MathRevolution wrote:

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Math Revolution GMAT math practice question]

If \(m\) and \(n\) are integers, is \(mn\) an odd integer?

1) \(m(n+1)\) is even

2) \((m+1)n\) is even

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) = EVENTarget question: Is mn an odd integer? Given: m and n are integers Statement 1: m(n+1) is even Let's test some values.

There are several values of m and n that satisfy statement 1. Here are two:

Case a: m = 1 and n = 1. Notice that m(n + 1) = 1(1+1) = 2, which is even. In this case, mn = (1)(1) = 1. So, the answer to the target question is

YES, mn IS oddCase b: m = 2 and n = 2. Notice that m(n + 1) = 2(2+1) = 6, which is even. In this case, mn = (2)(2) = 4. So, the answer to the target question is

NO, mn is NOT oddSince we cannot answer the

target question with certainty, statement 1 is NOT SUFFICIENT

Statement 2: (m+1)n is evenLet's test some values (again).

IMPORTANT: When testing values a second time, check to see if you ran reuse either of the cases you used in statement 1. If we do that here, we'll see that we can reuse both cases:

Case a: m = 1 and n = 1. Notice that (m+1)n = (1+1)1 = 2, which is even. In this case, mn = (1)(1) = 1. So, the answer to the target question is

YES, mn IS oddCase b: m = 2 and n = 2. Notice that (m+1)n = (2+1)2 = 6, which is even. In this case, mn = (2)(2) = 4. So, the answer to the target question is

NO, mn is NOT oddSince we cannot answer the

target question with certainty, statement 1 is NOT SUFFICIENT

Statements 1 and 2 combined Notice that we were able to use the

same counter-examples to show that each statement ALONE is not sufficient.

So, the same counter-examples will satisfy the two statements COMBINED.

In other words,

Case a: m = 1 and n = 1. So, the answer to the target question is

YES, mn IS oddCase b: m = 2 and n = 2. So, the answer to the target question is

NO, mn is NOT oddSince we cannot answer the

target question with certainty, the combined statements are NOT SUFFICIENT

Answer: E

Cheers,

Brent

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