If x and y are integers, is x^3+3x-y an even number?

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[Math Revolution GMAT math practice question]

If x and y are integers, is x^3+3x-y an even number?

1) x=11
2) y=10

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by Brent@GMATPrepNow » Wed Aug 22, 2018 4:56 am

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Max@Math Revolution wrote:[Math Revolution GMAT math practice question]

If x and y are integers, is x³ + 3x - y an even number?

1) x = 11
2) y = 10
-----ASIDE-------------------------
Some important rules:
1. ODD +/- ODD = EVEN
2. ODD +/- EVEN = ODD
3. EVEN +/- EVEN = EVEN
4. (ODD)(ODD) = ODD
5. (ODD)(EVEN) = EVEN
6. (EVEN)(EVEN) = EVEN

-------------------------------------
Target question: Is x³ + 3x - y an even number?

Statement 1: x = 11
Let's TEST some values.
There are several values of x and y that satisfy statement 1. Here are two:
Case a: x = 11 and y = 0. In this case, x³ + 3x - y = 11³ + 3(11) - 0 = ODD + ODD - EVEN = EVEN. So, the answer to the target question is YES, x³ + 3x - y is even
Case b: x = 11 and y = 1. In this case, x³ + 3x - y = 11³ + 3(11) - 1 = ODD + ODD - ODD= ODD. So, the answer to the target question is NO, x³ + 3x - y is NOT even
Since we cannot answer the target question with certainty, statement 1 is NOT SUFFICIENT

Statement 2: y = 10
IMPORTANT: Notice that x³ + 3x is EVEN for all integer values of x. Here's why.
If x is EVEN, then x³ + 3x = EVEN³ + 3(EVEN) = EVEN + EVEN = EVEN
If x is ODD, then x³ + 3x = ODD³ + 3(ODD) = ODD + ODD = EVEN
So, we can see that x³ + 3x is always EVEN, regardless of the value of x.

Statement 2 tells us that y is EVEN.
So, x³ + 3x - y = EVEN - EVEN = EVEN
This means the answer to the target question is YES, x³ + 3x - y is even
Since we can answer the target question with certainty, statement 2 is SUFFICIENT

Answer: B

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Brent
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by fskilnik@GMATH » Wed Aug 22, 2018 12:02 pm

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by Max@Math Revolution » Thu Aug 23, 2018 11:47 pm

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=>
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. We then recheck the question.

x^3+3x is always even number, regardless of the value of x. If y is even, then x^3+3x-y is an even number, and if y is odd, then x^3+3x-y is odd.

Thus, condition 2) is sufficient.

Condition 1) is not sufficient since it tells us nothing about the value of y.

Therefore, B is the answer.
Answer: B