Free practice questions/GRE General Test

GRE General Test — Data Analysis

36 free practice questions with full explanations.

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Question 1

A survey of 150 students found that 90 take Spanish and 60 take French, with 25 taking both. How many students take neither language?

A) 15
B) 20
C) 25
D) 30
E) 35

Show answer & explanation

Correct answer: C) 25

By inclusion-exclusion, students taking at least one language = 90 + 60 - 25 = 125. Students taking neither = 150 - 125 = 25.

Question 2

A committee of 3 people is to be chosen from a group of 8 candidates. How many different committees are possible?

A) 24
B) 40
C) 56
D) 64
E) 336

Show answer & explanation

Correct answer: C) 56

Since order does not matter, this is a combination: C(8,3) = 8!/(3!5!) = (8x7x6)/(3x2x1) = 336/6 = 56.

Question 3

The probability that a particular machine part fails within a year is 0.08. What is the probability that it does NOT fail within a year?

A) 0.08
B) 0.12
C) 0.80
D) 0.90
E) 0.92

Show answer & explanation

Correct answer: E) 0.92

Since probabilities of complementary events sum to 1, P(does not fail) = 1 - 0.08 = 0.92.

Question 4

A data set consists of the values 12, 15, 15, 18, 20. What is the mode of this data set?

A) 12
B) 15
C) 16
D) 18
E) 20

Show answer & explanation

Correct answer: B) 15

The mode is the value that appears most frequently. 15 appears twice, more than any other value.

Question 5

If a fair six-sided die is rolled twice, what is the probability that both rolls show a number greater than 4?

A) 1/9
B) 1/6
C) 1/3
D) 2/3
E) 4/9

Show answer & explanation

Correct answer: A) 1/9

Numbers greater than 4 on a six-sided die are 5 and 6 -- probability 2/6 = 1/3 per roll. For two independent rolls both showing such a number: (1/3) x (1/3) = 1/9.

Question 6

A bag has 3 red, 4 blue, and 3 green marbles. What is the probability of drawing a green marble?

A) 3/7
B) 1/3
C) 4/10
D) 1/10
E) 3/10

Show answer & explanation

Correct answer: E) 3/10

Total=10. P(green)=3/10.

Question 7

What is the mean of {6, 14, 10, 18, 22}?

A) 18
B) 10
C) 14
D) 12
E) 16

Show answer & explanation

Correct answer: C) 14

Sum=70. Mean=70/5=14.

Question 8

What is the median of {9, 3, 17, 11, 5, 21}?

A) 8
B) 10
C) 9
D) 11
E) 10.5

Show answer & explanation

Correct answer: B) 10

Sorted: 3,5,9,11,17,21. Median = (9+11)/2=10.

Question 9

What is the mode of {5, 8, 8, 12, 15, 8, 20}?

A) 15
B) 20
C) 5
D) 8
E) 12

Show answer & explanation

Correct answer: D) 8

8 appears three times, more than any other value.

Question 10

A fair coin is flipped 4 times. What is the probability of getting all heads?

A) 1/16
B) 1/4
C) 1/8
D) 1/2
E) 1/32

Show answer & explanation

Correct answer: A) 1/16

P = (1/2)^4 = 1/16.

Question 11

If a fair coin is flipped 3 times, what is the probability of getting exactly 2 heads?

A) 1/8
B) 1/4
C) 3/8
D) 1/2
E) 5/8

Show answer & explanation

Correct answer: C) 3/8

There are 2^3 = 8 equally likely outcomes. The outcomes with exactly 2 heads are HHT, HTH, THH -- 3 outcomes. Probability = 3/8.

Question 12

A data set consists of 5 numbers with a mean of 20. If four of the numbers are 15, 18, 22, and 25, what is the fifth number?

A) 15
B) 18
C) 20
D) 22
E) 25

Show answer & explanation

Correct answer: C) 20

Sum of all 5 numbers = 5 x 20 = 100. Sum of the four known numbers = 15+18+22+25 = 80. Fifth number = 100 - 80 = 20.

Question 13

What is the standard deviation of the data set consisting of 5, 5, 5, 5, 5?

A) 0
B) 1
C) 5
D) 10
E) 25

Show answer & explanation

Correct answer: A) 0

When every value in a data set is identical, there is no variation from the mean, so the standard deviation is 0.

Question 14

In how many ways can 4 people be arranged in a row?

A) 4
B) 8
C) 16
D) 24
E) 256

Show answer & explanation

Correct answer: D) 24

The number of arrangements of 4 distinct people is 4! = 4x3x2x1 = 24.

Question 15

A data set consists of the values 4, 7, 7, 9, 13. What is the median of this data set?

A) 4
B) 7
C) 8
D) 9
E) 13

Show answer & explanation

Correct answer: B) 7

With the data already in order (4, 7, 7, 9, 13), the median is the middle (3rd) value: 7.

Question 16

A bag contains 5 red marbles and 3 blue marbles. If one marble is drawn at random, what is the probability that it is blue?

A) 3/8
B) 3/5
C) 5/8
D) 5/3
E) 1/3

Show answer & explanation

Correct answer: A) 3/8

Total marbles = 5 + 3 = 8. Probability of blue = 3/8.

Question 17

A bag contains 4 white balls and 6 black balls. If one ball is drawn at random, what is the probability that it is white?

A) 2/5
B) 3/5
C) 2/3
D) 3/10
E) 1/2

Show answer & explanation

Correct answer: A) 2/5

Total balls = 4 + 6 = 10. Probability of white = 4/10, which simplifies to 2/5.

Question 18

A committee of 3 people is to be chosen from a group of 4 men and 3 women. How many different committees are possible, with no restriction on composition?

A) 21
B) 35
C) 42
D) 105
E) 210

Show answer & explanation

Correct answer: B) 35

The committee is chosen from 7 people total, and order does not matter: C(7,3) = 7!/(3!4!) = (7x6x5)/(3x2x1) = 210/6 = 35.

Question 19

A survey found that 65% of respondents prefer coffee to tea. If 140 respondents prefer tea, and every respondent has a preference for one or the other, how many total respondents were surveyed?

A) 300
B) 350
C) 400
D) 420
E) 450

Show answer & explanation

Correct answer: C) 400

If 65% prefer coffee, then 35% prefer tea. 0.35 x total = 140. Total = 140/0.35 = 400.

Question 20

A data set has values 3, 6, 6, 9, 11. What is the mean of this data set?

A) 6
B) 6.5
C) 7
D) 7.5
E) 9

Show answer & explanation

Correct answer: C) 7

Mean = (3+6+6+9+11)/5 = 35/5 = 7.

Question 21

From a group of 5 finalists, how many different ways can a 1st place and 2nd place winner be selected (order matters)?

A) 5
B) 10
C) 15
D) 20
E) 25

Show answer & explanation

Correct answer: D) 20

This is a permutation problem: P(5,2) = 5!/(5-2)! = 5 x 4 = 20.

Question 22

A data set consists of the values 5, 8, 8, 12, 17. What is the range of this data set?

A) 8
B) 9
C) 10
D) 12
E) 17

Show answer & explanation

Correct answer: D) 12

Range = maximum - minimum = 17 - 5 = 12.

Question 23

A jar contains 5 red, 4 blue, and 3 green marbles. If one marble is drawn at random, what is the probability that it is NOT green?

A) 1/4
B) 1/3
C) 3/4
D) 3/5
E) 5/12

Show answer & explanation

Correct answer: C) 3/4

Total marbles = 5+4+3 = 12. P(green) = 3/12 = 1/4. P(not green) = 1 - 1/4 = 3/4.

Question 24

How many distinct ways can the letters in the word "MATH" be arranged?

A) 4
B) 8
C) 16
D) 24
E) 256

Show answer & explanation

Correct answer: D) 24

With 4 distinct letters, the number of arrangements is 4! = 4x3x2x1 = 24.

Question 25

A survey found that 55% of respondents support a new policy. If 275 respondents support the policy, and every respondent either supports or opposes it, how many respondents were surveyed in total?

A) 450
B) 480
C) 490
D) 500
E) 540

Show answer & explanation

Correct answer: D) 500

0.55 x total = 275. Total = 275/0.55 = 500.

Question 26

A data set has a mean of 40 and consists of 8 values. If a new value of 76 is added to the data set, what is the new mean?

A) 42
B) 44
C) 46
D) 48
E) 50

Show answer & explanation

Correct answer: B) 44

Original sum = 8 x 40 = 320. New sum = 320 + 76 = 396. New count = 9. New mean = 396/9 = 44.

Question 27

A standard six-sided die is rolled twice. What is the probability that the sum of the two rolls is 7?

A) 1/12
B) 1/36
C) 1/3
D) 7/36
E) 1/6

Show answer & explanation

Correct answer: E) 1/6

Outcomes summing to 7: (1,6),(2,5),(3,4),(4,3),(5,2),(6,1) = 6 outcomes out of 36 total. 6/36 = 1/6.

Question 28

A data set has a mean of 20 and consists of 10 values. If one value of 30 is removed, what is the new mean of the remaining 9 values?

A) 18.9 (approximately)
B) 20
C) 17.8
D) 19.5
E) 21

Show answer & explanation

Correct answer: A) 18.9 (approximately)

Original sum = 20 x 10 = 200. Removing 30: new sum = 170. New mean = 170/9 ≈ 18.9.

Question 29

In a group of 50 students, 30 take Spanish, 20 take French, and 8 take both. How many students take neither language?

A) 10
B) 8
C) 12
D) 6
E) 0

Show answer & explanation

Correct answer: B) 8

Students taking at least one = 30 + 20 - 8 = 42 (inclusion-exclusion). Neither = 50 - 42 = 8.

Question 30

A jar contains 5 red, 3 blue, and 2 green marbles. If one marble is drawn at random, what is the probability it is NOT blue?

A) 3/10
B) 1/2
C) 7/10
D) 3/5
E) 4/5

Show answer & explanation

Correct answer: C) 7/10

P(blue) = 3/10, so P(not blue) = 1 - 3/10 = 7/10.

Question 31

The median of the data set {12, 7, 22, 9, 15} is:

A) 9
B) 15
C) 13
D) 12
E) 22

Show answer & explanation

Correct answer: D) 12

Sorted: 7, 9, 12, 15, 22. The middle value (3rd of 5) is 12.

Question 32

What is the mean of {8, 13, 19, 24, 31}?

A) 17
B) 18
C) 19
D) 20
E) 21

Show answer & explanation

Correct answer: C) 19

Sum=95. Mean=95/5=19.

Question 33

What is the mode of {7, 11, 11, 14, 18, 11, 22}?

A) 14
B) 22
C) 7
D) 11
E) 18

Show answer & explanation

Correct answer: D) 11

11 appears three times, more than any other value.

Question 34

A bag has 5 red, 6 blue, and 4 green marbles. What is the probability of drawing a red marble?

A) 1/4
B) 2/5
C) 5/14
D) 1/5
E) 1/3

Show answer & explanation

Correct answer: E) 1/3

Total=15. P(red)=5/15=1/3.

Question 35

A fair coin is flipped 5 times. What is the probability of getting all tails?

A) 1/32
B) 1/16
C) 1/8
D) 1/10
E) 1/64

Show answer & explanation

Correct answer: A) 1/32

P = (1/2)^5 = 1/32.

Question 36

What is the median of {14, 2, 27, 9, 6, 33}?

A) 9
B) 11.5
C) 14
D) 10
E) 12

Show answer & explanation

Correct answer: B) 11.5

Sorted: 2,6,9,14,27,33. Median = (9+14)/2=11.5.

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