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If 375y = x^2, and x and y are positive integers then which of the fol

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Carcass
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If 375y = x^2, and x and y are positive integers then which of the fol [#permalink] New post   21 Jul 2022, 02:48
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If \(375y = x^2\), and \(x\) and \(y\) are positive integers then which of the following must be an integer?

I. \(\frac{y}{15}\)

II. \(\frac{y}{30}\)

III. \(\frac{(y^2)}{25}\)

a) I only
b) III only
c) I and II
d) I and III
e) I, II and III


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D
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SeaOyster1
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Re: If 375y = x^2, and x and y are positive integers then which of the fol [#permalink] New post   21 Jul 2022, 03:08
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Solution -

We can write - 375 = (3)(5)(5)(5) = (3)(5)(5²)

For 375y to be a perfect square, the prime factorization of y must contain at least one 3 and one 5.
In other words, y must be a multiple of 15.

If y is a multiple of 15, then y/15 must be an integer and y²/25 must be an integer.
Hence, Statements I and III are correct.

Therefore, the correct answer choice is D
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Re: If 375y = x^2, and x and y are positive integers then which of the fol [#permalink] New post   21 Jul 2022, 06:17
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Carcass wrote:
If \(375y = x^2\), and \(x\) and \(y\) are positive integers then which of the following must be an integer?

I. \(\frac{y}{15}\)

II. \(\frac{y}{30}\)

III. \(\frac{(y^2)}{25}\)

a) I only
b) III only
c) I and II
d) I and III
e) I, II and III



375 = (3)(5)(5)(5) = (3)(5)(5²)
In order for 375y to be a perfect square, the prime factorization of y must contain at least one 3 and one 5.
In other words, y must be a multiple of 15.

If y is a multiple of 15, then y/15 must be an integer and y²/25 must be an integer.
So I and III must be integers.

Answer: D
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gmatclubot
Re: If 375y = x^2, and x and y are positive integers then which of the fol [#permalink]
21 Jul 2022, 06:17
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