Bunuel wrote:
GMAT CLUB'S FRESH CHALLENGE QUESTION:
At a certain library, 12 students borrowed a total of 71 books. If the range of the number of books borrowed per student was 5, which of the following CANNOT be the number of students who borrowed 6 books?
I. 9
II. 10
III. 11
A. I only
B. III only
C. II and III only
D. I and III only
E. I, II and III
Let’s analyze each Roman Numeral.
I. 9
If 9 people borrowed 6 books, we have 71 - 54 = 17 books for the remaining 3 people. If we let x = the least number of books borrowed by 1 of the 3 people, then x + 5 = the greatest number of books borrowed by another person.
Let y = the number of books borrowed by the last person.
Notice that 0 ≤ x ≤ y ≤ x + 5 and none of x, y, x + 5 can be 6. So we have:
x + x + 5 + y = 17
2x + y = 12
We see that x can’t be 7 or more (otherwise, y will be negative).
If x = 5, then y = 2 and x + 5 = 10. But the range is 10 - 2 = 8, not 5.
If x = 4, then y = 4 and x + 5 = 9. We see that 4 + 4 + 9 = 17 and the range is 9 - 4 = 5.
So it’s possible to have 9 people who borrowed 6 books each.
II. 10
If 10 people borrowed 6 books, we have 71 - 60 = 11 books for the remaining 2 people.
If we let x = the least number of books borrowed by 1 of the 2 people, then x + 5 = the most number of books borrowed by the other person.
Notice neither x nor x + 5 can be 6. So we have:
x + x + 5 = 11
2x = 6
x = 3
We see that the range is 3 + 8 = 11 and the range is 8 - 3 = 5. So it’s possible to have 10 people who borrowed 6 books each.
III. 11
If 11 people borrowed 6 books, we have 71 - 66 = 5 books for the remaining person. But then the range is 6 - 5 = 1, not 5. So 11 CAN’T be the number of students who borrowed 6 books each.
Answer: B
_________________
5-star rated online GMAT quant
self study course
See why Target Test Prep is the top rated GMAT quant course on GMAT Club. Read Our Reviews
If you find one of my posts helpful, please take a moment to click on the "Kudos" button.