M7MBA wrote: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
Statement I: 9 students borrow 6 books each
Let the other 3 students be A, B and C.
Since 9 students borrow 6 books each, the list of borrowed books is as follows:
A, B, C,
6, 6, 6, 6, 6, 6, 6, 6, 6, 6.
Books borrowed by A+B+C = (total books borrowed) - (books borrowed by the 9 students in blue) = 71 - (9*6) = 17.
Since A+B+C = 17, here is one way a range of 5 can be yielded:
A=4, B=4,
6, 6, 6, 6, 6, 6, 6, 6, 6, C=9.
Since Statement I is possible, the correct answer cannot include I.
Eliminate A, D and E.
Statement II: 10 students borrow 6 books each
Let the other 2 students be A and B.
Since 10 students borrow 6 books each, the list of borrowed books is as follows:
A, B,
6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6.
Books borrowed by A+B = (total books borrowed) - (books borrowed by the 10 students in blue) = 71 - (10*6) = 11.
Since A+B=11, a range of 5 can be yielded as follows:
A=3,
6, 6, 6, 6, 6, 6, 6, 6, 6, B=8.
Since Statement II is possible, the correct answer cannot include II.
Eliminate C.
The correct answer is
B.
Private tutor exclusively for the GMAT and GRE, with over 20 years of experience.
Followed here and elsewhere by over 1900 test-takers.
I have worked with students based in the US, Australia, Taiwan, China, Tajikistan, Kuwait, Saudi Arabia -- a long list of countries.
My students have been admitted to HBS, CBS, Tuck, Yale, Stern, Fuqua -- a long list of top programs.
As a tutor, I don't simply teach you how I would approach problems.
I unlock the best way for YOU to solve problems.
For more information, please email me (Mitch Hunt) at
[email protected].
Student Review #1
Student Review #2
Student Review #3
