If xy = y, what is the value of |x| + |y|? (1) x = -1 (2) y = 0

Question

If  xy=y , what is the value of  |x|+|y| ?

(1)  x=-1 
(2)  y=0

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cdrectenwald · Answer

I like A

When we know that X = -1 we then know that -y = y which I only believe is true for 0. This we know abs(x) + abs(y)

B is not sufficient because we don’t know x

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littlesourris · Answer

Does someone have the OA for this question ?
Why not B ? 
xy=y => x= y/y=1 => |x| + |y| = 1+|y|

Bunuel · Answer

You cannot reduce  xy=y  by y to get  x=1 . That's because y can be 0, and we cannot divide by 0. By doing so, you lose a solution, namely y = 0.

What you can do is rearrange and factor out y:

xy=y 
 xy-y=0 
 y(x-1)=0 
 y=0  or  x=1  (or both)

Never reduce an equation by a variable (or expression with a variable) if you are not certain that the variable (or expression containing the variable) is not equal to zero. We cannot divide by zero.

Back to the question;

If  xy=y , what is the value of  |x|+|y| ?

(1)  x=-1

Since x = -1, then x is not 1, and thus y must be 0 for the equation ( xy=y ) to hold. Therefore,  |x|+|y|=1+0=1 . Sufficient.

(2)  y=0

When  y=0 , then from  xy=y , x can be any number, therefore we cannot determine the specific value of  |x|+|y| . Not sufficient.

Answer: A.

Hope it's clear.

If xy = y, what is the value of |x| + |y|? (1) x = -1 (2) y = 0

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