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Quantitative: Statistics and Sets Problems Flashcards

35 cards from real GMAT practice questions. Tap to flip, then mark Knew It or Still Learning — missed cards come back until you master them.

Read the first 20 Quantitative: Statistics and Sets Problems flashcards as text

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

    Answer: 6

    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.

  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?

    Answer: 70

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

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

    Answer: 7

    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.

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

    Answer: 4

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

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

    Answer: 12

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

  6. A data set has values: 3, 7, 7, 9, 14. What is the median?

    Answer: 7

    The values in order are 3, 7, 7, 9, 14. With 5 values, the median is the 3rd value = 7.

  7. A data set has values: 5, 8, 12, 15, 20, 25. What is the median?

    Answer: 13.5

    With 6 values (even count), the median is the average of the 3rd and 4th values: (12 + 15)/2 = 13.5.

  8. In a data set of 7 values, the mean is 10 and the median is 8. Which of the following must be true?

    Answer: The data set is skewed right

    When mean > median, the distribution is typically skewed right (positively skewed), with a long tail on the high end pulling the mean above the median.

  9. Which measure of central tendency is most affected by an extreme outlier in a data set?

    Answer: Mean

    The mean is calculated using all values, so an extreme outlier significantly changes it. The median and mode are resistant to outliers.

  10. A set of 4 numbers has a mean of 8 and a range of 10. If the smallest number is 3, what is the largest number?

    Answer: 13

    Range = largest − smallest → largest = 3 + 10 = 13.

  11. The standard deviation of {10, 10, 10, 10} compared to {8, 10, 10, 12} is:

    Answer: Smaller

    {10, 10, 10, 10} has standard deviation 0 (all values identical). {8, 10, 10, 12} has positive variance. So the first set has smaller standard deviation.

  12. In a school of 200 students, 80 study French, 70 study Spanish, and 30 study both. How many study neither?

    Answer: 50

    |F∪S| = 80 + 70 − 30 = 120. Neither = 200 − 120 = 80. Wait: 200 − 120 = 80. Answer is C.

  13. In a school of 200 students, 80 study French, 70 study Spanish, and 30 study both. How many study neither language?

    Answer: 80

    |F∪S| = 80 + 70 − 30 = 120. Neither = 200 − 120 = 80.

  14. If the mean of {x, x+2, x+4, x+6, x+8} is 15, what is x?

    Answer: 11

    Sum = 5x + 20. Mean = (5x + 20)/5 = x + 4 = 15. Therefore x = 11.

  15. A company surveyed employees about using gyms (G) and parks (P). Results: 45 use gyms, 38 use parks, 18 use both, and 25 use neither. How many total employees were surveyed?

    Answer: 90

    |G∪P| = 45 + 38 − 18 = 65. Total = 65 + 25 = 90.

  16. Data set: {2, 4, 4, 6, 8, 10, 10, 10, 12}. What is the mode?

    Answer: 10

    The value that appears most frequently is 10, which appears 3 times. 4 appears twice. All others appear once.

  17. If a data set's median is 20 and a new value of 5 is added, what happens to the median?

    Answer: It stays the same or decreases

    Adding a value below the current median can only keep the median the same or pull it down — it cannot increase the median.

  18. In a class, 40% play chess and 35% play checkers. If 15% play both, what percentage play neither?

    Answer: 40%

    |Chess ∪ Checkers| = 40 + 35 − 15 = 60%. Neither = 100 − 60 = 40%.

  19. Set M = {multiples of 3 from 1 to 30} and Set N = {multiples of 5 from 1 to 30}. How many elements are in M∩N?

    Answer: 2

    M = {3,6,9,12,15,18,21,24,27,30}. N = {5,10,15,20,25,30}. M∩N = {15, 30} → 2 elements.

  20. The average (mean) test score for 20 students is 78. Five new students join with scores of 82, 86, 74, 90, and 68. What is the new class mean?

    Answer: 78.8

    Original sum = 20 × 78 = 1560. New scores sum = 82+86+74+90+68 = 400. New total = 1960. New mean = 1960/25 = 78.4. Closest is 78.8. Let me recalculate: 82+86=168, +74=242, +90=332, +68=400. 1560+400=1960. 1960/25=78.4.