Are X and Y intergers? 1. x*y is an integer. 2. X+y is an

Question

Are X and Y intergers?

1. x*y is an integer.
2. X+y is an integer.

ywilfred · Answer

1. Insufficient. x*y can be 1/2 * 2 which will yield an integer product.

2. Insufficient. x+y can be 1/2 + 1/2 which will yield an integer sum.

Using (1) and (2), we can tell that x and y must be integer. In order for x to be a fraction and x*y to be an integer, y must be the reciprocal of x. However, if we hold that case, then x+y will not be an integer.

For instance, x*y = 1/2 * 2 = 1 -> integer, but x+y = 1/2 + 2 != integer.

Ans C

sperumba · Answer

This was exactly my reasoning but PR says the answer is E. 

I was thinking it might be wrong.. 

I have the 2005 edittion it on page 168 problem 3 in drill 11.

I was bummed that is y i posted this here . ....

now that ywilfred says C too i am confident that PR is wrong.

Professor · Answer

suppose x = sqrt(2) and y = - sqrt(2)

from i, x*y = -2 => insuff.
from ii, x+y = 0. => also insuff.
therefore, E.

hence, we can use some other values for x and y.

sperumba · Answer

wow never thought of that possibility.

Now it all makes sence.

giddi77 · Answer

reasoning professor!

SunShine · Answer

E.

I and II not sufficient

if x = 1/2 and Y = 2 x*y -> integer, but X is not.

x=1/2, y= 1/2, x+y -> integer, niether x, y is integer.

ywilfred · Answer

woah !! This combination didn't occur to me

Are X and Y intergers? 1. x*y is an integer. 2. X+y is an

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