GMAT Quantitative: Statistics and Sets Problems 1

Question 1

In a class of 30 students, 18 play soccer, 14 play basketball, and 8 play both. How many students play neither sport?

Accepted Answer

6

Answer

Soccer only: 18 − 8 = 10. Basketball only: 14 − 8 = 6. Both: 8. Total playing at least one: 10 + 6 + 8 = 24. Neither: 30 − 24 = 6.

Question 2

In a survey of 100 people, 60 drink coffee, 50 drink tea, and 20 drink both. How many drink coffee or tea but NOT both?

Accepted Answer

70

Answer

Coffee only: 60 − 20 = 40. Tea only: 50 − 20 = 30. Coffee or tea but not both = 40 + 30 = 70.

Question 3

Set A = {1, 2, 3, 4, 5} and Set B = {3, 4, 5, 6, 7}. What is |A∪B| − |A∩B|?

Accepted Answer

7

Answer

A∩B = {3,4,5}, so |A∩B| = 3. A∪B = {1,2,3,4,5,6,7}, so |A∪B| = 7. 7 − 3 = 4. Wait, recalculate: 7 − 3 = 4. Answer is 4.

Question 4

Set A = {1, 2, 3, 4, 5} and Set B = {3, 4, 5, 6, 7}. What is |A∪B| − |A∩B|?

Accepted Answer

4

Answer

A∩B = {3,4,5}, |A∩B| = 3. A∪B = {1,2,3,4,5,6,7}, |A∪B| = 7. 7 − 3 = 4.

Question 5

The mean of five numbers is 12. If four of the numbers are 10, 14, 8, and 16, what is the fifth number?

Accepted Answer

12

Answer

Sum of five numbers = 5 × 12 = 60. Sum of known four = 10 + 14 + 8 + 16 = 48. Fifth number = 60 − 48 = 12.

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