If x and y are integers, is x odd? (1) xy + y is odd (2) y is odd

Question

If x and y are integers, is x odd?

(1) xy + y is odd
(2) y is odd

Sarmadk5 · Answer

Solution:- E

(1) xy+y= odd
As odd x odd =even 
 Even x even = even 
 even + odd = odd

Statement 1 Not sufficient

Statement (2) y is odd , not sufficient , no information about X .

Combined both :- not sufficient.

Answer is (E) Neither Sufficient

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sumit99kr · Answer

S1) xy + y is odd i.e, y(x+1) is odd. Product of two quantities is odd only when both are odd. 
'y' is odd and (x+1) is odd. 
If (x+1) is odd then x is even. 
Hence S1 is sufficient.

S2) y is odd, we cannot conclude anything about x, hence not sufficient.

Hence I would go with A.

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Sarmadk5 · Answer

ScottTargetTestPrep · Answer

Statement One Alone:

\Rightarrow  xy + y is odd

Remember that if a number is odd, then all of its factors must also be odd. If we factor y out of xy + y, we obtain y(x + 1). Since y(x + 1) is odd, both y and x + 1 must be odd, which means x is even. Thus, the answer to the question is no. Statement one alone is suffcient.

Eliminate answer choices B, C, and E.

Statement Two Alone:

\Rightarrow  y is odd

Without any information about x, we cannot determine whether x is even or odd. Statement two alone is not suffcient.

Answer: A

gmatophobia · Answer

Statement 1

xy + y = odd

Case 1:  y is odd

xy = odd - odd = even

We know y is odd, so x = even

Case 2:  y is even

xy = odd - even = odd

This is not possible, as y is even so the product of two integers has to be even. We will discard case 2.

The statement is sufficient.

Statement 2

y is odd

Insufficient.

Option A

If x and y are integers, is x odd? (1) xy + y is odd (2) y is odd

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GMAT Data Sufficiency (DS) Questions

If x and y are integers, is x odd? (1) xy + y is odd (2) y is odd

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