MathRevolution wrote:
[
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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