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# When 240n is the square of an integer, what is the least possible valu

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Math Revolution GMAT Instructor
Joined: 16 Aug 2015
Posts: 7252
GMAT 1: 760 Q51 V42
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When 240n is the square of an integer, what is the least possible valu  [#permalink]

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20 Jul 2017, 01:08
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15% (low)

Question Stats:

80% (01:02) correct 20% (01:34) wrong based on 67 sessions

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When 240n is the square of an integer, what is the least possible value of n?

A. 10
B. 15
C. 20
D. 25
E. 30

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"Only $149 for 3 month Online Course" "Free Resources-30 day online access & Diagnostic Test" "Unlimited Access to over 120 free video lessons - try it yourself" Senior CR Moderator Status: Long way to go! Joined: 10 Oct 2016 Posts: 1354 Location: Viet Nam Re: When 240n is the square of an integer, what is the least possible valu [#permalink] ### Show Tags 20 Jul 2017, 01:41 MathRevolution wrote: When 240n is the square of an integer, what is the least possible value of n? A. 10 B. 15 C. 20 D. 25 E. 30 $$240 = 2^4 * 3 * 5$$. Since $$240n$$ is the square of an integer, $$n$$ must be as this form $$n=3*5*k^2$$. Hence $$k \geq 15$$. The answer is B. _________________ Senior SC Moderator Joined: 22 May 2016 Posts: 2654 When 240n is the square of an integer, what is the least possible valu [#permalink] ### Show Tags 20 Jul 2017, 15:49 1 1 MathRevolution wrote: When 240n is the square of an integer, what is the least possible value of n? A. 10 B. 15 C. 20 D. 25 E. 30 If 240n is the square of an integer, then as a perfect square it must have an even number of prime factors (or: all prime factors of a perfect square need to be in pairs). 240's prime factors are 2$$^4$$ x 3$$^1$$ x 5$$^1$$ The four powers of 2 are fine. But we are missing one 3 and one 5. The least possible value for n must be (3 * 5) = 15. (And 240n = 3,600) Answer B _________________ Listen, are you breathing just a little, and calling it a life? -- Mary Oliver For practice SC questions with official explanations that were posted and moderated by the SC Team, go to SC Butler here: https://gmatclub.com/forum/project-sc-butler-get-2-sc-questions-everyday-281043.html Math Revolution GMAT Instructor Joined: 16 Aug 2015 Posts: 7252 GMAT 1: 760 Q51 V42 GPA: 3.82 Re: When 240n is the square of an integer, what is the least possible valu [#permalink] ### Show Tags 23 Jul 2017, 18:28 ==> From $$240n=4^2(3)(5)n=integer^2$$, the least possible value of n becomes (3)(5)=15. The answer is B. Answer: B _________________ MathRevolution: Finish GMAT Quant Section with 10 minutes to spare The one-and-only World’s First Variable Approach for DS and IVY Approach for PS with ease, speed and accuracy. "Only$149 for 3 month Online Course"
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Re: When 240n is the square of an integer, what is the least possible valu   [#permalink] 23 Jul 2017, 18:28
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