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GRE GRE Test Exam Questions
Graduate Record Examination Test: Verbal, Quantitative, Analytical Writing (Page 21 )

Updated On: 10-Mar-2026
Page 21 of 119
PDF with 793 Questions

In a group of 10 people, exactly 4 are vegetarians. A committee of 3 will be formed by randomly selecting 3 people from the group. How many of the possible 3-member committees would include exactly 2 vegetarian members?

  1. 3
  2. 5
  3. 15
  4. 24
  5. 36

Answer(s): E

Explanation:

Since there are 4 vegetarians, the number of ways to choose 2 vegetarians from these 4 is given by the combination formula:



Since there are 6 non-vegetarians, the number of ways to choose 1 non-vegetarian from these 6 is:



Since we choose 2 vegetarians and 1 non-vegetarian, the total number of possible committees is:
6 × 6 = 36



A survey of 500 households found that 450 households had a microwave oven, 300 had a food processor, and 150 had a trash compactor. Each of the 500 households had at least one of the appliances, and more than 100 households had all three appliances.
Which of the following could be the number of households that had a food processor and a trash compactor but no microwave oven? (Choose all that apply.)

  1. 5
  2. 35
  3. 50
  4. 65
  5. 100

Answer(s): A,B,C,D,E

Explanation:

Let:
M be the number of households with a microwave.

F be the number of households with a food processor.

T be the number of households with a trash compactor.

x be the number of households that have all three appliances. We know that x > 100.

Total households = |M| + |F| + |T| - (Households with exactly two appliances) - 2x.
500 = 450 + 300 + 150 - (Households with exactly two appliances) - 2x.
500 = 900 - (Households with exactly two appliances) - 2x.
Households with exactly two appliances + 2x = 400.
The households with exactly two appliances consist of:
Households with a microwave and a food processor only.

Households with a microwave and a trash compactor only.

Households with a food processor and a trash compactor only, which we denote as y.

Since we know that the total of all these must be 400 - 2x, we solve:
y 400 - 2(100), since x > 100.
y 200.
Now we check the answer choices: 5, 35, 50, 65, and 100. Since all these values are less than or equal to 200, they are all valid possibilities.



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A square plot of land has the same perimeter as a rectangular plot of land that measures 25 meters by 35 meters. If both plots of land are level, what is the area of the square plot of land? (Enter your answer as an integer or a decimal in the answer box. Backspace to erase.)

  1. 900

Answer(s): A

Explanation:

The perimeter P of a rectangle is given by the formula:

P = 2 × (length + width)

For the rectangular plot, the length is 25 meters and the width is 35 meters. So, the perimeter of the rectangular plot is:

P = 2 × (25 + 35) = 2 × 60 = 120 meters

The perimeter of the square is the same as the perimeter of the rectangular plot, which is 120 meters. The perimeter of a square is given by:

P = 4 × side length

Let the side length of the square be s. Since the perimeter is 120 meters, we have:

4 × s = 120



The area A of a square is given by:

A = s2

A = 302 = 900 square meters



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An apple falls straight to the ground from a tree branch 8 meters above the ground. The apple's height above the ground, t seconds after it starts falling, is H meters, where H = 8 - 4.9t2 and t 0. How many seconds after the apple starts falling does it hit the ground?

Give your answer to the nearest 0.1 second. (Enter your answer as an integer or a decimal in the answer box.
Backspace to erase.)

  1. 1.3

Answer(s): A

Explanation:

H = 8 - 4.9t2, where t is the number of seconds after the apple starts falling.

The apple hits the ground when H = 0, so we set up the equation:

8 - 4.9t2 = 0
4.9t2 = 8



t 1.28

Rounding 1.28 to the nearest 0.1, we get 1.3 seconds.



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A lecture hall has 15 rows of seats. There are n - 2 seats in the first row and n seats in each of the other rows. If there are no other seats in the lecture hall and the total number of seats in the lecture hall is between 180 and 200, what is the total number of seats in the lecture hall? (Enter your answer as an integer or a decimal in the answer box. Backspace to erase.)

  1. 193

Answer(s): A

Explanation:

The lecture hall has 15 rows of seats.

The first row has n - 2 seats.

Each of the other 14 rows has n seats.

The total number of seats, T, can be calculated as:

T = (n - 2) + 14n
T = (n - 2) + 14n = 15n - 2

We are told that the total number of seats, T, is between 180 and 200:

180 < 15n - 2 < 200
182 < 15n < 202



12.13 < n < 13.47

Since n must be an integer, the only possible value for n is 13.

Substitute n = 13 into the equation for the total number of seats:

T = 15(13) - 2 = 195 - 2 = 193



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