MathRevolution wrote:

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Math Revolution GMAT math practice question]

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

\(1) x=11\)

\(2) y=10\)

-----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 evenCase 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 evenSince we cannot answer the

target question with certainty, statement 1 is NOT SUFFICIENT

Statement 2: y = 10IMPORTANT: 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 evenSince we can answer the

target question with certainty, statement 2 is SUFFICIENT

Answer: B

Cheers,

Brent

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