Let a, b, and c be three integers, and let a be a perfect square. If a/b = b/c, then which one of the following statements must be true?
(A) c must be an even number
(B) c must be an odd number
(C) c must be a perfect square
(D) c must not be a perfect square
(E) c must be a prime number
The OA is C.
Can any expert help me with this PS question please? I can't understand it. Thanks.
Let a, b, and c be three integers, and let a be a perfect...
This topic has expert replies
-
- Moderator
- Posts: 2209
- Joined: Sun Oct 15, 2017 1:50 pm
- Followed by:6 members
GMAT/MBA Expert
- Jay@ManhattanReview
- GMAT Instructor
- Posts: 3008
- Joined: Mon Aug 22, 2016 6:19 am
- Location: Grand Central / New York
- Thanked: 470 times
- Followed by:34 members
We have a/b = b/c;LUANDATO wrote:Let a, b, and c be three integers, and let a be a perfect square. If a/b = b/c, then which one of the following statements must be true?
(A) c must be an even number
(B) c must be an odd number
(C) c must be a perfect square
(D) c must not be a perfect square
(E) c must be a prime number
The OA is C.
Can any expert help me with this PS question please? I can't understand it. Thanks.
Thus, ac = b^2
=> √(ac) = b
√a*√c = Integer
Integer*√c --> Integer; we are given that a is a perfect square, thus √a = integer
Since the product of an integer and √c is an integer, it implies that √c is an integer or c is a perfect square integer.
The correct answer: C
Hope this helps!
-Jay
Download free ebook: Manhattan Review GMAT Quantitative Question Bank Guide
_________________
Manhattan Review GMAT Prep
Locations: New York | New Delhi | Seoul | Cairo | and many more...
Schedule your free consultation with an experienced GMAT Prep Advisor! Click here.