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If x and y are integers, is y an odd integer?

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If x and y are integers, is y an odd integer?  [#permalink]

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New post 01 Oct 2018, 04:29
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A
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C
D
E

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  35% (medium)

Question Stats:

70% (01:39) correct 30% (01:16) wrong based on 20 sessions

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Re: If x and y are integers, is y an odd integer?  [#permalink]

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New post 01 Oct 2018, 04:35
Bunuel wrote:
If x and y are integers, is y an odd integer?

(1) y(y + 2)= x(x + 1)
(2) x is not an even integer


Question: is y an odd integer?


Statement 1: y(y + 2)= x(x + 1)

x(x+1) is product of two consecutive integers which must be EVEN becaus ethere is always one even integer between two consecutive integers
i.e. y(y+2) should also be even BUT either y and y+2 both be even or both will be ODD therefore we may concludet hat y MUST be EVEN

SUFFICIENT

Statement 2: x is not an even integer
No relation of y with x hence
NOT SUFFICIENT

Answer: Option A
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Re: If x and y are integers, is y an odd integer?  [#permalink]

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New post 01 Oct 2018, 04:49
1
Given that x and y are integers. We are asked to find if y is an odd integer or not.
From statement 1 we know that
y(y+2) = x(x+1)
Analyzing RHS first,
We get to know that x(x+1) = product of consecutive integers = which is always even.
Say, if x is odd then x+1 is even => x(x+1) = odd*even = even
If x is even then x+1 is odd => x(x+1) = even*odd = even
So, RHS is always even.
So, y(y+2) = even.
Now, Analyzing LHS, we get that,
y(y+2) = product of consecutive odd or even integers.
So, for LHS = RHS , y(y+2) = even ==> y(y+2) is the product of consecutive even integers.
Because, if y(y+2) is product of consecutive odd integers then y(y+2) is odd, which is contradictory to LHS.
Hence y is an even integer.
So Statement 1 is sufficient.

Statement 2 gives us the information of x being an odd integer, but per say we do not have any information regarding the relationship between x and y.
So, statement 2 is insufficient.

Corollary: For this question Statement is enough. But without wholly analyzing statement 1 , one may fall into the trap of taking the support of statement 2. Hence mark the wrong option C.
Finally, the correct option is A.
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Re: If x and y are integers, is y an odd integer? &nbs [#permalink] 01 Oct 2018, 04:49
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