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If n is an integer and 3n/7 is a perfect square, the smallest possible

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Carcass
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If n is an integer and 3n/7 is a perfect square, the smallest possible [#permalink] New post   11 Aug 2021, 01:08
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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


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Question part of the project GRE Quant/Math Extreme Challenge Daily (2021) Edition
GRE - Math Book
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C
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nikhilinuganti
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Re: If n is an integer and 3n/7 is a perfect square, the smallest possible [#permalink] New post   11 Aug 2021, 01:59
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For the solution to be a perfect square we need n to be a multiple of 7 and also can be factored to form a perfect square.

Looking at the options all of B,C and D hold true. But the question asks for the smallest integer value
so if n=21 and n 21 can be written as 3*7. The equation now becomes (3*3*7)/7 which is equal to 9, perfect square.

The answer is C
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Re: If n is an integer and 3n/7 is a perfect square, the smallest possible [#permalink] New post   15 Jan 2022, 12:30
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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


Kudos for the right answer and explanation
Question part of the project GRE Quant/Math Extreme Challenge Daily (2021) Edition
GRE - Math Book

STRATEGY: As with all GRE Problem Solving questions, we should immediately ask ourselves, Can I use the answer choices to my advantage?
In this case, we can easily test the answer choices.
In most cases, we should then give ourselves about 20 seconds to identify a faster approach. However, in this case, the numbers are nice and small. So, testing shouldn't take more than 30 seconds...


We'll begin with the smallest number test answers choices in ascending value...

A. If n = 3, we get: \(\frac{3n}{7}=\frac{3(3)}{7}=\frac{9}{7}\). Not a perfect square. Eliminate A

B. If n = 7, we get: \(\frac{3n}{7}=\frac{3(7)}{7}=3\). Not a perfect square. Eliminate B

C. If n = 21, we get: \(\frac{3n}{7}=\frac{3(21)}{7}=9\). Perfect square!

Answer: C
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Abhineet08
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If n is an integer and 3n/7 is a perfect square, the smallest possible [#permalink] New post   15 Jan 2022, 14:51
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Yes, I agree with the strategy but I feel it can be solved within 10 sec, 3n/7 for it to be a perfect square you need "n" to be a multiple of 7 and 3, so the smallest number is 21, boom solved.
#Primefactorization

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If n is an integer and 3n/7 is a perfect square, the smallest possible [#permalink]
15 Jan 2022, 14:51
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