question_number int64 1 18 | question stringlengths 163 376 | options dict | content_domain stringclasses 5
values | skill stringlengths 11 77 | final_answer stringlengths 1 3 ⌀ | answer stringlengths 1.6k 4.67k | gen_ques stringlengths 148 2.18k | gen_ans stringlengths 1 4.86k | __index_level_0__ int64 0 16 |
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1 | The equation (9x + 5 = a(x + b)), where (a) and (b) are constants, has no solutions. Which of the following must be true?\n\nI. (a = 9)\nII. (b = 5)\nIII. (b \neq 0) | {
"A": "None",
"B": "I only",
"C": "I and II only",
"D": "I and III only"
} | Algebra | Linear equations in one variable | B | Okay, let's break this down step by step.
1. **Start with the given equation:**
`(9x + 5 = a(x + b))`
2. **Distribute the constant `a` on the right side:**
`9x + 5 = ax + ab`
3. **Rearrange the equation to group terms with `x` on one side and constant terms on the other:**
Subtract `ax` from both side... | The equation (k+2)x + 8 = 5x + m), where (k) and (m) are constants, has no solutions. Which of the following must be true?
I. (k = 3)
II. (m = 8)
III. (k + m
eq 11)
{'A': 'I only', 'B': 'II only', 'C': 'I and II only', 'D': 'I and III only'} | Okay, let's analyze the given equation and the conditions for having no solutions.
1. **Start with the given equation:**
`(k+2)x + 8 = 5x + m`
2. **Rearrange the equation to group terms with `x` on one side and constant terms on the other:**
Subtract `5x` from both sides:
`(k+2)x - 5x + 8 = m`
Subtr... | 0 |
2 | To earn money for college, Avery works two part-time jobs: A and B. She earns $10 per hour working at job A and $20 per hour working at job B. In one week, Avery earned a total of (s) dollars for working at job B. The graph above represents all possible combinations of the number of hours Avery could have worked at the... | {
"A": "128",
"B": "160",
"C": "200",
"D": "320"
} | Algebra | Linear equations in two variables | 320 | **1. Define Variables:**
Let *h_A* be the number of hours Avery worked at job A.
Let *h_B* be the number of hours Avery worked at job B.
Rate for job A = $10 per hour.
Rate for job B = $20 per hour.
**2. Interpret the Problem Statement and the Graph:**
The problem states that Avery earned *s* dollars from job B. It al... | Brian works two part-time jobs, Job X and Job Y. He earns $15 per hour working at Job X. In one week, Brian earned a total of $450 from both jobs. The graph represents all possible combinations of the number of hours Brian could have worked at Job X (horizontal axis) and Job Y (vertical axis) to earn a total of $450. P... | **1. Define Variables and Equation:**Let *h_X* be the number of hours worked at Job X and *h_Y* be the number of hours worked at Job Y.Let *r_X* be the hourly rate for Job X and *r_Y* be the hourly rate for Job Y.The total earnings, *T*, is given by the equation: *r_X* *h_X* + *r_Y* *h_Y* = *T*.**2. Use Given Informati... | 1 |
3 | An object hangs from a spring. l = 30 + 2*w. The formula relates the length (L), in centimeters, of the spring to the weight (W), in newtons, of the object. Which of the following describes the meaning of the 2 in this context? | {
"A": "The length, in centimeters, of the spring with no weight attached",
"B": "The weight, in newtons, of an object that will stretch the spring 30 centimeters",
"C": "The increase in the weight, in newtons, of the object for each one-centimeter increase in the length of the spring",
"D": "The increase in th... | Algebra | Linear functions | D | Okay, let's break down this problem step by step.
1. **Understand the Formula:** The formula given is L = 30 + 2*W.
* L represents the length of the spring in centimeters (cm).
* W represents the weight of the object in newtons (N).
* The formula describes a linear relationship between the weight at... | A science experiment tracks the temperature of a liquid substance as it is heated. The temperature, T, in degrees Celsius, after M minutes of heating is given by the equation T = 25 + 3M. Which of the following describes the meaning of the number 25 in this equation?
given options
{'A': 'The increase in temperature, i... | Okay, let's analyze the given equation and the meaning of its components.
1. **Understand the Formula:** The equation is T = 25 + 3M.
* T represents the temperature in degrees Celsius.
* M represents the number of minutes of heating.
* This is a linear equation relating temperature (T) to time (M).
... | 2 |
4 | Store A sells raspberries for $5.50 per pint and blackberries for $3.00 per pint. Store B sells raspberries for $6.50 per pint and blackberries for $8.00 per pint. A certain purchase of raspberries and blackberries would cost $37.00 at Store A or $66.00 at Store B. How many pints of blackberries are in this purchase? | {
"A": "4",
"B": "5",
"C": "8",
"D": "12"
} | Algebra | Systems of two linear equations in two variables | B | **1. Define Variables:**
Let `r` be the number of pints of raspberries purchased.
Let `b` be the number of pints of blackberries purchased.
**2. Set up Equations based on Store Costs:**
* **Store A:** The cost is $5.50 per pint of raspberries and $3.00 per pint of blackberries. The total cost is $37.00.
Equatio... | Store P sells notebooks for $4.50 each and pens for $2.50 each. Store Q sells notebooks for $5.00 each and pens for $3.50 each. A certain purchase of notebooks and pens would cost $52.00 at Store P or $65.00 at Store Q. How many notebooks are in this purchase?
given options
{'A': '6', 'B': '8', 'C': '10', 'D': '12'}
... | A | 3 |
5 | Ken is working this summer as part of a crew on a farm. He earned $8 per hour for the first 10 hours he worked this week. Because of his performance, his crew leader raised his salary to $10 per hour for the rest of the week. Ken saves 90% of his earnings from each week. What is the least number of hours he must work t... | {
"A": "38",
"B": "33",
"C": "22",
"D": "16"
} | Algebra | Linear inequalities in one or two variables | 'C' | Okay, let's break this problem down step by step.
1. **Calculate Ken's earnings for the first 10 hours:**
* Hourly rate = $8
* Hours worked = 10
* Earnings = Rate × Hours = $8/hour × 10 hours = $80
2. **Define the variable for the remaining hours:**
* Let 'h' be the number of hours Ken works... | Maria is working a summer job at a bookstore. She earns $12 per hour for the first 15 hours she works each week. Due to her excellent performance, her manager increases her wage to $15 per hour for any additional hours worked that week. Maria saves 80% of her total earnings each week. What is the minimum number of addi... | Okay, let's solve this problem step by step.
1. **Calculate Maria's earnings for the first 15 hours:**
* Hourly rate = $12
* Hours worked = 15
* Earnings = Rate × Hours = $12/hour × 15 hours = $180
2. **Define the variable for the additional hours:**
* Let 'x' be the number of additional hou... | 4 |
6 | In the expression below, (b) and (c) are positive integers. If the expression is equivalent to (x + b) and (x \neq b), which of the following could be the value of (c)?\n\n(x^2 - c)/(x - b) | {
"A": "4",
"B": "6",
"C": "8",
"D": "10"
} | Advanced Math | Equivalent expressions | 'A' | Okay, let's break this down step by step.
**1. Understand the Given Information:**
We are given the expression (x² - c) / (x - b).
We are told this expression is equivalent to (x + b).
We know that b and c are positive integers.
We are also given the condition x ≠ b (this prevents the denominator from being zero).
**... | In the expression below, $k$ and $m$ are positive integers. If the expression is equivalent to $x^2 + m$ (and $x^2 \neq m$), which of the following could be the value of $k$?
$\frac{x^4 - k}{x^2 - m}$
given options
{'A': '9', 'B': '12', 'C': '15', 'D': '18'} | Okay, let's break this down step by step.
**1. Understand the Given Information:**
We are given the expression $\frac{x^4 - k}{x^2 - m}$.
We are told this expression is equivalent to $x^2 + m$.
We know that $k$ and $m$ are positive integers.
We are also given the condition $x^2 \neq m$ (this prevents the denominator f... | 5 |
7 | Given the system of equations:\n[y = x^2 + 2x + 1] and [x + y + 1 = 0]. If (x₁, y₁) and (x₂, y₂) are the two solutions to the system, what is the value of y₁ + y₂? | {
"A": "-3",
"B": "-2",
"C": "-1",
"D": "1"
} | Algebra | Nonlinear equations in one variable and systems of equations in two variables | null | Okay, let's solve this system of equations step-by-step.
**1. Understand the Problem:**
We are given a system of two equations: one representing a parabola and the other representing a line. We need to find the points of intersection, (x₁, y₁) and (x₂, y₂), and then calculate the sum of their y-coordinates (y₁ + y₂).
... | Given the system of equations:
[y = x² - 2]
[y = 4x - 5]
If (x₁, y₁) and (x₂, y₂) are the two solutions to the system, what is the value of y₁ + y₂? | Okay, let's solve this system of equations step-by-step.
**1. Understand the Problem:**
We are given a system of two equations: one representing a parabola and the other representing a line. We need to find the points of intersection, (x₁, y₁) and (x₂, y₂), and then calculate the sum of their y-coordinates (y₁ + y₂).
... | 6 |
8 | The following table shows values of x and their corresponding values of f(x):\n| x | f(x) |\n|---|------|\n| 1 | a |\n| 2 | a^5 |\n| 3 | a^9 |\nGiven that f(k) = a^{29}, what is the value of k? | {
"A": "7",
"B": "8",
"C": "9",
"D": "10"
} | Algebra | Exponential function behavior and pattern recognition | 'B' | * **Step 1: Analyze the given data**
We are given a table showing the relationship between x and f(x):
* When x = 1, f(x) = a = a^1
* When x = 2, f(x) = a^5
* When x = 3, f(x) = a^9
* **Step 2: Identify the pattern in the exponents**
Let's look at the exponents of 'a' corresponding to the... | The following table shows values of x and their corresponding values of f(x):
| x | f(x) |
|---|------|
| 2 | a^7 |
| 4 | a^13 |
| 6 | a^19 |
Given that f(k) = a^37, what is the value of k?
(Assume a is a positive constant and a
eq 1)
options:
{
"A": "11",
"B": "12",
"C": "13",
"D": "14"
} | {
"B": "12"
} | 7 |
9 | Anita created a batch of green paint by mixing 2 ounces of blue paint with 3 ounces of yellow paint. She must mix a second batch using the same ratio of blue and yellow paint as the first batch. If she uses 5 ounces of blue paint for the second batch, how much yellow paint should Anita use? | {
"A": "Exactly 5 ounces",
"B": "3 ounces more than the amount of yellow paint used in the first batch",
"C": "1.5 times the amount of yellow paint used in the first batch",
"D": "1.5 times the amount of blue paint used in the second batch"
} | Problem-Solving and Data Analysis | Ratios, rates, proportional relationships, and units | 'D' | **1. Understand the Ratio:**
Anita's first batch used 2 ounces of blue paint and 3 ounces of yellow paint. The ratio of blue paint to yellow paint is 2:3. This can also be written as a fraction: (Amount of Blue Paint) / (Amount of Yellow Paint) = 2 / 3.
**2. Apply the Ratio to the Second Batch:**
The second batch must... | A metal alloy is created by mixing copper and zinc in a specific ratio. A small sample of the alloy contains 12 grams of copper and 8 grams of zinc. A company needs to produce a large batch of this alloy. If the large batch must contain a total of 150 grams of zinc and copper combined, how many grams of copper are need... | B | 8 |
10 | 37% of the items in a box are green. Of those, 37% are also rectangular. Of the green rectangular items, 42% are also metal. Which of the following is closest to the percentage of the items in the box that are not rectangular green metal items? | {
"A": "1.16%",
"B": "57.50%",
"C": "94.25%",
"D": "98.84%"
} | Problem-Solving and Data Analysis | Percentages | 'C' | Okay, let's break this down step by step.
1. **Find the percentage of items that are green:**
* Given: 37% of the items are green.
* Percentage (Green) = 37% = 0.37
2. **Find the percentage of items that are green AND rectangular:**
* We are told that 37% *of the green items* are also rectangular.... | In a large collection of objects, 40% are blue. Of the blue objects, 65% are square. Among the blue square objects, 30% are wooden. Which of the following is closest to the percentage of objects in the collection that are not blue square wooden objects?
A) 7.80%
B) 65.00%
C) 92.20%
D) 94.25% | Here is the step-by-step solution:
1. **Find the percentage of objects that are blue:**
* Given: 40% of the objects are blue.
* Percentage (Blue) = 40% = 0.40
2. **Find the percentage of objects that are blue AND square:**
* We are told that 65% *of the blue objects* are also square.
* So, w... | 9 |
11 | The mean amount of time that the 20 employees of a construction company have worked for the company is 6.7 years. After one of the employees leaves the company, the mean amount of time that the remaining employees have worked for the company is reduced to 6.25 years. How many years did the employee who left the company... | {
"A": "0.45",
"B": "2.30",
"C": "9.00",
"D": "15.25"
} | Problem-Solving and Data Analysis | One-variable data: distributions and measures of center and spread | null | Okay, let's break this down step by step.
1. **Understand the initial situation:**
* Number of employees = 20
* Mean years worked = 6.7 years
* The mean is calculated as (Total years worked by all employees) / (Number of employees).
* So, we can calculate the initial total years worked by all ... | A group of 25 students had a mean score of 80 on a test. After one more student joined the group and took the same test, the mean score for all 26 students was 81.5. What was the score of the student who joined the group?
$\(A)\ 39$
$\(B)\ 81.5$
$\(C)\ 117.5$
$\(D)\ 119$ | Here is the step-by-step solution:
1. **Calculate the initial total score:** The initial group had 25 students, and their mean score was 80. The total sum of scores for these 25 students is the mean multiplied by the number of students.
Total score (initial) = Mean score (initial) * Number of students (initial)
... | 10 |
13 | One of these participants will be selected at random. What is the probability of selecting a participant from Group A, given that the participant is at least 10 years of age?\n\nAge Group | Group A | Group B | Group C | Total\n---|---|---|---|---\n0–9 years | 7 | 6 | 17 | 30\n10–19 years | 14 | 4 | 12 | 30\n20+ years |... | {
"A": "23/60",
"B": "14/30",
"C": "14/60",
"D": "23/90"
} | Probability | Conditional probability | A | Okay, let's break this down step-by-step.
1. **Understand the Question:** We need to find the probability of selecting a participant from Group A *given that* we know the participant is at least 10 years old. This is a conditional probability problem.
2. **Identify the Condition:** The condition is that the partici... | A survey asked students about their preferred subject. The results are summarized in the table below.
Preferred Subject | 9th Grade | 10th Grade | 11th Grade | 12th Grade | Total
---|---|---|---|---|---
Math | 40 | 35 | 30 | 25 | 130
Science | 30 | 45 | 50 | 40 | 165
English | 25 | 20 | 15 | 10 | 70
History | 15 | 20 ... | Okay, let's break this down step-by-step.
1. **Understand the Question:** We need to find the probability of selecting a student who prefers Science, *given that* we know the student is in 10th grade or higher. This is a conditional probability problem.
2. **Identify the Condition:** The condition is that the stude... | 11 |
14 | Given two random samples of votes for a proposition: Sample A (52% in favor, ±4.2%) and Sample B (48% in favor, ±1.6%). Which of the following is the most appropriate reason that the margin of error for Sample A is greater than the margin of error for Sample B? | {
"A": "Sample A had a smaller number of votes that could not be recorded.",
"B": "Sample A had a higher percentage of favorable responses.",
"C": "Sample A had a larger sample size.",
"D": "Sample A had a smaller sample size."
} | Problem-Solving and Data Analysis | Understanding of statistical sampling and margin of error | 'D' | * **Understanding Margin of Error (MoE):** The margin of error in a statistical survey indicates the range within which the true population parameter (in this case, the true percentage of voters in favor) is likely to fall, based on the sample results. It quantifies the uncertainty due to random sampling.
* **Form... | Two polling organizations conducted surveys on public support for a proposed policy.
Poll 1 reported 60% support with a margin of error of \( \pm 3 \) percentage points.
Poll 2 reported 55% support with a margin of error of \( \pm 5 \) percentage points.
Assuming both polls used the same confidence level, which of t... | C | 12 |
15 | To determine the mean number of children per household in a community, Tabitha surveyed 20 families at a playground. For the 20 families surveyed, the mean number of children per household was 2.4. Which of the following statements must be true? | {
"A": "The mean number of children per household in the community is 2.4.",
"B": "A determination about the mean number of children per household in the community should not be made because the sample size is too small.",
"C": "The sampling method is flawed and may produce a biased estimate of the mean number of... | Problem-Solving and Data Analysis | Evaluating statistical claims: observational studies and experiments | C | **Step-by-step thinking:**
1. **Identify the Goal:** The goal is to estimate the mean number of children per household in a *community*.
2. **Identify the Population:** The population is all households in the community.
3. **Identify the Sample:** The sample consists of 20 families surveyed at a playground.
4. **I... | To estimate the average age of registered voters in a town, a researcher surveyed 50 people at a local college campus bookstore. The average age of the 50 people surveyed was 21 years. Which of the following statements must be true?
given options
{'A': 'The average age of registered voters in the town is approximately... | **Step-by-step thinking:**
1. **Identify the Goal:** The researcher wants to estimate the average age of registered voters in the *town*.
2. **Identify the Population:** The population is all registered voters in the town.
3. **Identify the Sample:** The sample consists of 50 people surveyed at a local college camp... | 13 |
18 | Triangle ABC is similar to triangle DEF, where A corresponds to D and C corresponds to F. Angles C and F are right angles. If tan(A) = \sqrt{3} and DF = 125, what is the length of DE? | {
"A": "125√3/3",
"B": "125√3/2",
"C": "125√3",
"D": "250"
} | Geometry and Trigonometry | Right triangles and trigonometry | 250 | Okay, let's break down the problem step-by-step.
1. **Understand Similarity:** We are given that triangle ABC is similar to triangle DEF (△ABC ~ △DEF). This means their corresponding angles are equal, and the ratios of their corresponding sides are equal. The correspondence is A ↔ D, B ↔ E, C ↔ F.
* So, ∠A = ∠D... | Triangle PQR is similar to triangle XYZ, where P corresponds to X and R corresponds to Z. Angles R and Z are right angles. If sin(P) = 1/2 and XY = 300, what is the length of XZ?
given options
{'A': '150', 'B': '150√3', 'C': '300√3', 'D': '300'} | Okay, let's break down the problem step-by-step.
1. **Understand Similarity:** Given that triangle PQR is similar to triangle XYZ (△PQR ~ △XYZ) with P corresponding to X, Q to Y, and R to Z. This means their corresponding angles are equal (∠P = ∠X, ∠Q = ∠Y, ∠R = ∠Z) and the ratios of their corresponding sides are equ... | 16 |
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