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# If n is an integer and 3n/7 is a perfect square

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Founder
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If n is an integer and 3n/7 is a perfect square [#permalink]  27 Aug 2018, 09:47
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Question Stats:

78% (00:29) correct 21% (00:16) wrong based on 32 sessions
If n is an integer and $$\frac{3n}{7}$$ is a perfect square, the smallest possible value of n is

A. 3

B. 7

C. 21

D. 42

E. 147
[Reveal] Spoiler: OA

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Intern
Joined: 29 Jun 2018
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Kudos [?]: 17 [1] , given: 0

Re: If n is an integer and 3n/7 is a perfect square [#permalink]  28 Aug 2018, 06:51
1
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Just plug the value and see the smallest value which will give a square. 21 is the answer which gives 9 (a square of 3)
Manager
Joined: 06 Jun 2018
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Re: If n is an integer and 3n/7 is a perfect square [#permalink]  07 Sep 2018, 19:26
Carcass wrote:
If n is an integer and $$\frac{3n}{7}$$ is a perfect square, the smallest possible value of n is

A. 3

B. 7

C. 21

D. 42

E. 147

$$\frac{3n}{7}$$ = perfect square.

Note: As 3 is not divisible by 7 , n must be a multiple of 7.

So, we must pick up a number in such a manner thus after division still we can form a perfect square.

27 = 7*3

So,

$$\frac{3*21}{7}$$ = $$3^2$$

Thus the best answer is C.
Manager
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Kudos [?]: 23 [0], given: 15

Re: If n is an integer and 3n/7 is a perfect square [#permalink]  13 Sep 2018, 12:40
This has options so we can plug in and check:
1) 3(3)/ 7 = NO
2) 3(7)/ 7 = NO
3) 3 (7 x 3)/ 7 = 9 = YES

Manager
Joined: 19 Mar 2018
Posts: 58
Followers: 1

Kudos [?]: 23 [0], given: 15

Re: If n is an integer and 3n/7 is a perfect square [#permalink]  13 Sep 2018, 12:41
This has options so we can plug in and check:
1) 3(3)/ 7 = NO
2) 3(7)/ 7 = NO
3) 3 (7 x 3)/ 7 = 9 = YES

Re: If n is an integer and 3n/7 is a perfect square   [#permalink] 13 Sep 2018, 12:41
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