Free practice questions/GMAT Focus Edition
GMAT Focus Edition — Statistics, Sets & Probability
6 free practice questions with full explanations.
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Start freeQuestion 1
The set {4, 7, 9, 12, 13} has a mean equal to its median. If the number 12 is replaced with 22, what is the new mean?
- A) 9
- B) 9.5
- C) 10
- D) 11
Show answer & explanation
Correct answer: D) 11
Original sum = 4+7+9+12+13 = 45. Replacing 12 with 22: new sum = 45-12+22 = 55. New mean = 55/5 = 11.
Question 2
A bag contains 4 red balls and 6 blue balls. If two balls are drawn without replacement, what is the probability that both are red?
- A) 2/15
- B) 4/25
- C) 6/45
- D) 1/5
Show answer & explanation
Correct answer: A) 2/15
P(first red) = 4/10. P(second red | first red) = 3/9. P(both red) = (4/10)(3/9) = 12/90 = 2/15.
Question 3
In a class of 50 students, 30 take French, 25 take Spanish, and 10 take both. How many students take neither language?
- A) 5
- B) 8
- C) 10
- D) 12
Show answer & explanation
Correct answer: A) 5
Students taking at least one = 30 + 25 - 10 = 45. Students taking neither = 50 - 45 = 5.
Question 4
A committee of 3 people is to be chosen from a group of 8 people. How many different committees are possible?
- A) 24
- B) 48
- C) 56
- D) 64
Show answer & explanation
Correct answer: C) 56
This is a combination: C(8,3) = 8!/(3!5!) = (8x7x6)/(3x2x1) = 336/6 = 56.
Question 5
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
Show answer & explanation
Correct answer: C) 3/8
There are 2^3 = 8 total outcomes. The number of ways to get exactly 2 heads out of 3 flips is C(3,2) = 3. Probability = 3/8.
Question 6
Which of the following sets has the largest standard deviation?
- A) {5, 5, 5, 5}
- B) {3, 4, 5, 6, 7}
- C) {4, 5, 5, 5, 6}
- D) {1, 5, 5, 5, 9}
Show answer & explanation
Correct answer: D) {1, 5, 5, 5, 9}
Standard deviation measures spread from the mean. Set D has values furthest from its mean (5), with deviations of 4 on both ends, giving it the largest spread.
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