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# If m and n are integers, is mn an odd integer?

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Math Revolution GMAT Instructor
Joined: 16 Aug 2015
Posts: 6949
GMAT 1: 760 Q51 V42
GPA: 3.82
If m and n are integers, is mn an odd integer?  [#permalink]

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30 Sep 2018, 23:39
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Difficulty:

45% (medium)

Question Stats:

66% (01:51) correct 34% (01:38) wrong based on 65 sessions

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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

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MathRevolution: Finish GMAT Quant Section with 10 minutes to spare
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"Only $149 for 3 month Online Course" "Free Resources-30 day online access & Diagnostic Test" "Unlimited Access to over 120 free video lessons - try it yourself" Director Joined: 18 Jul 2018 Posts: 670 Location: India Concentration: Finance, Marketing WE: Engineering (Energy and Utilities) Re: If m and n are integers, is mn an odd integer? [#permalink] ### Show Tags 30 Sep 2018, 23:50 From statement 1: m(n+1) is even. Let's consider numbers for easy simplification. m=1 n=3 then m(n+1) is even and mn = 3. Odd If m=2 n=4 then m(n+1) is even but mn = 8. Even. Insufficient. From statement 2: Same case as above. Insufficient. Combining both gives 2mn+m+n as even. 2mn will always be even. So m+n has to be even. If m=1 n=3. m+n is even Or If m=2 n=4. m+n is even. But mn will be even and odd. Hence Combining also doesn't give a unique answer. E is the answer. _________________ Press +1 Kudo If my post helps! CEO Status: GMATINSIGHT Tutor Joined: 08 Jul 2010 Posts: 2775 Location: India GMAT: INSIGHT Schools: Darden '21 WE: Education (Education) Re: If m and n are integers, is mn an odd integer? [#permalink] ### Show Tags 01 Oct 2018, 01:59 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 Question: Is mn odd? Question: Are each if m and n odd? Statement 1: $$m(n+1)$$ is even i.e. either m is even and n+1 is even OR m is odd and n+1 is even or m and n+1 both are even i.e. either m is even and n is odd OR m is odd and n is odd i.e. mn may be even or mn may be Odd NOT SUFFICIENT Statement 2: $$(m+1)n$$ is even i.e. either n is even and m+1 is even OR n is odd and m+1 is even or m and n+1 both are even i.e. either n is even and m is odd OR n is odd and m is odd i.e. mn may be even or mn may be Odd NOT SUFFICIENT Combining the two statements i.e. either n is even and m is odd OR n is odd and m is odd i.e. mn may be even or mn may be Odd NOT SUFFICIENT Answer: Option E _________________ Prosper!!! GMATinsight Bhoopendra Singh and Dr.Sushma Jha e-mail: info@GMATinsight.com I Call us : +91-9999687183 / 9891333772 Online One-on-One Skype based classes and Classroom Coaching in South and West Delhi http://www.GMATinsight.com/testimonials.html ACCESS FREE GMAT TESTS HERE:22 ONLINE FREE (FULL LENGTH) GMAT CAT (PRACTICE TESTS) LINK COLLECTION CEO Joined: 11 Sep 2015 Posts: 3431 Location: Canada Re: If m and n are integers, is mn an odd integer? [#permalink] ### Show Tags 01 Oct 2018, 06:03 Top Contributor 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) = EVEN Target 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 odd Case 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 odd Since we cannot answer the target question with certainty, statement 1 is NOT SUFFICIENT Statement 2: (m+1)n is even Let'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 odd Case 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 odd Since 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 odd Case b: m = 2 and n = 2. So, the answer to the target question is NO, mn is NOT odd Since we cannot answer the target question with certainty, the combined statements are NOT SUFFICIENT Answer: E Cheers, Brent _________________ Test confidently with gmatprepnow.com Math Revolution GMAT Instructor Joined: 16 Aug 2015 Posts: 6949 GMAT 1: 760 Q51 V42 GPA: 3.82 Re: If m and n are integers, is mn an odd integer? [#permalink] ### Show Tags 03 Oct 2018, 01:23 => 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. Modifying the question: mn is odd only when both m and n are odd. So, the question asks if both m and n are odd. Conditions 1) and 2), when applied together, tell us that either both m and n are odd numbers or both m and n are even numbers. Since we don’t have a unique solution, both conditions, taken together, are not sufficient. Therefore, E is the answer. Answer: E _________________ MathRevolution: Finish GMAT Quant Section with 10 minutes to spare The one-and-only World’s First Variable Approach for DS and IVY Approach for PS with ease, speed and accuracy. "Only$149 for 3 month Online Course"
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Re: If m and n are integers, is mn an odd integer?   [#permalink] 03 Oct 2018, 01:23
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