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If x and y are integers, is x^2+x+y an even number?

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Math Revolution GMAT Instructor
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If x and y are integers, is x^2+x+y an even number? [#permalink]

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New post 05 Dec 2017, 01:00
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A
B
C
D
E

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  25% (medium)

Question Stats:

71% (00:41) correct 29% (00:40) wrong based on 41 sessions

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[GMAT math practice question]

If \(x\) and \(y\) are integers, is \(x^2+x+y\) an even number?

1) \(x=5\)
2) \(y=5\)
[Reveal] Spoiler: OA

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Re: If x and y are integers, is x^2+x+y an even number? [#permalink]

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New post 05 Dec 2017, 01:34
First, we can easily get rid of powers, because it doesn't affect the process of reasomning

(1) x=5=Odd, so we have
Odd+Odd+ Even/Odd =Even+ Even/Odd=Even/Odd
Insufficient
(2) y=5=Odd
1 case: x=Even
Even+Even+Odd=Odd
2 case: x=Odd
Odd+Odd+Odd=Odd
Sufficient

Answer B
Expert Post
Math Revolution GMAT Instructor
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Re: If x and y are integers, is x^2+x+y an even number? [#permalink]

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New post 06 Dec 2017, 23:58
=>

Forget conventional ways of solving math questions. For DS problems, the VA (Variable Approach) method is the quickest and easiest way to find the answer without actually solving the problem. Remember that equal numbers of variables and independent equations ensure a solution.

The first step of the VA (Variable Approach) method is to modify the original condition and the question, and then recheck the question.

Since \(x^2+x=x(x+1)\) is always even, the question is really asking, “is y even?”. Condition 1) tells us nothing about the value of y, so it is not sufficient. Since condition 2) tells us that y = 5, it is sufficient, and the answer is B.
Condition 2)
Setting \(y = 5 yields\)
\(x^2+x+y = x^2+x+5 = x(x+1) + 5,\)
which is odd since x(x+1) is the product of two consecutive integers, one of which must be even.
The answer is ‘no’.
This is sufficient by CMT(Common Mistake Type) 1.

Therefore, the answer is B.
Normally, in problems which require 2 or more additional equations, such as those in which the original conditions include 2 variables, or 3 variables and 1 equation, or 4 variables and 2 equations, each of conditions 1) and 2) provide an additional equation. In these problems, the two key possibilities are that C is the answer (with probability 70%), and E is the answer (with probability 25%). Thus, there is only a 5% chance that A, B or D is the answer. This occurs in common mistake types 3 and 4. Since C (both conditions together are sufficient) is the most likely answer, we save time by first checking whether conditions 1) and 2) are sufficient, when taken together. Obviously, there may be cases in which the answer is A, B, D or E, but if conditions 1) and 2) are NOT sufficient when taken together, the answer must be E).

Answer: B
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Re: If x and y are integers, is x^2+x+y an even number?   [#permalink] 06 Dec 2017, 23:58
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