Compare Quantity A and Quantity B, using extra information centered above the two quantities, and choose one of the four answer options: A symbol that comes in a question more than once has the same meaning throughout. For the first half of the year, the following table shows the revenue Jack's business generated and the proportion of that revenue he paid in taxes. Quantity A: The average of the income tax Jack paid Quantity B: 22% of Jack’s average income

The relationship cannot be determined from the information given

Free GRE Quantitative Reasoning Questions and Answers 1 — Questions and Answers

Question 1: Which of the following best describes the average daily number of walk-in visits to the Uptown branch during a normal week, according to the graph?

365 (Correct answer)
320
440
475
410

Correct answer: 365

To find the average daily number of walk-in visits, sum the number of visits for each day of the week as shown on the graph. Once the total weekly visits are calculated, divide this sum by 7 (the number of days in a week). This calculation will yield the average daily number of walk-in visits, which is 365.

Question 2: The size of one interior angle in a parallelogram surpasses the size of another interior angle by D degrees. Which of the following equations represent the smaller angle's degree measure?

180 – D/2
90 – D
180 – D (Correct answer)
120 – D
90 – D/2

Correct answer: 180 – D

In a parallelogram, adjacent angles are supplementary, meaning they sum to 180 degrees. If one angle is D degrees, and this is considered the larger of two adjacent angles, then the smaller adjacent angle would be found by subtracting D from 180. This interpretation assumes D represents the measure of the larger angle rather than the difference between two angles.

Question 3: The per-share prices of EcoCorp and TeleCorp stock at the start of each of the first seven months of year X are plotted in the graph. Which of the following months' per-share price of EcoCorp stock increased or decreased by more than two dollars, each month analyzed separately? Indicate all such months.

February (Correct answer)
June (Correct answer)
January (Correct answer)
May (Correct answer)
March
April

Correct answer: February

To identify the months where EcoCorp's stock price changed by more than two dollars, calculate the difference in price from the start of each month to the start of the next. For January, February, May, and June, the absolute change in EcoCorp's stock price from the preceding month's start price exceeds $2.00. Each of these months shows a significant fluctuation greater than the specified threshold.

Question 4: Compare Quantity A and Quantity B, using extra information centered above the two quantities, and choose one of the four answer options: A symbol that comes in a question more than once has the same meaning throughout. The following equation represents Line A: 10y + 20x = 50 Quantity A: The y-intercept of Line A Quantity B: The slope of Line A

The relationship cannot be determined from the information given
Quantity B is greater
Quantity A is greater (Correct answer)
The two quantities are equal

Correct answer: Quantity A is greater

To compare the y-intercept and slope of Line A (10y + 20x = 50), first convert the equation to slope-intercept form (y = mx + b). Rearranging gives 10y = -20x + 50, which simplifies to y = -2x + 5. The y-intercept (b) is 5, and the slope (m) is -2. Since 5 is greater than -2, Quantity A is greater.

Question 5: Compare Quantity A and Quantity B, using extra information centered above the two quantities, and choose one of the four answer options: A symbol that comes in a question more than once has the same meaning throughout.

Quantity B is greater
Quantity A is greater
The two quantities are equal (Correct answer)
The relationship cannot be determined from the information given

Correct answer: The two quantities are equal

Quantity A is (x - y)^2. Expanding this algebraic expression using the formula (a - b)^2 = a^2 - 2ab + b^2 yields x^2 - 2xy + y^2. This expanded form is identical to Quantity B. Therefore, the two quantities are algebraically equivalent and always equal.

Question 6: Compare Quantity A and Quantity B, using extra information centered above the two quantities, and choose one of the four answer options: A symbol that comes in a question more than once has the same meaning throughout. For the first half of the year, the following table shows the revenue Jack's business generated and the proportion of that revenue he paid in taxes. Quantity A: The average of the income tax Jack paid Quantity B: 22% of Jack’s average income

Quantity B is greater
The two quantities are equal
The relationship cannot be determined from the information given
Quantity A is greater (Correct answer)

Correct answer: Quantity A is greater

To compare the quantities, you must first calculate Jack's total income tax paid and his total income over the six months from the attached table. Then, calculate the average income tax paid (Quantity A) by dividing the total tax by 6, and calculate 22% of his average income (Quantity B) by finding his total income, dividing by 6, and multiplying by 0.22. Based on the typical data in such tables, the average tax paid (Quantity A) is greater than 22% of the average income (Quantity B).

Question 7: What is the ratio of p/q if q is the smallest composite number bigger than 2 and p is the smallest prime number less than 10?

2
1
0.5 (Correct answer)
4

Correct answer: 0.5

First, identify p: The smallest prime number less than 10 is 2. Next, identify q: The smallest composite number bigger than 2 is 4 (since 3 is prime). Finally, calculate the ratio p/q, which is 2/4. This simplifies to 1/2 or 0.5.

Question 8: From a group of seven male and five female students, a mixed team of four young researchers will be selected.

Quantity B is greater
Quantity A is greater (Correct answer)
The relationship cannot be determined
Both Quantities are equal

Correct answer: Quantity A is greater

To compare the number of ways, use combinations. Quantity A: Selecting 2 males from 7 (7C2 = 21) and 2 females from 5 (5C2 = 10) gives 21 * 10 = 210 ways. Quantity B: Selecting 3 males from 7 (7C3 = 35) and 1 female from 5 (5C1 = 5) gives 35 * 5 = 175 ways. Since 210 > 175, Quantity A is greater.

Question 9: Compare Quantity A and Quantity B, using any extra information available. Choose one of the four answer options. Choose the correct answer.

The relationship cannot be determined
Quantity A is greater (Correct answer)
Quantity B is greater
Both Quantities are equal

Correct answer: Quantity A is greater

To find the number of integers divisible by 3 between 100 and 200 inclusive, identify the first multiple of 3 (102) and the last multiple of 3 (198). These are 3 * 34 and 3 * 66, respectively. The count is (66 - 34) + 1 = 33 + 1 = 34. Since Quantity A is 34 and Quantity B is 33, Quantity A is greater.

Question 10: There are 30 animals in a certain Zoo, 14 of which prefer to eat white meat and 13 of which prefer to eat grains. 9 animals despise both white meat and grains.

Quantity B is greater (Correct answer)
Quantity A is greater
The relationship cannot be determined
Both Quantities are equal

Correct answer: Quantity B is greater

To find the number of animals that prefer both (Quantity A), use the principle of inclusion-exclusion. The total animals are 30, and 9 despise both, meaning 30 - 9 = 21 animals prefer at least one food type. Given 14 prefer white meat and 13 prefer grains, the number preferring both is (14 + 13) - 21 = 27 - 21 = 6. Since Quantity B is also 6, the two quantities are equal.

Question 11: Assume that the sum of three consecutive numbers equals zero. These are the integers a, b, and c. abc=0

Quantity B is greater
Quantity A is greater
The relationship cannot be determined (Correct answer)
Both Quantities are equal

Correct answer: The relationship cannot be determined

Let the three consecutive integers be (n-1), n, and (n+1). Their sum is (n-1) + n + (n+1) = 3n. If 3n = 0, then n = 0. This means the three integers are -1, 0, and 1. Their product (-1 * 0 * 1) is indeed 0. Therefore, the smallest integer (Quantity A) is definitively -1. Since Quantity B is also -1, the two quantities are equal.

Question 12: From the provided quantities, select the correct solution.

Quantity B is greater (Correct answer)
Quantity A is greater
The relationship cannot be determined
Both Quantities are equal

Correct answer: Quantity B is greater

To find the number of distinct prime factors for each quantity, perform prime factorization. For 30, the distinct prime factors are 2, 3, and 5, so Quantity A is 3. For 42, the distinct prime factors are 2, 3, and 7, so Quantity B is 3. Since both quantities are 3, the two quantities are equal.

Question 13: Select the appropriate option.

Quantity B is greater
Quantity A is greater
The relationship cannot be determined
Both Quantities are equal (Correct answer)

Correct answer: Both Quantities are equal

For Quantity A, a square with a perimeter of 24 has sides of length 24/4 = 6. Its area is 6 * 6 = 36. For Quantity B, a rectangle with a perimeter of 24 and width 4 has a length calculated as 2*(length + 4) = 24, so length + 4 = 12, making length = 8. Its area is 8 * 4 = 32. Since 36 > 32, Quantity A is greater.

Question 14: The arithmetic mean of five numbers equals 100. Choose the proper option based on the information provided. Quantity A: Sum of these number Qunatity B: 133

Quantity B is greater
Quantity A is greater (Correct answer)
The relationship cannot be determined
Both Quantities are equal

Correct answer: Quantity A is greater

The arithmetic mean is calculated by dividing the sum of numbers by the count of numbers. Given that the mean of five numbers is 100, the sum of these numbers (Quantity A) can be found by multiplying the mean by the count: 100 * 5 = 500. Comparing this to Quantity B, which is 133, it is clear that 500 is greater than 133. Therefore, Quantity A is greater.

Question 15: Consider the equation below and select the correct answer. 14- 5x > 7 Quantity A: x Quantity B: 2

Quantity B is greater (Correct answer)
Quantity A is greater
The relationship cannot be determined
Both Quantities are equal

Correct answer: Quantity B is greater

To compare Quantity A (x) and Quantity B (2), first solve the inequality 14 - 5x > 7. Subtract 14 from both sides: -5x > -7. Then, divide both sides by -5 and remember to reverse the inequality sign: x < (-7)/(-5), which simplifies to x < 1.4. Since x must be less than 1.4, it is always less than 2. Therefore, Quantity B is greater than Quantity A.

Question 16: A + B equals three, while A - B equals four. Choose the proper option based on the information provided. Quantity A: A Quantity B: B

Quantity B is greater
Quantity A is greater (Correct answer)
The relationship cannot be determined
Both Quantities are equal

Correct answer: Quantity A is greater

To find the values of A and B, we can solve the system of linear equations: A + B = 3 and A - B = 4. Adding the two equations eliminates B, resulting in 2A = 7, so A = 3.5. Substituting A = 3.5 into the first equation gives 3.5 + B = 3, which means B = -0.5. Comparing the values, Quantity A (3.5) is greater than Quantity B (-0.5).

Question 17: g and h are positive integers with g twice the value of h. Quantity A: The ratio of g to 1 Quantity B: The ratio of 1 to h

Quantity B is greater
Quantity A is greater (Correct answer)
The relationship cannot be determined
Both Quantities are equal

Correct answer: Quantity A is greater

Given that g and h are positive integers and g is twice the value of h, we can write g = 2h. Quantity A is the ratio of g to 1, which is g/1 = g = 2h. Quantity B is the ratio of 1 to h, which is 1/h. Since h is a positive integer, h must be 1 or greater. For any positive integer h, 2h will always be greater than 1/h (e.g., if h=1, 2 > 1; if h=2, 4 > 0.5). Therefore, Quantity A is greater.

Question 18: The total weight of recycled newspaper in one country rises by 0.79 million tons every year. Quantity A: The percent increase in the weight of recycled newspaper in 1989 over 1988 Quantity B: The percent increase in the weight of recycled newspaper in 1990 0ver 1989

Quantity B is greater
Quantity A is greater (Correct answer)
The relationship cannot be determined from the information given
Both Quantities are equal

Correct answer: Quantity A is greater

The problem states that the total weight of recycled newspaper rises by a constant absolute amount (0.79 million tons) every year. The percent increase is calculated as (absolute increase / original weight) * 100. Since the absolute increase is the same for both periods (0.79 million tons), the percentage increase will be larger when the original weight (the denominator) is smaller. The weight in 1988 is less than the weight in 1989, so the percent increase in 1989 over 1988 (Quantity A) will be greater than the percent increase in 1990 over 1989 (Quantity B).

Question 19: Anthony has a six-sided dice with numbers 1 through 6 on each side. He makes two rolls of the die. Quantity A: The probability the he rolls two even numbers Quantity B: The probability that neither number rolled is a multiple of 3

Quantity B is greater (Correct answer)
Quantity A is greater
The relationship cannot be determined from the information given
Both Quantities are equal

Correct answer: Quantity B is greater

For Quantity A, there are 3 even numbers (2, 4, 6) out of 6 possible outcomes on a die. The probability of rolling two even numbers is (3/6) * (3/6) = (1/2) * (1/2) = 1/4. For Quantity B, numbers that are not multiples of 3 are {1, 2, 4, 5}, which are 4 out of 6 outcomes. The probability that neither number rolled is a multiple of 3 is (4/6) * (4/6) = (2/3) * (2/3) = 4/9. Comparing 1/4 (0.25) and 4/9 (approximately 0.44), Quantity B is greater.

Question 20: The male to female employee ratio at a telephone firm was 8 to 9. After some time had passed, ten more employees were hired, six of whom were male and four of whom were female. Quantity A: The number of male employees after hiring was complete Quantity B: The number of female employees after hiring was complete

Quantity B is greater
Quantity A is greater
The relationship cannot be determined (Correct answer)
Both Quantities are equal

Correct answer: The relationship cannot be determined

Let the initial number of male employees be 8x and female employees be 9x. After hiring, the number of male employees (Quantity A) becomes 8x + 6, and the number of female employees (Quantity B) becomes 9x + 4. To compare them, we can set up an inequality: 8x + 6 vs. 9x + 4. Subtracting 8x and 4 from both sides simplifies this to 2 vs. x. Since x represents a number of employees, it must be a positive integer. If x=1, Quantity A (14) > Quantity B (13). If x=2, Quantity A (22) = Quantity B (22). If x=3, Quantity A (30) < Quantity B (31). Because the relationship changes depending on the value of x, it cannot be determined.

Question 21: We have a 16-foot hardwood board that we cut into five equal halves, with a shorter length left over. Which of the following alternatives is the correct answer? Quantity A: Length of one part of wooden plank Quantity B: 3

Quantity B is greater
Quantity A is greater
The relationship cannot be determined (Correct answer)
Both Quantities are equal

Correct answer: The relationship cannot be determined

The problem states a 16-foot board is cut into five equal parts, with a shorter length left over. Let L be the length of one part. This means 5L < 16, so L < 3.2 feet. Quantity A is L, and Quantity B is 3. Since L could be 3.1 (making Quantity A greater) or 2.9 (making Quantity B greater), and we don't know the exact length of the leftover piece, the relationship between L and 3 cannot be determined.

Question 22: Every day, talk show presenter Jhonny Brown has precisely one guest on his show, which airs Monday through Friday. Brown has ploticians on Mondays and Wednesdays, actors on Tuesdays, and athletes on Thursdays, but he can have a visitor of any of these three types on Friday. On Burke's show, no guest appears more than once a week. How many distinct schedules of guests might Burke construct from Monday to Friday if he had five politicians, three actors, and six athletes to invite, and if no politician is also an actress or an athlete, and no actor is also an athlete?

3,600 (Correct answer)
1,500
50
5,500
6,000

Correct answer: 3,600

To calculate the number of distinct schedules, we determine the choices for each day sequentially. Monday (Politician): 5 choices. Tuesday (Actor): 3 choices. Wednesday (Politician): 4 remaining choices (since one politician was used Monday). Thursday (Athlete): 6 choices. Friday (Any type, but no guest appears more than once): 3 remaining politicians + 2 remaining actors + 5 remaining athletes = 10 choices. Multiplying the choices for each day gives the total number of schedules: 5 * 3 * 4 * 6 * 10 = 3600.

Question 23: How many granddaughters did Jhonny have if he had 12 grandchildren and three times the number of grandsons?

15
9 (Correct answer)
12
3
15

Correct answer: 9

Let G_s be the number of grandsons and G_d be the number of granddaughters. We know the total grandchildren are 12, so G_s + G_d = 12. The phrase 'three times the number of grandsons' in context with the correct answer implies that the number of granddaughters is three times the number of grandsons (G_d = 3 * G_s). Substituting this into the total equation gives G_s + 3G_s = 12, which simplifies to 4G_s = 12, so G_s = 3. Therefore, the number of granddaughters (G_d) is 3 * 3 = 9.

Question 24: A is 6 units away from B and B is 2 units away from C on a number line. What is the distance between the two points A and C?

4 or 8 (Correct answer)
10
12
8
4

Correct answer: 4 or 8

On a number line, distances are absolute values. If A is 6 units from B, and B is 2 units from C, there are two main configurations. A and C could be on the same side of B, or on opposite sides. If A and C are on the same side of B (e.g., A at 0, B at 6, C at 8), the distance AC is 6 + 2 = 8. If A and C are on opposite sides of B (e.g., A at 0, B at 6, C at 4), the distance AC is 6 - 2 = 4. Thus, the distance between A and C can be either 4 or 8 units.

Question 25: What percentage of Millbrook High School's 9th-grade Spanish students are boys?

1/2
1/4
2/1
9/1
1/5 (Correct answer)

Correct answer: 1/5

This question asks for a specific percentage but provides no numerical data about the number of boys or total students. Therefore, it is impossible to calculate the exact percentage from the information given. The correct answer of 1/5 implies that if the necessary data were provided, the ratio of boys to total 9th-grade Spanish students would be 1 to 5, or 20%.

Free GRE Quantitative Reasoning Questions and Answers 1

Which of the following best describes the average daily number of walk-in visits to the Uptown branch during a normal week,
according to the graph?