MathRevolution wrote:
[
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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