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

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

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New post 27 Aug 2018, 10:47
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  5% (low)

Question Stats:

90% (00:48) correct 10% (00:57) wrong based on 56 sessions

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Re: If n is an integer and 3n/7 is a perfect square  [#permalink]

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New post 27 Aug 2018, 10:52
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

Use options

(A) \(\frac{3*3}{7} = \frac{9}{7}\)

(B) \(\frac{3*7}{7} = 3\)

(C) \(\frac{3*21}{7} = 9 = 3^2\)

(D) \(\frac{3*42}{7} = 18\)

(E) \(\frac{3*147}{7} = 3*21 = 3^2*7\)


Answer must be (C)
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Re: If n is an integer and 3n/7 is a perfect square  [#permalink]

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New post 27 Aug 2018, 11:22
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

3 is not divisible by 3. Thus n has to be the multiple of 7. We are looking for least value.

Option C.

\(\frac{3*27}{7}\)= 9 or \(3^2\) that meets our condition.
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Re: If n is an integer and 3n/7 is a perfect square   [#permalink] 27 Aug 2018, 11:22
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