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02 Mar 2018, 01:17
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57% (01:41) correct
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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 \(2\)
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 \(2\)
02 Mar 2018, 02:54
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MathRevolution
[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 \(2\)
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
03 Mar 2018, 01:39
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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
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
