GMAT Quantitative: Statistics and Sets Problems 3 — Questions and Answers
Question 1: A data set has standard deviation 0. What must be true?
- The mean is 0
- All values are equal (Correct answer)
- The median is 0
- The range is large
Correct answer: All values are equal
A standard deviation of 0 means there is no spread, so every value is identical.
Question 2: If every value in a data set is increased by 10, what happens to the standard deviation?
- Increases by 10
- Decreases by 10
- Stays the same (Correct answer)
- Doubles
Correct answer: Stays the same
Adding a constant shifts all values equally, leaving the spread unchanged.
Question 3: The set {x, 5, 8, 12} has a mean of 8. What is x?
- 5
- 7 (Correct answer)
- 8
- 11
Correct answer: 7
The sum must be 32, so x = 32 − 25 = 7.
Question 4: How many subsets does a set with 4 elements have?
- 4
- 8
- 16 (Correct answer)
- 24
Correct answer: 16
A set of n elements has 2^n subsets, and 2^4 = 16.
Question 5: The median of {4, 9, 11, 16} is which value?
- 9
- 10 (Correct answer)
- 11
- 11.5
Correct answer: 10
With an even count, the median is the average of the two middle values: (9 + 11)/2 = 10.
Question 6: If A ⊆ B and B has 10 elements, what is the maximum size of A?
- 0
- 5
- 9
- 10 (Correct answer)
Correct answer: 10
A subset can equal the whole set, so A can have up to 10 elements.
Question 7: Seven students scored 80, 85, 90, 90, 95, 100, and 70. What is their average score?
- 85
- 87 (Correct answer)
- 88
- 90
Correct answer: 87
The scores sum to 610, and 610/7 ≈ 87.
GMAT Quantitative: Statistics and Sets Problems 3
A data set has standard deviation 0.
What must be true?