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For the integers x and y, if xy is a multiple of 25, is y a multiple o

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New post 02 Mar 2018, 01:17
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[GMAT math practice question]

For the integers \(x\) and \(y\), if \(xy\) is a multiple of \(25\), is \(y\) a multiple of \(5\)?

1) \(x-y\) is a multiple of \(5\)
2) \(x\) is a multiple of \(2\)

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Re: For the integers x and y, if xy is a multiple of 25, is y a multiple o  [#permalink]

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New post 02 Mar 2018, 02:54
MathRevolution wrote:
[GMAT math practice question]

For the integers \(x\) and \(y\), if \(xy\) is a multiple of \(25\), is \(y\) a multiple of \(5\)?

1) \(x-y\) is a multiple of \(5\)
2) \(x\) is a multiple of \(2\)


x*y is a multiple of 25, which is 5^2. This means Either both x and y have at least one '5' each in their prime factorisation, Or its also possible that one of x/y does not have any '5' and the other one of x/y has at least two 5's in its prime factorisation.
(then only x*y will be a multiple of 5^2)

Also if sum (or difference) of two integers is a multiple of 5, then Either each one of them is a multiple of 5 Or none of the two integers is a multiple of 5.

(1) x-y is a multiple of 5, so either each of them is a multiple of 5 Or none of the two integers is a multiple of 5. But the latter case is Not possible here since x*y is divisible by 5^2. So it means each of x/y must have at least one 5, so 'y' is a multiple of 5. Sufficient.

(2) x is a multiple of 2, this doesn't tell anything about divisibility by 5 of y. Not sufficient.

Hence A answer
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Re: For the integers x and y, if xy is a multiple of 25, is y a multiple o  [#permalink]

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New post 03 Mar 2018, 01:39
2
Given: x times y is a multiple of 25,
2 scenarios : Both x and y Are multiple of 5
b) Either x or y is a multiple of 25

Statement 1:
(1) x-y is a multiple of 5. Either each of them is a multiple of 5 or none of the two integers is a multiple of 5. 2nd case is out of consideration. SUFFICIENT.
(2) x is a multiple of 2, but is X a multiple of 10 or 25. We dont know. INUFFICIENT
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Re: For the integers x and y, if xy is a multiple of 25, is y a multiple o  [#permalink]

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New post 04 Mar 2018, 19:24
=>

Forget conventional ways of solving math questions. For DS problems, the VA (Variable Approach) method is the quickest and easiest way to find the answer without actually solving the problem. Remember that equal numbers of variables and independent equations ensure a solution.

The first step of the VA (Variable Approach) method is to modify the original condition and the question, and then recheck the question.

Since \(xy = 25 =5^2\), \(x\) is a multiple of \(5\) or \(y\) is a multiple of \(5\). If \(x\) is a multiple of \(5\), \(y = x – 5\) is also a multiple of \(5\). Thus the condition 1) is sufficient.

Condition 2)
Since we don’t have any information from the condition 2), it is not sufficient.

Therefore, A is the answer.

Answer: A
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Re: For the integers x and y, if xy is a multiple of 25, is y a multiple o &nbs [#permalink] 04 Mar 2018, 19:24
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