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# If y is a positive integer, is (y^3 + 5)^2/4 an integer ?

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If y is a positive integer, is (y^3 + 5)^2/4 an integer ?  [#permalink]

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27 Jun 2018, 06:37
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If y is a positive integer, is $$\frac{(y^3 + 5)^2}{4}$$ an integer ?

(1) The square root of y has three prime factors.
(2) Each prime factor of $$y^3$$ is greater than 5.

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If y is a positive integer, is (y^3 + 5)^2/4 an integer ?  [#permalink]

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27 Jun 2018, 07:40
If y is a positive integer, is $$\frac{(y^3 + 5)^2}{4}$$ an integer ?

This will happen if $$(y^3+5)^2$$ is div by 4 or y^3+5 is div by 2, meaning " y is an odd number"

(1) The square root of y has three prime factors.
Even y will have three factors..
Can be all odd or can have 2 as a factor
Insufficient

(2) Each prime factor of $$y^3$$ is greater than 5.
This means y is odd as only 2 is even prime number..
Ans is YES always..
Sufficient

B
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1) Absolute modulus : http://gmatclub.com/forum/absolute-modulus-a-better-understanding-210849.html#p1622372
2)Combination of similar and dissimilar things : http://gmatclub.com/forum/topic215915.html
3) effects of arithmetic operations : https://gmatclub.com/forum/effects-of-arithmetic-operations-on-fractions-269413.html

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If y is a positive integer, is (y^3 + 5)^2/4 an integer ? &nbs [#permalink] 27 Jun 2018, 07:40
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# If y is a positive integer, is (y^3 + 5)^2/4 an integer ?

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