collection of tough problems from G PREP - 42

[abhasjha]

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.

[sanju09]

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.

(1) with y (3 y + 7) = x, x surely is a multiple of y. Sufficient

(2) with x (x - 1) = k y, we can never be sure that x is a multiple of y. Insufficient

[spoiler]A[/spoiler]

[ajith]

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.

(1) (3y+7)*y = x

say y=kx

(3kx+7)*kx = x
(3k+7)*k = 1

only possible if 3k+1 = k =1 which is not possible

Sufficient


2)y = k * (x-1)*x

Sufficient to conclude that x is a multiple of y
[spoiler]

D[/spoiler]

[sanju09]

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.

(1) (3y+7)*y = x

say y=kx

(3kx+7)*kx = x
(3k+7)*k = 1

only possible if 3k+1 = k =1 which is not possible

Sufficient


2)y = k * (x-1)*x

Sufficient to conclude that x is a multiple of y
[spoiler]

D[/spoiler]

What's the difference in a factor and a multiple?

[ajith]

What's the difference in a factor and a multiple?

Oops a mistake in my answer - Thanks Sanju