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if X and Y are integers greater than 1, is X a multiple of Y ?

(1) 3y² +7y = x (2) X²- X is a a multiple of Y

i came up with something like this:

statement :1

y=3; 27+21=84 y=2; 12+14=26 so they are multiple

but i cannot

figure out B can anyone explain it clearly

2 means that X(X-1) is multiple of Y. In the product X(X-1), there are two case (even three case) a. X is multiple of Y, but X-1 is not b. X-1 is multiple of Y, but X is not c. must be X(X-1) just enough to be multiple of Y

Re: DS from Gmat Prep - multiple of y [#permalink]

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28 Jan 2009, 19:48

ongste wrote:

Hi,

I am not sure whether this question has been asked here before,..

If x and y are integers greater than 1, is x a multiple of y?

i) 3y^2 + 7y = x ii) x^2 - x is a multiple of y

thanks

i) 3y^2 + 7y = x y (3y + 7) = x since y is an integer, (3y + 7) is also an integer. x is (3y + 7) times of y. suff.

ii) x^2 - x = yk x (x - 1) = yk

Not suff cuz we do not know whether k is an integer. however x, y and (x-1) all are integers, by k = ? do not know. lets say x = 5, x-1 = 4 and y = 3. k = 20/3. no x = 5, x-1 = 4 and y = 10. k = 2. yes.

If x and y are integers greater than 1, is x a multiple of y?

1) 3y^2 + 7y = x

2) x^2 - x is a multiple of y

The answer is A.

Using 1 we get x = 3y^2 + 7y x =y(3y+7)

So clearly from above x is a multiple of y. So 1 is sufficient.

Using 2 we get x^2 -x = y y = x(x-1).

So from above we get y is multiple of x and x-1. So x will be a multiple of y in case both x =y=2 we get 2 = 2*(2-1). However not true for other values of x, so 2 is insufficient.

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