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If x and y are both positive integers, is y a multiple of 7?

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Veritas Prep GMAT Instructor
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If x and y are both positive integers, is y a multiple of 7? [#permalink]

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New post 08 Jan 2018, 21:01
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If \(x\) and \(y\) are both positive integers, is \(y\) a multiple of 7?

(1) \((x^3)(y^3) = 441^3\)
(2) \(x\) is a single digit integer
[Reveal] Spoiler: OA

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Aaron J. Pond
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Re: If x and y are both positive integers, is y a multiple of 7? [#permalink]

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New post 08 Jan 2018, 21:26
AaronPond wrote:
If \(x\) and \(y\) are both positive integers, is \(y\) a multiple of 7?

(1) \((x^3)(y^3) = 441^3\)
(2) \(x\) is a single digit integer



Points to consider..
1) x andy are positive integers..

From statement I, x*y = 441=1*3*3*7*7
So x can be 9, y 49.... Yes y is multiple of 7
x can be 49, y 9..... Ans NO
Insufficient

From statement II..
Nothing about y..
Insufficient

Combined...
x can be 1,3,7 or 9
In each case y will be MULTIPLE of 7
Sufficient
C
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Absolute modulus :http://gmatclub.com/forum/absolute-modulus-a-better-understanding-210849.html#p1622372
Combination of similar and dissimilar things : http://gmatclub.com/forum/topic215915.html


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Re: If x and y are both positive integers, is y a multiple of 7? [#permalink]

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New post 08 Jan 2018, 21:39
Statement #1 tells us that \((x^3)(y^3) = 441^3\). This can be mathematically simplified down to \((x)(y)=441\). Therefore, both \(x\) and \(y\) are factors of \(441\).

Factoring \(441\) isn't hard, especially once we realize that \(441\) is not only divisible by \(9\), but \(441 = 450-9\).

Factoring a common \(9\) out of this expression gives us:

\(450-9 = 9(50-1) = 9*49 = 3*3*7*7\)

\(x\) or \(y\) could be any combination of these prime values. \(y\) could be equal to 3 (not a multiple of 7), and it could also be equal to 7 (obviously, a multiple of 7.) Statement #1 is clearly insufficient.

Statement #2 is profoundly insufficient by itself. It tells us nothing about \(y\), so it is easy to eliminate.

As we combine the statements together, we can now ask ourselves the question, "does it matter that \(x\) is a single digit integer?" If \(x\) must be a single digit integer, there are only four possible solutions: \(x\)\(=1,3,7,\) or \(9\).

Given these four values for \(x\), here are the possible values for \(x\) and \(y\) (notice that there is no reason to actually multiply them out, since the problem only wants us to find out if \(y\) is a multiple of 7.)

(\(x\)) *(\(y\))
\(1\) * (\(3*3*7*7\))
\(3\)*(\(3*7*7\))
\(7\)*(\(3*3*7\))
\(9\)*(\(7*7\))

In every case, \(y\) must be a multiple of 7. Combining these two statements together is sufficient.

The answer is C.
_________________

Aaron J. Pond
Veritas Prep Elite-Level Instructor

Hit "+1 Kudos" if my post helped you understand the GMAT better.
Look me up at https://www.veritasprep.com/gmat/aaron-pond/ if you want to learn more GMAT Jujitsu.

Re: If x and y are both positive integers, is y a multiple of 7?   [#permalink] 08 Jan 2018, 21:39
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