If y and x are positive integers, is y divisible by x?

Question

(1) y = x^2 + x
(2) x has the same prime factors as y.

goforgmat · Answer

I marked D but the answer should be A..

1.(x^2 +x)/x-->divisible
2. say x =a^m*b^n*c^l 
case 1: if y= a^m-1 * b ^n-1 *c^l -1 y is not divisible by x
case 2:if y= a^m+1 * b ^n+1 *c^l +1 y is divisible by x

Hence A

Abhishek009 · Answer

First option is easy for everyone.

For the 2nd option I suggest plugging in some values will work.

Let X = 225 , Y = 15

X = 3^2 x  5^2

Y =  5  x  3

Now the question asks -

Certainly 15/225 is not divisible.

HowdyPartner · Answer

First glance -- DS. Also, divisibility --> signalling factors/number properties.

Statement 1:  This is saying that y is equal to x squared, plus x. In other words, x squared has all of the factors of x (and more) and then we add x, which is a multiple of x. So y is equal to multiples of x, so it is divisible by x.  Sufficient.

Statement 2: This is an answer trap. Although x has all the same prime factors as y, we are not told whether x has more, less or the same number of prime factors, for each prime factor, as y. As a result, the answer to the question stem could be yes or no. Insufficient

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If y and x are positive integers, is y divisible by x?

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