Source: Magoosh
If k is an integer, what is the smallest possible value of k such that 1040k is the square of an integer?
A. 2
B. 5
C. 10
D. 15
E. 65
The OA is E
If k is an integer, what is the smallest possible value of k such that 1040kis the square of an integer?
This topic has expert replies
-
- Moderator
- Posts: 2205
- Joined: Sun Oct 15, 2017 1:50 pm
- Followed by:6 members
Timer
00:00
Your Answer
A
B
C
D
E
Global Stats
GMAT/MBA Expert
- Scott@TargetTestPrep
- GMAT Instructor
- Posts: 7223
- Joined: Sat Apr 25, 2015 10:56 am
- Location: Los Angeles, CA
- Thanked: 43 times
- Followed by:29 members
Solution:BTGmoderatorLU wrote: ↑Wed Apr 21, 2021 9:54 amSource: Magoosh
If k is an integer, what is the smallest possible value of k such that 1040k is the square of an integer?
A. 2
B. 5
C. 10
D. 15
E. 65
The OA is E
Let’s prime factorize 1040 first:
1040 = 10 x 104 = 2 x 5 x 4 x 26 = 2 x 5 x 2 x 2 x 2 x 13 = 2^4 x 5 x 13
In order for a number to be a perfect square, the exponent of any particular prime factor of the number must be even. Therefore, in order for 1040k to be a perfect square, it must have an even number of 5s and 13s (notice it already has an even number of 2s). Since we want k to be the smallest possible positive integer, k must be 5 x 13 = 65 so that 1040k will have two 5s and two 13s.
Answer: E
Scott Woodbury-Stewart
Founder and CEO
[email protected]
See why Target Test Prep is rated 5 out of 5 stars on BEAT the GMAT. Read our reviews