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Intern  Joined: 23 Jan 2020
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If x is a positive integer such that x^2 is a multiple of 56, what is  [#permalink]

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If x is a positive integer such that x^2 is a multiple of 56, what is the least possible value of x?

A. 14
B. 22
C. 26
D. 28
E. 56

Originally posted by cristinaolt19 on 23 Jan 2020, 05:33.
Last edited by Bunuel on 29 Mar 2020, 12:23, edited 1 time in total.
Renamed the topic and edited the question.
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Re: If x is a positive integer such that x^2 is a multiple of 56, what is  [#permalink]

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cristinaolt19 wrote:
If x is a positive integer such that x^2 is a multiple of 56, what is the least possible value of x?

x^2 = 56k
x^2 = 2^3*7*k
k must make powers of 2 and 7 even, so that 2^3*7*k becomes a perfect square. The least value of k is therefore 2*7.

So, x^2 = 2^3*7*k = 2^4*7^2.
x = 2^2*7.

P.S. We have specific rules of posting a question on the forum: https://gmatclub.com/forum/rules-to-pos ... 08733.html Please read and edit the first post: provide the source, options and the OA. Thank you.
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Re: If x is a positive integer such that x^2 is a multiple of 56, what is  [#permalink]

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cristinaolt19 wrote:
If x is a positive integer such that x^2 is a multiple of 56, what is the least possible value of x?

$$56 = 8*7$$
or $$2^3 *7$$
thus x^2 should atleast have factors of the form $$2^3 *7$$
and since x an integer $$x^2$$ should be a perfect square
thus $$x^2$$ should be of the form $$2^4 *7^2$$
or$$x = 2^2*7$$
= 28
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Re: If x is a positive integer such that x^2 is a multiple of 56, what is  [#permalink]

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Do these types of questions belong to the GMAT exam? I have doubt Bunuel.
Please clarify, if it is, where can we practice this type of questions.
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Re: If x is a positive integer such that x^2 is a multiple of 56, what is  [#permalink]

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rajatchopra1994 wrote:
Do these types of questions belong to the GMAT exam? I have doubt Bunuel.
Please clarify, if it is, where can we practice this type of questions.

We have similar questions in OG . Yeah the format of question is incorrect. Missing things are options in this questions.
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Re: If x is a positive integer such that x^2 is a multiple of 56, what is  [#permalink]

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cristinaolt19 wrote:
If x is a positive integer such that x^2 is a multiple of 56, what is the least possible value of x?

x^2 = 56k

x^2 = 2^3 * 7 * k

Which means k has to be at minimum 2*7

Therefore x is 2^2 * 7 = 28 (Ans)
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Re: If x is a positive integer such that x^2 is a multiple of 56, what is  [#permalink]

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cristinaolt19 wrote:
If x is a positive integer such that x^2 is a multiple of 56, what is the least possible value of x?

Since x^2/56 = integer, we need to find the smallest perfect square that is a multiple of 56 or 2^3 * 7. That perfect square is 2^4 * 7^2, so x = 2^2 * 7^1 = 28.
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