github.com/Kaffaljidhmah2/MATH-Perturb | calibration | Number Theory | Number Theory | simple |
1440 | 23:simple | 16,493,720,117,963,827,000 | Level 5 | test | In how many ways can $8$ people sit around a round table if no two of the $3$ people Pierre, Rosa, and Thomas can sit next to each other? (Seating arrangements which are rotations of each other are treated as the same.) | 23 | math-perturb | df4840f680fce405c9449008564574961c7f4df1 | math_perturb/math_perturb_simple.jsonl | 2130821d4235dc1f5d962bee7f84a096651bf98fcb17b6dcfd3d0a48875ba5bb | https://github.com/Kaffaljidhmah2/MATH-Perturb | calibration | Counting & Probability | Counting & Probability | simple |
251 | 260:simple | 8,709,621,588,000,338,000 | Level 5 | test | Find the number of integer values of $k$ in the closed interval $[-250,250]$ for which the equation $\log(kx)=2\log(x+2)$ has exactly one real solution. | 260 | math-perturb | df4840f680fce405c9449008564574961c7f4df1 | math_perturb/math_perturb_simple.jsonl | 2130821d4235dc1f5d962bee7f84a096651bf98fcb17b6dcfd3d0a48875ba5bb | https://github.com/Kaffaljidhmah2/MATH-Perturb | calibration | Intermediate Algebra | Intermediate Algebra | simple |
1.6800000000000002 | 726:simple | 1,652,235,417,434,122,200 | Level 5 | test | Bill walks $\frac{1}{2}$ mile south, then $\frac{3}{4}$ mile east, and finally $1$ mile south. How many miles is he, in a direct line, from his starting point? Express your answer as a decimal to the nearest hundredth. | 726 | math-perturb | df4840f680fce405c9449008564574961c7f4df1 | math_perturb/math_perturb_simple.jsonl | 2130821d4235dc1f5d962bee7f84a096651bf98fcb17b6dcfd3d0a48875ba5bb | https://github.com/Kaffaljidhmah2/MATH-Perturb | calibration | Prealgebra | Prealgebra | simple |
5 | 731:simple | 17,682,420,522,897,404,000 | Level 5 | test | A worker receives an annual wage of $\$20{,}000$, which he always deposits into a savings account at the end of the year. By the end of the third year (when he makes the third deposit), he wants to have at least $\$63,050$ in the account to finance the purchase of a house. What is the minimal compound interest rate tha... | 731 | math-perturb | df4840f680fce405c9449008564574961c7f4df1 | math_perturb/math_perturb_simple.jsonl | 2130821d4235dc1f5d962bee7f84a096651bf98fcb17b6dcfd3d0a48875ba5bb | https://github.com/Kaffaljidhmah2/MATH-Perturb | calibration | Algebra | Algebra | simple |
"4-2\\sqrt{2}" | 749:simple | 12,482,803,133,339,910,000 | Level 5 | train | In square $ABCD$, points $E$ and $H$ lie on $\overline{AB}$ and $\overline{DA}$, respectively, so that $AE=AH.$ Points $F$ and $G$ lie on $\overline{BC}$ and $\overline{CD}$, respectively, and points $I$ and $J$ lie on $\overline{EH}$ so that $\overline{FI} \perp \overline{EH}$ and $\overline{GJ} \perp \overline{EH}$. ... | 749 | math-perturb | df4840f680fce405c9449008564574961c7f4df1 | math_perturb/math_perturb_simple.jsonl | 2130821d4235dc1f5d962bee7f84a096651bf98fcb17b6dcfd3d0a48875ba5bb | https://github.com/Kaffaljidhmah2/MATH-Perturb | calibration | Geometry | Geometry | simple |
18 | 1958:simple | 11,069,928,362,238,080,000 | Level 5 | test | How many square units are in the region satisfying the inequalities $y \ge |x|$ and $y \le -|x|+6$? Express your answer as a decimal. | 1,958 | math-perturb | df4840f680fce405c9449008564574961c7f4df1 | math_perturb/math_perturb_simple.jsonl | 2130821d4235dc1f5d962bee7f84a096651bf98fcb17b6dcfd3d0a48875ba5bb | https://github.com/Kaffaljidhmah2/MATH-Perturb | calibration | Algebra | Algebra | simple |
176 | 1964:simple | 16,952,899,955,603,188,000 | Level 5 | train | Let $A = \{1, 2, 3, 4, 5, 6\}$, and let $N$ be the number of functions $f$ from set $A$ to set $A$ such that $f(f(x))$ is a constant function. Find the remainder when $N$ is divided by $1000$. | 1,964 | math-perturb | df4840f680fce405c9449008564574961c7f4df1 | math_perturb/math_perturb_simple.jsonl | 2130821d4235dc1f5d962bee7f84a096651bf98fcb17b6dcfd3d0a48875ba5bb | https://github.com/Kaffaljidhmah2/MATH-Perturb | calibration | Counting & Probability | Counting & Probability | simple |
"(-\\infty, -1) \\cup (-1, \\infty)" | 1992:simple | 9,202,727,360,503,980,000 | Level 5 | train | What is the range of the function $y = \frac{x^2 + 3x + 2}{x+2}$? (Express your answer using interval notation.) | 1,992 | math-perturb | df4840f680fce405c9449008564574961c7f4df1 | math_perturb/math_perturb_simple.jsonl | 2130821d4235dc1f5d962bee7f84a096651bf98fcb17b6dcfd3d0a48875ba5bb | https://github.com/Kaffaljidhmah2/MATH-Perturb | calibration | Algebra | Algebra | simple |
"\\frac{1232}{6561}" | 2007:simple | 3,682,216,980,027,533,000 | Level 5 | test | Pat wants to select 8 pieces of fruit to bring in the car for the people he's driving to Montana with. He randomly chooses each piece of fruit to be an orange, an apple, or a banana. What is the probability that either exactly 4 of the pieces of fruit are oranges or exactly 6 of the pieces of fruit are apples? | 2,007 | math-perturb | df4840f680fce405c9449008564574961c7f4df1 | math_perturb/math_perturb_simple.jsonl | 2130821d4235dc1f5d962bee7f84a096651bf98fcb17b6dcfd3d0a48875ba5bb | https://github.com/Kaffaljidhmah2/MATH-Perturb | calibration | Counting & Probability | Counting & Probability | simple |
"\\frac{7}{5}" | 2041:simple | 4,020,542,636,584,728,600 | Level 5 | test | What is the value of $x$ if $-\frac23(x-5) = (x+1)$? | 2,041 | math-perturb | df4840f680fce405c9449008564574961c7f4df1 | math_perturb/math_perturb_simple.jsonl | 2130821d4235dc1f5d962bee7f84a096651bf98fcb17b6dcfd3d0a48875ba5bb | https://github.com/Kaffaljidhmah2/MATH-Perturb | calibration | Prealgebra | Prealgebra | simple |
"4(3-2x)(3+2x)" | 2099:simple | 17,706,815,726,354,895,000 | Level 5 | train | Factor $36-16x^2$. | 2,099 | math-perturb | df4840f680fce405c9449008564574961c7f4df1 | math_perturb/math_perturb_simple.jsonl | 2130821d4235dc1f5d962bee7f84a096651bf98fcb17b6dcfd3d0a48875ba5bb | https://github.com/Kaffaljidhmah2/MATH-Perturb | calibration | Algebra | Algebra | simple |
"\\frac{7 \\sqrt{3}}{3}" | 2432:simple | 7,930,819,287,261,935,000 | Level 5 | train | Find the maximum value of
\[y = \tan \left( x + \frac{2 \pi}{3} \right) - \tan \left( x + \frac{\pi}{6} \right) + 2\cos \left( x + \frac{\pi}{6} \right)\]for $-\frac{5 \pi}{12} \le x \le -\frac{\pi}{3}.$ | 2,432 | math-perturb | df4840f680fce405c9449008564574961c7f4df1 | math_perturb/math_perturb_simple.jsonl | 2130821d4235dc1f5d962bee7f84a096651bf98fcb17b6dcfd3d0a48875ba5bb | https://github.com/Kaffaljidhmah2/MATH-Perturb | calibration | Precalculus | Precalculus | simple |
-1 | 2439:simple | 5,768,454,652,118,643,000 | Level 5 | train | Let $z = \cos \frac{2 \pi}{7} + i \sin \frac{2 \pi}{7}.$ Compute
\[\frac{z}{1 + z^2} + \frac{z^2}{1 + z^4} + \frac{z^3}{1 + z^6} + 1.\] | 2,439 | math-perturb | df4840f680fce405c9449008564574961c7f4df1 | math_perturb/math_perturb_simple.jsonl | 2130821d4235dc1f5d962bee7f84a096651bf98fcb17b6dcfd3d0a48875ba5bb | https://github.com/Kaffaljidhmah2/MATH-Perturb | calibration | Precalculus | Precalculus | simple |
"\\{-2\\} \\cup [0,6)" | 2680:simple | 16,295,377,957,535,975,000 | Level 5 | test | Solve
\[\frac{x(x + 2)^2}{x - 6} \le 0.\]Enter your answer using interval notation. | 2,680 | math-perturb | df4840f680fce405c9449008564574961c7f4df1 | math_perturb/math_perturb_simple.jsonl | 2130821d4235dc1f5d962bee7f84a096651bf98fcb17b6dcfd3d0a48875ba5bb | https://github.com/Kaffaljidhmah2/MATH-Perturb | calibration | Intermediate Algebra | Intermediate Algebra | simple |
104 | 3165:simple | 15,302,710,227,545,813,000 | Level 5 | test | Determine the smallest non-negative integer $a$ that satisfies the congruences: \begin{align*} &a\equiv 2\pmod 3,\\ &a\equiv 4\pmod 5,\\ &a\equiv 6\pmod 7,\\ &a\equiv 5\pmod 9. \end{align*} | 3,165 | math-perturb | df4840f680fce405c9449008564574961c7f4df1 | math_perturb/math_perturb_simple.jsonl | 2130821d4235dc1f5d962bee7f84a096651bf98fcb17b6dcfd3d0a48875ba5bb | https://github.com/Kaffaljidhmah2/MATH-Perturb | calibration | Number Theory | Number Theory | simple |
0 | 3188:simple | 17,310,286,424,394,790,000 | Level 5 | train | Let $\omega$ be a complex number such that $\omega^5 = 1$ and $\omega \ne 1.$ Compute
\[\omega^{16} + \omega^{18} + \omega^{20} + \dots + \omega^{54}.\] | 3,188 | math-perturb | df4840f680fce405c9449008564574961c7f4df1 | math_perturb/math_perturb_simple.jsonl | 2130821d4235dc1f5d962bee7f84a096651bf98fcb17b6dcfd3d0a48875ba5bb | https://github.com/Kaffaljidhmah2/MATH-Perturb | calibration | Intermediate Algebra | Intermediate Algebra | simple |
36 | 1:hard | 946,911,833,822,010,100 | Level 5 | test | Below is a portion of the graph of a function, $y=h(x)$:
[asy]
import graph; size(8cm); real lsf=0.5; pen dps=linewidth(0.7)+fontsize(10); defaultpen(dps); pen ds=black; real xmin=-0.75,xmax=8.25,ymin=-1.25,ymax=10.25;
pen cqcqcq=rgb(0.75,0.75,0.75);
/*grid*/ pen gs=linewidth(0.7)+cqcqcq+linetype("2 2"); real gx=1,g... | 1 | math-perturb | df4840f680fce405c9449008564574961c7f4df1 | math_perturb/math_perturb_hard.jsonl | 418ca51e02f3b639a919dda72b5201ce35ac6c6d7d31c3231735beb4ea012dd7 | https://github.com/Kaffaljidhmah2/MATH-Perturb | full | Algebra | Algebra | hard |
0 | 2:hard | 14,343,020,606,387,870,000 | Level 5 | train | Let $A$ be a point on the circle $x^2 + y^2 - 12x + 16 = 0,$ and let $B$ be a point on the parabola $y^2 = 4x.$ Find the smallest possible distance $AB.$ | 2 | math-perturb | df4840f680fce405c9449008564574961c7f4df1 | math_perturb/math_perturb_hard.jsonl | 418ca51e02f3b639a919dda72b5201ce35ac6c6d7d31c3231735beb4ea012dd7 | https://github.com/Kaffaljidhmah2/MATH-Perturb | full | Intermediate Algebra | Intermediate Algebra | hard |
52 | 3:hard | 3,497,551,728,562,768,400 | Level 5 | train | The volume of the parallelepiped determined by the three-dimensional vectors $\mathbf{a}$, $\mathbf{b}$, and $\mathbf{c}$ is 4. Find the volume of the parallelepiped determined by the vectors $\mathbf{a} + \mathbf{b} + \mathbf{c},$ $\mathbf{b} + 3 \mathbf{c},$ and $\mathbf{c} - 7 \mathbf{a}.$ | 3 | math-perturb | df4840f680fce405c9449008564574961c7f4df1 | math_perturb/math_perturb_hard.jsonl | 418ca51e02f3b639a919dda72b5201ce35ac6c6d7d31c3231735beb4ea012dd7 | https://github.com/Kaffaljidhmah2/MATH-Perturb | full | Precalculus | Precalculus | hard |
"0 or 4" | 5:hard | 14,114,920,179,565,263,000 | Level 5 | test | If the parabola $y_1 = x^2 + 2x + 7$ and the line $y_2 = bx + 6$ intersect at only one point, what is the value of $b$? | 5 | math-perturb | df4840f680fce405c9449008564574961c7f4df1 | math_perturb/math_perturb_hard.jsonl | 418ca51e02f3b639a919dda72b5201ce35ac6c6d7d31c3231735beb4ea012dd7 | https://github.com/Kaffaljidhmah2/MATH-Perturb | full | Algebra | Algebra | hard |
"11\\sqrt{3}/2" | 6:hard | 2,671,688,557,340,235,000 | Level 5 | test | Find the area of an equiangular hexagon with side lengths 1,2,3,1,2,3 in that order. | 6 | math-perturb | df4840f680fce405c9449008564574961c7f4df1 | math_perturb/math_perturb_hard.jsonl | 418ca51e02f3b639a919dda72b5201ce35ac6c6d7d31c3231735beb4ea012dd7 | https://github.com/Kaffaljidhmah2/MATH-Perturb | full | Geometry | Geometry | hard |
35 | 8:hard | 12,207,079,882,829,290,000 | Level 5 | train | 23 people attend a party. Each person shakes hands with at least three other people. What is the minimum possible number of handshakes? | 8 | math-perturb | df4840f680fce405c9449008564574961c7f4df1 | math_perturb/math_perturb_hard.jsonl | 418ca51e02f3b639a919dda72b5201ce35ac6c6d7d31c3231735beb4ea012dd7 | https://github.com/Kaffaljidhmah2/MATH-Perturb | full | Counting & Probability | Counting & Probability | hard |
48 | 9:hard | 16,114,938,629,197,572,000 | Level 5 | test | A number is tripled, then decreased by $13.7$. The result is greater than $125.28$. What is the smallest even integer that satisfies this condition? | 9 | math-perturb | df4840f680fce405c9449008564574961c7f4df1 | math_perturb/math_perturb_hard.jsonl | 418ca51e02f3b639a919dda72b5201ce35ac6c6d7d31c3231735beb4ea012dd7 | https://github.com/Kaffaljidhmah2/MATH-Perturb | full | Prealgebra | Prealgebra | hard |
5 | 12:hard | 3,072,226,485,132,058,000 | Level 5 | test | Find the smallest positive integer $n$ such that $$ 617n \equiv 943 \pmod{18}. $$ | 12 | math-perturb | df4840f680fce405c9449008564574961c7f4df1 | math_perturb/math_perturb_hard.jsonl | 418ca51e02f3b639a919dda72b5201ce35ac6c6d7d31c3231735beb4ea012dd7 | https://github.com/Kaffaljidhmah2/MATH-Perturb | full | Number Theory | Number Theory | hard |
72.8 | 13:hard | 8,339,483,311,491,676,000 | Level 5 | train | In order to compute the volume of a particular cone, Juan first measures the length of the perimeter of its base, and then measures the height of the cone. Juan's measurement has an error of up to $20\%$. What is the largest possible percent error, in percent, in Juan's computed volume of the cone? | 13 | math-perturb | df4840f680fce405c9449008564574961c7f4df1 | math_perturb/math_perturb_hard.jsonl | 418ca51e02f3b639a919dda72b5201ce35ac6c6d7d31c3231735beb4ea012dd7 | https://github.com/Kaffaljidhmah2/MATH-Perturb | full | Prealgebra | Prealgebra | hard |
24500 | 14:hard | 16,992,760,041,179,402,000 | Level 5 | train | Two arithmetic sequences $A$ and $B$ both begin with 30 and have common differences of absolute value 10, with sequence $A$ increasing and sequence $B$ decreasing. What is the absolute value of the difference between the sum of the first 50 term of sequence $A$ and the sum of the first 50 term of sequence $B$? | 14 | math-perturb | df4840f680fce405c9449008564574961c7f4df1 | math_perturb/math_perturb_hard.jsonl | 418ca51e02f3b639a919dda72b5201ce35ac6c6d7d31c3231735beb4ea012dd7 | https://github.com/Kaffaljidhmah2/MATH-Perturb | full | Algebra | Algebra | hard |
79 | 17:hard | 4,383,082,206,941,614,000 | Level 5 | train | Line segment $\overline{AB}$ is a radius of a circle with $AB = 15$. Point $C$, not equal to $A$ or $B$, lies on the circle. As point $C$ moves around the circle, the centroid (center of mass) of $\triangle ABC$ traces out a closed curve missing two points. To the nearest positive integer, what is the area of the regio... | 17 | math-perturb | df4840f680fce405c9449008564574961c7f4df1 | math_perturb/math_perturb_hard.jsonl | 418ca51e02f3b639a919dda72b5201ce35ac6c6d7d31c3231735beb4ea012dd7 | https://github.com/Kaffaljidhmah2/MATH-Perturb | full | Geometry | Geometry | hard |
"5^{2/3}" | 18:hard | 11,001,739,947,703,687,000 | Level 5 | train | Find the smallest solution to the equation \[\lfloor x^3 \rfloor - \lfloor x \rfloor^3 = 17.\] | 18 | math-perturb | df4840f680fce405c9449008564574961c7f4df1 | math_perturb/math_perturb_hard.jsonl | 418ca51e02f3b639a919dda72b5201ce35ac6c6d7d31c3231735beb4ea012dd7 | https://github.com/Kaffaljidhmah2/MATH-Perturb | full | Intermediate Algebra | Intermediate Algebra | hard |
22878 | 19:hard | 13,618,336,854,934,274,000 | Level 5 | train | What is the sum of all the three-digit positive integers that contains at least two $9$? | 19 | math-perturb | df4840f680fce405c9449008564574961c7f4df1 | math_perturb/math_perturb_hard.jsonl | 418ca51e02f3b639a919dda72b5201ce35ac6c6d7d31c3231735beb4ea012dd7 | https://github.com/Kaffaljidhmah2/MATH-Perturb | full | Algebra | Algebra | hard |
"4\\pi-8" | 20:hard | 5,188,374,347,733,637,000 | Level 5 | train | What is the area of the circle defined by $x^2-6x +y^2-14y +42=0$ that lies above the line $y=7+2\sqrt{2}$? | 20 | math-perturb | df4840f680fce405c9449008564574961c7f4df1 | math_perturb/math_perturb_hard.jsonl | 418ca51e02f3b639a919dda72b5201ce35ac6c6d7d31c3231735beb4ea012dd7 | https://github.com/Kaffaljidhmah2/MATH-Perturb | full | Algebra | Algebra | hard |
"3\\sqrt{3}/4" | 22:hard | 363,833,246,297,605,100 | Level 5 | train | Find the maximum value of \[\sin \theta \cdot (1 + \cos \theta)\]for $0 < \theta < \pi.$ | 22 | math-perturb | df4840f680fce405c9449008564574961c7f4df1 | math_perturb/math_perturb_hard.jsonl | 418ca51e02f3b639a919dda72b5201ce35ac6c6d7d31c3231735beb4ea012dd7 | https://github.com/Kaffaljidhmah2/MATH-Perturb | full | Precalculus | Precalculus | hard |
"\\emptyset" | 242:hard | 12,391,813,268,182,380,000 | Level 5 | train | For what values of $j$ does the equation $(2x+7)(x-5) = -43 + jx^3$ have triple real roots? Express your answer as a list of numbers, separated by commas. | 242 | math-perturb | df4840f680fce405c9449008564574961c7f4df1 | math_perturb/math_perturb_hard.jsonl | 418ca51e02f3b639a919dda72b5201ce35ac6c6d7d31c3231735beb4ea012dd7 | https://github.com/Kaffaljidhmah2/MATH-Perturb | full | Algebra | Algebra | hard |
0 | 243:hard | 13,219,421,660,870,312,000 | Level 5 | test | Let $(a_1,b_1),$ $(a_2,b_2),$ $\dots,$ $(a_n,b_n)$ be the ordered pairs $(a,b)$ of real numbers such that the polynomial \[p(x) = ((x-a)^2 + 2ax + b)^2 +2a((x-a)^2 + 2ax + b) - b\] has exactly one real root and no nonreal complex roots. Find $a_1 + b_1 + a_2 + b_2 + \dots + a_n + b_n.$ | 243 | math-perturb | df4840f680fce405c9449008564574961c7f4df1 | math_perturb/math_perturb_hard.jsonl | 418ca51e02f3b639a919dda72b5201ce35ac6c6d7d31c3231735beb4ea012dd7 | https://github.com/Kaffaljidhmah2/MATH-Perturb | full | Intermediate Algebra | Intermediate Algebra | hard |
"\\sqrt{2}-1" | 245:hard | 11,172,474,800,445,583,000 | Level 5 | train | Let $S$ be the set of all real values of $x$ with $0 < x < \frac{\pi}{4}$ such that $\sin x$, $\cos x$, and $\tan x$ form the side lengths (in some order) of a right triangle. Compute the sum of $\tan^2 x$ over all $x$ in $S$. | 245 | math-perturb | df4840f680fce405c9449008564574961c7f4df1 | math_perturb/math_perturb_hard.jsonl | 418ca51e02f3b639a919dda72b5201ce35ac6c6d7d31c3231735beb4ea012dd7 | https://github.com/Kaffaljidhmah2/MATH-Perturb | full | Precalculus | Precalculus | hard |
"2\\times(2^n-2)/3+1" | 246:hard | 6,680,821,030,536,222,000 | Level 5 | test | For any $n\geq 1$ and $n$ is an odd number, there is a polynomial $P$ such that for every real number $x$,
\[
x^{2^n} + x^{2^{n-1}} + 1 = (x^2 + x + 1) P(x).
\]When $P$ is written in standard polynomial form, how many of its coefficients are nonzero? | 246 | math-perturb | df4840f680fce405c9449008564574961c7f4df1 | math_perturb/math_perturb_hard.jsonl | 418ca51e02f3b639a919dda72b5201ce35ac6c6d7d31c3231735beb4ea012dd7 | https://github.com/Kaffaljidhmah2/MATH-Perturb | full | Intermediate Algebra | Intermediate Algebra | hard |
45 | 247:hard | 1,460,286,389,765,687,600 | Level 5 | test | Find the degree measure of the least positive angle $\theta$ for which \[\tan \theta = \frac{\cos 5^\circ \cos 20^\circ \sin 85^\circ+ \cos 35^\circ \cos 50^\circ \sin 25^\cric - \sin 5^\circ \sin 20^\circ\sin 85^\circ - \sin 35^\circ \sin 50^\circ \sin 25^\cric}{\sin 5^\circ \cos 20^\circ \cos85^\cric+ \sin 35^\circ \... | 247 | math-perturb | df4840f680fce405c9449008564574961c7f4df1 | math_perturb/math_perturb_hard.jsonl | 418ca51e02f3b639a919dda72b5201ce35ac6c6d7d31c3231735beb4ea012dd7 | https://github.com/Kaffaljidhmah2/MATH-Perturb | full | Precalculus | Precalculus | hard |
4056 | 249:hard | 9,286,401,172,666,923,000 | Level 5 | train | Consider sequences that consist entirely of $A$'s, $B$'s and $C$'s and that have the property that every run of consecutive $A$'s has even length, every run of consecutive $C$'s has even length, and every run of consecutive $B$'s has odd length. Examples of such sequences are $AA$, $CC$, $AACC$, $B$, and $AABCC$, while... | 249 | math-perturb | df4840f680fce405c9449008564574961c7f4df1 | math_perturb/math_perturb_hard.jsonl | 418ca51e02f3b639a919dda72b5201ce35ac6c6d7d31c3231735beb4ea012dd7 | https://github.com/Kaffaljidhmah2/MATH-Perturb | full | Counting & Probability | Counting & Probability | hard |
240 | 250:hard | 6,858,936,163,838,733,000 | Level 5 | train | For how many integer values of $n$ between 1 and 240 inclusive does the decimal representation of $\frac{n^3-n}{240}$ terminate? | 250 | math-perturb | df4840f680fce405c9449008564574961c7f4df1 | math_perturb/math_perturb_hard.jsonl | 418ca51e02f3b639a919dda72b5201ce35ac6c6d7d31c3231735beb4ea012dd7 | https://github.com/Kaffaljidhmah2/MATH-Perturb | full | Number Theory | Number Theory | hard |
"(2^6) *( 3^4) * (5^2)" | 254:hard | 4,535,320,816,430,772,700 | Level 5 | train | Cindy wishes to arrange her coins into $X$ piles, each consisting of the same number of coins, $Y$. Each pile will have more than one coin and no pile will have all the coins. If there are 103 possible values for $Y$ given all of the restrictions, what is the smallest number of coins she could have? | 254 | math-perturb | df4840f680fce405c9449008564574961c7f4df1 | math_perturb/math_perturb_hard.jsonl | 418ca51e02f3b639a919dda72b5201ce35ac6c6d7d31c3231735beb4ea012dd7 | https://github.com/Kaffaljidhmah2/MATH-Perturb | full | Number Theory | Number Theory | hard |
10 | 256:hard | 2,875,361,463,932,612,600 | Level 5 | train | Kimberly borrows $1000$ dollars from Lucy, with an interest rate that starts at 5% per month but increases by 0.5% every month (i.e., 5% in the first month, 5.5% in the second month, and so on). What is the least integer number of months after which Kimberly will owe more than twice as much as she borrowed? | 256 | math-perturb | df4840f680fce405c9449008564574961c7f4df1 | math_perturb/math_perturb_hard.jsonl | 418ca51e02f3b639a919dda72b5201ce35ac6c6d7d31c3231735beb4ea012dd7 | https://github.com/Kaffaljidhmah2/MATH-Perturb | full | Algebra | Algebra | hard |
6 | 259:hard | 17,782,498,233,262,494,000 | Level 5 | train | The modified Lucas numbers $L_n$ are given by the recursion $L_0 = 2, L_1 = 1$, and $L_n = (L_{n-1} + L_{n-2}) (mod 10)$. $S_n=L_{L_n}$. Find the units digit of $S_{L_{100}}$. | 259 | math-perturb | df4840f680fce405c9449008564574961c7f4df1 | math_perturb/math_perturb_hard.jsonl | 418ca51e02f3b639a919dda72b5201ce35ac6c6d7d31c3231735beb4ea012dd7 | https://github.com/Kaffaljidhmah2/MATH-Perturb | full | Number Theory | Number Theory | hard |
891 | 262:hard | 7,676,219,578,648,829,000 | Level 5 | train | Two numbers 90 and m share exactly three divisors, and m is less than 900. What is the greatest value of m? | 262 | math-perturb | df4840f680fce405c9449008564574961c7f4df1 | math_perturb/math_perturb_hard.jsonl | 418ca51e02f3b639a919dda72b5201ce35ac6c6d7d31c3231735beb4ea012dd7 | https://github.com/Kaffaljidhmah2/MATH-Perturb | full | Number Theory | Number Theory | hard |
25 | 271:hard | 17,686,454,130,118,062,000 | Level 5 | train | Let $n=2^{30}3^{19}.$ Let m be the positive integer divisors of $n^2$ are less than $n$ but do not divide $n$. How many positive integer divisors of $m^2$ are less than $m$ but do not divide $m$? | 271 | math-perturb | df4840f680fce405c9449008564574961c7f4df1 | math_perturb/math_perturb_hard.jsonl | 418ca51e02f3b639a919dda72b5201ce35ac6c6d7d31c3231735beb4ea012dd7 | https://github.com/Kaffaljidhmah2/MATH-Perturb | full | Number Theory | Number Theory | hard |
9 | 282:hard | 5,548,077,985,567,026,000 | Level 5 | test | There are 36 cars in my building's parking lot. All of the cars are red, white or blue, and a car can have either 2 doors or 4 doors. 10 of them are red, 21 of them are 4-door, 6 of them are blue, and 8 of them are 2-door and white. How many of the cars are 4-door and but not white? | 282 | math-perturb | df4840f680fce405c9449008564574961c7f4df1 | math_perturb/math_perturb_hard.jsonl | 418ca51e02f3b639a919dda72b5201ce35ac6c6d7d31c3231735beb4ea012dd7 | https://github.com/Kaffaljidhmah2/MATH-Perturb | full | Prealgebra | Prealgebra | hard |
15 | 283:hard | 11,747,494,225,784,830,000 | Level 5 | train | Find the greatest integer value of $b$ for which the expression $\frac{9x^3+4x^2+11x+7}{bx^2+bx+4}$ has a domain of all real numbers. | 283 | math-perturb | df4840f680fce405c9449008564574961c7f4df1 | math_perturb/math_perturb_hard.jsonl | 418ca51e02f3b639a919dda72b5201ce35ac6c6d7d31c3231735beb4ea012dd7 | https://github.com/Kaffaljidhmah2/MATH-Perturb | full | Algebra | Algebra | hard |
-5 | 293:hard | 15,322,745,898,138,247,000 | Level 5 | test | Find the minimum value of $x^8 + y^4 - 8*\sqrt[8]{1/4}xy$ over all real numbers $x$ and $y.$ | 293 | math-perturb | df4840f680fce405c9449008564574961c7f4df1 | math_perturb/math_perturb_hard.jsonl | 418ca51e02f3b639a919dda72b5201ce35ac6c6d7d31c3231735beb4ea012dd7 | https://github.com/Kaffaljidhmah2/MATH-Perturb | full | Intermediate Algebra | Intermediate Algebra | hard |
223317 | 304:hard | 14,064,938,075,412,916,000 | Level 5 | train | A paperboy delivers newspapers to 20 houses along Main Street. Wishing to save effort, he doesn't always deliver to every house, but to avoid being fired he never misses three consecutive houses. Compute the number of ways the paperboy could deliver papers in this manner. | 304 | math-perturb | df4840f680fce405c9449008564574961c7f4df1 | math_perturb/math_perturb_hard.jsonl | 418ca51e02f3b639a919dda72b5201ce35ac6c6d7d31c3231735beb4ea012dd7 | https://github.com/Kaffaljidhmah2/MATH-Perturb | full | Counting & Probability | Counting & Probability | hard |
10 | 325:hard | 7,748,655,551,534,488,000 | Level 5 | train | What is the minimum value of $z$ if $z=y^4+x^2+6x-4y+22?$ | 325 | math-perturb | df4840f680fce405c9449008564574961c7f4df1 | math_perturb/math_perturb_hard.jsonl | 418ca51e02f3b639a919dda72b5201ce35ac6c6d7d31c3231735beb4ea012dd7 | https://github.com/Kaffaljidhmah2/MATH-Perturb | full | Algebra | Algebra | hard |
-1 | 340:hard | 14,849,432,497,759,429,000 | Level 5 | test | Let $\alpha,$ $\beta,$ $\gamma,$ and $\delta$ be the roots of \[x^4 + kx^2 + 90x - 2009 = 0.\]If $\alpha \beta = 49$. What is $\gamma+\delta$? | 340 | math-perturb | df4840f680fce405c9449008564574961c7f4df1 | math_perturb/math_perturb_hard.jsonl | 418ca51e02f3b639a919dda72b5201ce35ac6c6d7d31c3231735beb4ea012dd7 | https://github.com/Kaffaljidhmah2/MATH-Perturb | full | Intermediate Algebra | Intermediate Algebra | hard |
53 | 341:hard | 725,803,999,891,422,000 | Level 5 | train | Mr. Mendez awards extra credit on quizzes to his students with quiz grades that exceed the class mean. Given that 107 students take the same quiz, and suppose the grades of students follow exactly the normal distribution, what is the largest number of students who can be awarded extra credit? | 341 | math-perturb | df4840f680fce405c9449008564574961c7f4df1 | math_perturb/math_perturb_hard.jsonl | 418ca51e02f3b639a919dda72b5201ce35ac6c6d7d31c3231735beb4ea012dd7 | https://github.com/Kaffaljidhmah2/MATH-Perturb | full | Prealgebra | Prealgebra | hard |
-11 | 497:hard | 9,810,034,880,496,937,000 | Level 5 | train | Expand $-(3-c)(c^{2.3}+2.3(3-c))+0.2$. What is the sum of the coefficients of the expanded form? | 497 | math-perturb | df4840f680fce405c9449008564574961c7f4df1 | math_perturb/math_perturb_hard.jsonl | 418ca51e02f3b639a919dda72b5201ce35ac6c6d7d31c3231735beb4ea012dd7 | https://github.com/Kaffaljidhmah2/MATH-Perturb | full | Algebra | Algebra | hard |
1737 | 498:hard | 5,314,227,086,687,367,000 | Level 5 | train | The rules for a race require that all runners start at $A$, touch any part of the 1200-meter wall, then immediately run towards $B$ and finish at $B$. What is the number of meters in the maximum distance a participant must run? Express your answer to the nearest meter. [asy]
import olympiad; import geometry; size(250);... | 498 | math-perturb | df4840f680fce405c9449008564574961c7f4df1 | math_perturb/math_perturb_hard.jsonl | 418ca51e02f3b639a919dda72b5201ce35ac6c6d7d31c3231735beb4ea012dd7 | https://github.com/Kaffaljidhmah2/MATH-Perturb | full | Geometry | Geometry | hard |
14208 | 506:hard | 8,517,070,995,237,566,000 | Level 5 | test | The five-digit number $N = 14{,}A0B$ is divisible by 24. Given that $A$ and $B$ are nonzero digits, what is the smallest possible value of $N$? | 506 | math-perturb | df4840f680fce405c9449008564574961c7f4df1 | math_perturb/math_perturb_hard.jsonl | 418ca51e02f3b639a919dda72b5201ce35ac6c6d7d31c3231735beb4ea012dd7 | https://github.com/Kaffaljidhmah2/MATH-Perturb | full | Prealgebra | Prealgebra | hard |
21 | 509:hard | 2,676,729,323,637,975,600 | Level 5 | train | Of the five points (3, 10), (6, 20), (12, 35), (18, 40) and (20, 50), what is the sum of the $x$-coordinates of the points that lie to the right of the line $y = 2x + 7$ in the coordinate plane? | 509 | math-perturb | df4840f680fce405c9449008564574961c7f4df1 | math_perturb/math_perturb_hard.jsonl | 418ca51e02f3b639a919dda72b5201ce35ac6c6d7d31c3231735beb4ea012dd7 | https://github.com/Kaffaljidhmah2/MATH-Perturb | full | Algebra | Algebra | hard |
"2+\\log_5 4" | 513:hard | 7,511,266,132,194,039,000 | Level 5 | test | What is the value of $b$ if $5^b + 5^b + 5^b + 5^b = 25^{(b-1)}$? Express your answer as a common fraction. | 513 | math-perturb | df4840f680fce405c9449008564574961c7f4df1 | math_perturb/math_perturb_hard.jsonl | 418ca51e02f3b639a919dda72b5201ce35ac6c6d7d31c3231735beb4ea012dd7 | https://github.com/Kaffaljidhmah2/MATH-Perturb | full | Algebra | Algebra | hard |
2 | 528:hard | 13,521,879,932,098,302,000 | Level 5 | test | The product of all the prime numbers between -50 and 50 is equal to $P$. What is the remainder when $P$ is divided by 16? | 528 | math-perturb | df4840f680fce405c9449008564574961c7f4df1 | math_perturb/math_perturb_hard.jsonl | 418ca51e02f3b639a919dda72b5201ce35ac6c6d7d31c3231735beb4ea012dd7 | https://github.com/Kaffaljidhmah2/MATH-Perturb | full | Number Theory | Number Theory | hard |
"\\frac{7}{10}" | 552:hard | 7,750,634,931,722,450,000 | Level 5 | test | Spinner I is divided into four equal sections labeled 2, 3, 4 and 5. Spinner II is divided into five equal sections labeled 1, 3, 5, 7 and 9. If each spinner is spun and the resulting numbers are multiplied, what is the probability that the product is a two-digit number? Express your answer as a common fraction in simp... | 552 | math-perturb | df4840f680fce405c9449008564574961c7f4df1 | math_perturb/math_perturb_hard.jsonl | 418ca51e02f3b639a919dda72b5201ce35ac6c6d7d31c3231735beb4ea012dd7 | https://github.com/Kaffaljidhmah2/MATH-Perturb | full | Prealgebra | Prealgebra | hard |
"\\infty" | 554:hard | 13,676,020,170,582,036,000 | Level 5 | test | How many integers $n$ satisfy both of the inequalities $4n + 3 > 25$ and $-7n + 5 < 24$? | 554 | math-perturb | df4840f680fce405c9449008564574961c7f4df1 | math_perturb/math_perturb_hard.jsonl | 418ca51e02f3b639a919dda72b5201ce35ac6c6d7d31c3231735beb4ea012dd7 | https://github.com/Kaffaljidhmah2/MATH-Perturb | full | Prealgebra | Prealgebra | hard |
[
3,
5.399
] | 567:hard | 3,390,807,404,734,134,300 | Level 5 | test | If the function $j(x)$ is defined only on domain $[-1,2]$, and is defined on this domain by the formula $$j(x) = \frac{2x}{\sin x}+1,$$ then what is the range of $j(x)$? Express your answer as an interval or as a union of intervals. If your answer includes any decimal, round it to three decimal places. | 567 | math-perturb | df4840f680fce405c9449008564574961c7f4df1 | math_perturb/math_perturb_hard.jsonl | 418ca51e02f3b639a919dda72b5201ce35ac6c6d7d31c3231735beb4ea012dd7 | https://github.com/Kaffaljidhmah2/MATH-Perturb | full | Algebra | Algebra | hard |
1 | 569:hard | 4,000,715,868,881,079,000 | Level 5 | train | For how many integer values of $a$ does the equation $$x^2 + ax + 8a^2 = 0$$ have integer solutions for $x$? | 569 | math-perturb | df4840f680fce405c9449008564574961c7f4df1 | math_perturb/math_perturb_hard.jsonl | 418ca51e02f3b639a919dda72b5201ce35ac6c6d7d31c3231735beb4ea012dd7 | https://github.com/Kaffaljidhmah2/MATH-Perturb | full | Algebra | Algebra | hard |
"\\arctan \\frac{1}{1-\\tan \\frac{\\pi}{12}}" | 590:hard | 4,797,370,625,396,603,000 | Level 5 | train | Equilateral triangle $ABC$ and square $BCDE$ are coplanar, as shown. $F$ is the intersection of $BC$ and $AD$. What is the number of degrees in the measure of angle $FED$?
[asy]
size(70);
draw((0,0)--(20,0)--(20,20)--(0,20)--cycle);
draw((0,20)--(10,37.3)--(20,20));
draw((10,37.3)--(20,0));
draw((0,0)--(14.7,20));
lab... | 590 | math-perturb | df4840f680fce405c9449008564574961c7f4df1 | math_perturb/math_perturb_hard.jsonl | 418ca51e02f3b639a919dda72b5201ce35ac6c6d7d31c3231735beb4ea012dd7 | https://github.com/Kaffaljidhmah2/MATH-Perturb | full | Prealgebra | Prealgebra | hard |
"n+1" | 607:hard | 13,496,670,813,164,556,000 | Level 5 | train | For all positive integers $n$, the $n$th triangular number $T_n$ is defined as $T_n = 1+2+3+ \cdots + n$. What is the greatest possible value of the greatest common divisor of $4T_n$ and $n^2-1$? | 607 | math-perturb | df4840f680fce405c9449008564574961c7f4df1 | math_perturb/math_perturb_hard.jsonl | 418ca51e02f3b639a919dda72b5201ce35ac6c6d7d31c3231735beb4ea012dd7 | https://github.com/Kaffaljidhmah2/MATH-Perturb | full | Number Theory | Number Theory | hard |
2 | 626:hard | 16,314,768,614,203,064,000 | Level 5 | train | Let
\[x^7 + 10x^6 - 10x^5 - 99x^4 + x^3 + 1 = p(x) q(x),\]where $p(x)$ and $q(x)$ are monic, non-constant polynomials with integer coefficients. Find $p(-1) + q(-1).$ | 626 | math-perturb | df4840f680fce405c9449008564574961c7f4df1 | math_perturb/math_perturb_hard.jsonl | 418ca51e02f3b639a919dda72b5201ce35ac6c6d7d31c3231735beb4ea012dd7 | https://github.com/Kaffaljidhmah2/MATH-Perturb | full | Intermediate Algebra | Intermediate Algebra | hard |
"30^\\circ" | 636:hard | 5,467,747,758,469,492,000 | Level 5 | test | Find the smallest positive integer $x$ (measured in degrees) such that \[\tan (x - 160^{\circ}) = \frac{\sin50^{\circ}}{1 - 2\sin^2 25^{\circ}}.\] | 636 | math-perturb | df4840f680fce405c9449008564574961c7f4df1 | math_perturb/math_perturb_hard.jsonl | 418ca51e02f3b639a919dda72b5201ce35ac6c6d7d31c3231735beb4ea012dd7 | https://github.com/Kaffaljidhmah2/MATH-Perturb | full | Precalculus | Precalculus | hard |
"1-2^{n-3}" | 640:hard | 3,589,115,400,477,556,000 | Level 5 | train | Simplify: $\frac{2^{n+4} - 2(4^n)}{2(2^{n+3})}$. Express your answer as a common fraction. | 640 | math-perturb | df4840f680fce405c9449008564574961c7f4df1 | math_perturb/math_perturb_hard.jsonl | 418ca51e02f3b639a919dda72b5201ce35ac6c6d7d31c3231735beb4ea012dd7 | https://github.com/Kaffaljidhmah2/MATH-Perturb | full | Algebra | Algebra | hard |
24 | 728:hard | 8,045,214,856,967,304,000 | Level 5 | test | Given a isosceles triangle whose side lengths are all integer multiples of 8, how many units are in the smallest possible perimeter of such a triangle? | 728 | math-perturb | df4840f680fce405c9449008564574961c7f4df1 | math_perturb/math_perturb_hard.jsonl | 418ca51e02f3b639a919dda72b5201ce35ac6c6d7d31c3231735beb4ea012dd7 | https://github.com/Kaffaljidhmah2/MATH-Perturb | full | Prealgebra | Prealgebra | hard |
4356 | 729:hard | 16,332,337,200,367,294,000 | Level 5 | test | Let $S$ be the set of all integers $k$ such that, if $k$ is in $S$, then $\frac{17k}{66}$ is a terminating decimal and $\sqrt{k}+\frac{1}{k}$ is a rational number. What is the smallest integer in $S$ that is greater than 2010? | 729 | math-perturb | df4840f680fce405c9449008564574961c7f4df1 | math_perturb/math_perturb_hard.jsonl | 418ca51e02f3b639a919dda72b5201ce35ac6c6d7d31c3231735beb4ea012dd7 | https://github.com/Kaffaljidhmah2/MATH-Perturb | full | Number Theory | Number Theory | hard |
75 | 734:hard | 2,359,931,113,497,385,500 | Level 5 | test | Amy's grandmother gave her 3 chocolate chip cookies (2 identical ones and 1 smaller cookie) and 4 identical sugar cookies. In how many different orders can Amy eat the cookies such that either she eats a chocolate chip cookie first, she eats a chocolate chip cookie last, or both? | 734 | math-perturb | df4840f680fce405c9449008564574961c7f4df1 | math_perturb/math_perturb_hard.jsonl | 418ca51e02f3b639a919dda72b5201ce35ac6c6d7d31c3231735beb4ea012dd7 | https://github.com/Kaffaljidhmah2/MATH-Perturb | full | Counting & Probability | Counting & Probability | hard |
"3,\\!889,\\!620" | 737:hard | 12,077,420,129,646,821,000 | Level 5 | train | In the local frisbee league, teams have 7 members and each of the 4 teams takes turns hosting tournaments. At each tournament, each team selects two members of that team to be on the tournament committee, except the host team, which selects three members and one member of the three will be selected as the committee cha... | 737 | math-perturb | df4840f680fce405c9449008564574961c7f4df1 | math_perturb/math_perturb_hard.jsonl | 418ca51e02f3b639a919dda72b5201ce35ac6c6d7d31c3231735beb4ea012dd7 | https://github.com/Kaffaljidhmah2/MATH-Perturb | full | Counting & Probability | Counting & Probability | hard |
"3k^2 - k" | 741:hard | 13,173,153,736,804,508,000 | Level 5 | train | Compute the number of ordered pairs of integers $(x,y)$ with $1\le x<y\le 4k$ such that $i^x+i^y$ is a real number. Here $k$ is an integer. Represent the results in a standard polynomial of $k$. | 741 | math-perturb | df4840f680fce405c9449008564574961c7f4df1 | math_perturb/math_perturb_hard.jsonl | 418ca51e02f3b639a919dda72b5201ce35ac6c6d7d31c3231735beb4ea012dd7 | https://github.com/Kaffaljidhmah2/MATH-Perturb | full | Intermediate Algebra | Intermediate Algebra | hard |
336 | 743:hard | 13,280,962,828,948,531,000 | Level 5 | test | Our basketball team has 10 players. We need to divide into two teams with the difference of number of people in each team no bigger than 2. In how many ways can we do this? | 743 | math-perturb | df4840f680fce405c9449008564574961c7f4df1 | math_perturb/math_perturb_hard.jsonl | 418ca51e02f3b639a919dda72b5201ce35ac6c6d7d31c3231735beb4ea012dd7 | https://github.com/Kaffaljidhmah2/MATH-Perturb | full | Counting & Probability | Counting & Probability | hard |
"\\sqrt{2}/3" | 744:hard | 16,848,084,375,772,211,000 | Level 5 | train | Any 10 points are taken inside or on a square with side length $1$. Let a be the smallest possible number with the property that it is always possible to select one pair of points from these 10 such that the distance between them is equal to or less than $a$. Then $a$ is:
$\textbf{(A)}\ \sqrt{3}/3\qquad \textbf{(B)}\ \... | 744 | math-perturb | df4840f680fce405c9449008564574961c7f4df1 | math_perturb/math_perturb_hard.jsonl | 418ca51e02f3b639a919dda72b5201ce35ac6c6d7d31c3231735beb4ea012dd7 | https://github.com/Kaffaljidhmah2/MATH-Perturb | full | Geometry | Geometry | hard |
10 | 750:hard | 3,501,717,234,784,486,000 | Level 5 | train | If $\left\lfloor n^2/9 \right\rfloor - \lfloor n/3 \rfloor^2 = 2$, then find the smallest integer values of $n$. | 750 | math-perturb | df4840f680fce405c9449008564574961c7f4df1 | math_perturb/math_perturb_hard.jsonl | 418ca51e02f3b639a919dda72b5201ce35ac6c6d7d31c3231735beb4ea012dd7 | https://github.com/Kaffaljidhmah2/MATH-Perturb | full | Algebra | Algebra | hard |
"-\\infty" | 751:hard | 14,315,493,819,159,032,000 | Level 5 | test | Let $x$ and $y$ be real numbers such that $x + y = 1.$ Find the minimum value of
\[x^4 y + xy^4.\] | 751 | math-perturb | df4840f680fce405c9449008564574961c7f4df1 | math_perturb/math_perturb_hard.jsonl | 418ca51e02f3b639a919dda72b5201ce35ac6c6d7d31c3231735beb4ea012dd7 | https://github.com/Kaffaljidhmah2/MATH-Perturb | full | Intermediate Algebra | Intermediate Algebra | hard |
"-\\frac{1168}{15625}+\\frac{2576}{15625}i" | 760:hard | 11,800,924,348,197,319,000 | Level 5 | train | Simplify the cubic of $\displaystyle\frac{2+2i}{4i-3}$. Express your answer as a complex number in the form $a+bi$, where $a$ and $b$ are real numbers. | 760 | math-perturb | df4840f680fce405c9449008564574961c7f4df1 | math_perturb/math_perturb_hard.jsonl | 418ca51e02f3b639a919dda72b5201ce35ac6c6d7d31c3231735beb4ea012dd7 | https://github.com/Kaffaljidhmah2/MATH-Perturb | full | Algebra | Algebra | hard |
135036 | 763:hard | 11,294,000,492,172,569,000 | Level 5 | test | A committee is to be made up from a group of 12 candidates. The committee must consist of a chairman, a vice chairman and at least one members-at-large. How many ways can the committee be chosen? | 763 | math-perturb | df4840f680fce405c9449008564574961c7f4df1 | math_perturb/math_perturb_hard.jsonl | 418ca51e02f3b639a919dda72b5201ce35ac6c6d7d31c3231735beb4ea012dd7 | https://github.com/Kaffaljidhmah2/MATH-Perturb | full | Counting & Probability | Counting & Probability | hard |
216 | 765:hard | 2,725,125,806,262,967,000 | Level 5 | test | The longest distance from the circle $x^2 + y^2 = 2x$ to the point $(4,4)$ can be written in the form $\sqrt[3]{m}$, where $m$ is an integer. Find $m$. | 765 | math-perturb | df4840f680fce405c9449008564574961c7f4df1 | math_perturb/math_perturb_hard.jsonl | 418ca51e02f3b639a919dda72b5201ce35ac6c6d7d31c3231735beb4ea012dd7 | https://github.com/Kaffaljidhmah2/MATH-Perturb | full | Algebra | Algebra | hard |
165 | 794:hard | 5,096,118,295,801,779,000 | Level 5 | test | How many ways are there to put 8 balls in 4 boxes if the boxes are distinguishable but balls are not? | 794 | math-perturb | df4840f680fce405c9449008564574961c7f4df1 | math_perturb/math_perturb_hard.jsonl | 418ca51e02f3b639a919dda72b5201ce35ac6c6d7d31c3231735beb4ea012dd7 | https://github.com/Kaffaljidhmah2/MATH-Perturb | full | Counting & Probability | Counting & Probability | hard |
0 | 847:hard | 6,145,812,503,744,001,000 | Level 5 | train | What is the minimum value of the expression $5x^2+10y^2+12xy-6x+4y+13$ for real $x$ and $y$? | 847 | math-perturb | df4840f680fce405c9449008564574961c7f4df1 | math_perturb/math_perturb_hard.jsonl | 418ca51e02f3b639a919dda72b5201ce35ac6c6d7d31c3231735beb4ea012dd7 | https://github.com/Kaffaljidhmah2/MATH-Perturb | full | Algebra | Algebra | hard |
"-\\infty" | 965:hard | 10,351,854,522,162,715,000 | Level 5 | train | Let $x,$ $y,$ and $z$ be positive real numbers. Find the minimum value of
\[\frac{(x^2 - 3x + 1)(y^2 - 3y + 1)(z^2 - 3z + 1)}{xyz}.\] | 965 | math-perturb | df4840f680fce405c9449008564574961c7f4df1 | math_perturb/math_perturb_hard.jsonl | 418ca51e02f3b639a919dda72b5201ce35ac6c6d7d31c3231735beb4ea012dd7 | https://github.com/Kaffaljidhmah2/MATH-Perturb | full | Intermediate Algebra | Intermediate Algebra | hard |
End of preview.
Encoding-tax MATH-Perturb evaluation mirror
Unofficial study mirror; not an author release. Evaluation only, not training. Source: https://github.com/Kaffaljidhmah2/MATH-Perturb/tree/df4840f680fce405c9449008564574961c7f4df1 Paper: https://arxiv.org/abs/2502.06453 Hard is primary; Simple is paired. Public release does not establish contamination-free evaluation. Original fields are preserved. Family-disjoint allocations are study metadata.
Upstream notices (verbatim)
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README.md
MATH-Perturb: Benchmarking LLMs' Math Reasoning Abilities against Hard Perturbations
Evaluation code and dataset for the ICML 2025 paper MATH-Perturb: Benchmarking LLMs' Math Reasoning Abilities against Hard Perturbations.
For more details and the leaderboard, please refer to the project page here.
Dataset Usage
The MATH-P-Simple and MATH-P-Hard datasets are located in math_perturb/. Each testset is a jsonl file, where each line represents a test datapoint in json format. You can load the dataset with the following Python code:
dataset = [json.loads(line) for line in open(filepath)]
Keys:
problem_id: A unique random problem id assigned to each of the original problem. The modified problems sharing the sameproblem_idare perturbed from the same original problem.problem: Problem statement.answer: Ground-truth answer to the problem.level: The difficulty level that originates from MATH dataset. The field will be"Level 5"for all the entries.type: Category of the math problem, e.g., Algebra, Calculus, etc.original_split: The split (trainv.s.test) where the original problem belongs.
Note: Please do not use MATH-P-Simple or MATH-P-Hard as training data.
Evaluation
The evaluation script extracts the answers within \boxed{}, post-processes the potentially unformatted answer string, and then utlizes SymPy package to check the equivalence of two latex strings. Please read the README for details. The entry point is the answer_check method in evaluate.py. This can be adapted both in evaluation and in RL training.
def answer_check(problem, solution_str, ground_truth, dataset_type):
"""
Checks if the predicted answer matches the ground truth answer.
Args:
problem (str): The problem statement.
solution_str (str): The solution string containing the predicted answer.
ground_truth (str): The ground truth answer string.
dataset_type (str): The type of dataset, either 'perturb' or 'original'.
Returns:
is_correct (bool): True if the predicted answer matches the ground truth answer, False otherwise.
"""
License
Copyright 2025 MATH-Perturb Team
Licensed under the Apache License, Version 2.0 (the "License"); you may not use this file except in compliance with the License. You may obtain a copy of the License at
http://www.apache.org/licenses/LICENSE-2.0
Unless required by applicable law or agreed to in writing, software distributed under the License is distributed on an "AS IS" BASIS, WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. See the License for the specific language governing permissions and limitations under the License.
Legal Compliance
Intended Usage:
- The dataset is only for academic research purposes, and we do not seek to monetize or commercialize the problems & answers.
- The MATH-Perturb datasets (both MATH-P-Simple and MATH-P-Hard) are intended to be used as test datasets (benchmarks) to evaluate large language models.
- The datasets should not be used for training the models under any circumstance.
Transformative differences from MATH dataset (Hendrycks et al., 2021):
- We have transformed the problems from the original MATH dataset by making edits directly to the problem statements.
- For our two variants MATH-P-Simple and MATH-P-Hard, we have worked on the modified problems ourselves to get the correct answers. We only released the final answers without the intermediate steps.
- We have ensured that the answers to our perturbed problems are different from the answers to the corresponding original problems.
Citation
Please consider citing our paper if you find it useful.
@article{huang2025math,
title={{MATH-Perturb}: Benchmarking {LLMs}' Math Reasoning Abilities against Hard Perturbations},
author={Kaixuan Huang and Jiacheng Guo and Zihao Li and Xiang Ji and Jiawei Ge and Wenzhe Li and Yingqing Guo and Tianle Cai and Hui Yuan and Runzhe Wang and Yue Wu and Ming Yin and Shange Tang and Yangsibo Huang and Chi Jin and Xinyun Chen and Chiyuan Zhang and Mengdi Wang},
journal={arXiv preprint arXiv:2502.06453},
year={2025}
}
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