GMAT Quantitative: Statistics and Sets Problems 2 — Questions and Answers
Question 1: The set {3, 7, 7, 11, 12} has what median?
- 7 (Correct answer)
- 8
- 11
- 12
Correct answer: 7
With 5 ordered values the median is the third value, which is 7.
Question 2: What is the mode of the data set {2, 4, 4, 6, 9, 9, 9}?
- 4
- 6
- 9 (Correct answer)
- No mode
Correct answer: 9
9 appears three times, more than any other value.
Question 3: The average of 5 numbers is 20. If a sixth number, 32, is added, what is the new average?
- 21
- 22 (Correct answer)
- 24
- 26
Correct answer: 22
The original sum is 100; adding 32 gives 132, and 132/6 = 22.
Question 4: If set A has 8 elements and set B has 5 elements, what is the maximum possible number of elements in A ∪ B?
- 5
- 8
- 13 (Correct answer)
- 40
Correct answer: 13
The union is largest when the sets are disjoint, giving 8 + 5 = 13.
Question 5: The range of a data set is 24 and its smallest value is 6. What is the largest value?
- 18
- 24
- 30 (Correct answer)
- 36
Correct answer: 30
Range = max − min, so max = 24 + 6 = 30.
Question 6: In a group of 30 people, 18 like coffee and 14 like tea, with 5 liking both. How many like neither?
- 3 (Correct answer)
- 5
- 7
- 9
Correct answer: 3
Liking at least one = 18 + 14 − 5 = 27, so 30 − 27 = 3 like neither.
Question 7: What is the arithmetic mean of the first five positive even integers?
- 5
- 6 (Correct answer)
- 10
- 30
Correct answer: 6
The integers 2, 4, 6, 8, 10 sum to 30, and 30/5 = 6.
GMAT Quantitative: Statistics and Sets Problems 2
The set {3, 7, 7, 11, 12} has what median?