If x and y are integers, is (x+y)(y+1) an even integer?

Question

If x and y are integers, is (x+y)(y+1) an even integer?
(1) x is an even integer.
(2) y is an even integer.

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chetan2u · Answer

Kudos for correct solutions

Harsh9676 · Answer

IMO A

The product of two integers is even when i) either of the integers is even , ii) both the integers is even

ST1 : X is even. (Even + Y) (Y+1) , Y can be even or odd and if Y is even , the entire expression is even and if Y is odd, again the expression is even.

St1 is sufficient.

St 2 : Y is even >> (X + Even) (Odd) = if X is odd, the expression is odd and if X is even, the expression is even.

Therefore St 2 is insufficient.

rajatchopra1994 · Answer

Explanation:

Given: x and y are integers
To find: (x+y)(y+1) an even integer?

Statement 1: x is an even integer.
Case 1: when y is even.
then (x+y) will be even, (y+1) will be odd.
So, Even X Odd will give  Even

Case 2: when y is odd
then (x+y) will be odd, (y+1) will be even.
So, Odd X Even will give  Even

Sufficient

(2) y is an even integer.
Case 1 : When x is even integer.
then (x+y) will be even, (y+1) will be odd.
So, Even X Odd will give  Even

Case 2: when x is odd
then (x+y) will be odd, (y+1) will be odd.
So, Odd X Odd will give  Odd

Not Sufficient

IMO-A

If x and y are integers, is (x+y)(y+1) an even integer?

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