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Question on Perfect Square 5

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by richachampion » Mon Oct 17, 2016 3:04 am
Positive integer y is a perfect square such that y is the product of 16, 9, 7 and r. Which of the following could be a value of r?

A. 2
B. 3
C. 5
D. 7
E. 9
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by richachampion » Mon Oct 17, 2016 3:04 am
OA: D
R I C H A,
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by fiza gupta » Mon Oct 17, 2016 4:52 am
Y(perfect square) = 16*9*7*r
16 and 9 are perfect square but not 7
so value of r will be 7 or multiple of 7
r = 7 or r = 7z(z should be perfect square)(7*4, 7*9....)

only option D satisfies
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by [email protected] » Mon Oct 17, 2016 9:56 am
Hi richachampion,

When you prime-factor a perfect square, each of the prime factors MUST show up an EVEN number of times...

eg. 9 = (3)(3) here, there are TWO 3s.
eg. 100 = (2)(2)(5)(5) here, there are TWO 2s and TWO 5s
eg. 16 = (2)(2)(2)(2) = here, there are FOUR 2s
Etc.

We're told that Y is a perfect square that is the product of 16, 9, 7 and R. Thus, prime-factoring Y will get us...

Y = (16)(9)(7)(R)
Y = (2)(2)(2)(2)(3)(3)(7)(R)

We have FOUR 2s and TWO 3s, but only ONE 7. We need there to be an even number of 7s, so the R must contain at least a '7.'

Final Answer: D

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