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12 Dec 2017, 23:44
Kudos
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B
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
95%
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Question Stats:
46% (02:42) correct
54%
(02:55)
wrong
based on 368
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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
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13 Dec 2017, 07:51
Kudos
Bookmarks
x1 + x2 + .... + x12 (in ascending order) = 71
Range = 5
Question: which of the following CANNOT be the number of students who borrowed 6 books
Start from high to low
iii) Number of students who borrowed 6 books = 11 (Assume x2.....x12)--> x1 + 11 * 6 = 71 --> x1 = 5. Here Range is 1. Not possible.
ii) Number of students who borrowed 6 books = 10 (Assume x2.....x11) --> x1 + 10 * 6 + x12 = 71 --> x1 + x12 = 11 --> x1 = 3 and x12 = 8.
Range = 5. Possible
i) Number of students who borrowed 6 books = 9 (Assume x3......x11) --> x1 + x2 + 9*6 + x3 = 71 --> x1 = x2 = 4 and x3 = 9.
Range = 5. Possible
Answer: B
Range = 5
Question: which of the following CANNOT be the number of students who borrowed 6 books
Start from high to low
iii) Number of students who borrowed 6 books = 11 (Assume x2.....x12)--> x1 + 11 * 6 = 71 --> x1 = 5. Here Range is 1. Not possible.
ii) Number of students who borrowed 6 books = 10 (Assume x2.....x11) --> x1 + 10 * 6 + x12 = 71 --> x1 + x12 = 11 --> x1 = 3 and x12 = 8.
Range = 5. Possible
i) Number of students who borrowed 6 books = 9 (Assume x3......x11) --> x1 + x2 + 9*6 + x3 = 71 --> x1 = x2 = 4 and x3 = 9.
Range = 5. Possible
Answer: B
General Discussion
01 Jun 2018, 11:31
Kudos
Bookmarks
Bunuel
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
