Another piece of cake: If x is an odd integer, is y an odd

Question

Another piece of cake:


If x is an odd integer, is y an odd integer?

(1) The average of x and y is odd.
(2) The average of x, y, and (y + 1) is an integer.

Amit05 · Answer

The Ans is A.

Given: X is odd.

1 : Av of x and y is Odd.
=> x+y = even

odd + odd = even
odd + even = odd
even + even = even

since x is odd, y has to be even. Hence we can say that y is NOT odd. Suff.

2: 
The average of x, y, and (y + 1) is an integer
=> x+y+y+1 = odd or even
=> x + 2y = odd or even
So, by plugging numbers, we find that there are 2 values for above eq'n. Insuff.

Hence Ans is A.

Ravshonbek · Answer

1.--suffice.

x-odd y?
to be odd, the average of two numbers, numbers should be each odd or even.
we already know that x is odd, and the average of x, y is odd so y has to be odd. 
odd+odd=even, the average can be odd 
suffice.

2. x+y+y+1, x+2y+1, from here we know that x is odd, 
x+2y+1=even we cannot conclude that y is odd 
insuff.

A

Sumithra Sen · Answer

I substituted Values with X being Odd and other values of Y

Another piece of cake: If x is an odd integer, is y an odd

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