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m is an even integer, and n is an odd integer. What is (-1)mn (-1)m-n {(-1)2m-1(3 + 2) - (-1)2n(3 - 2)}?

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m is an even integer, and n is an odd integer. What is (-1)mn (-1)m-n {(-1)2m-1(3 + 2) - (-1)2n(3 - 2)}?

by Max@Math Revolution » Fri Jul 03, 2020 1:49 am

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[GMAT math practice question]

m is an even integer, and n is an odd integer. What is (-1)^{mn} (-1)^{m-n} {(-1)^{2m-1}(3 + 2) - (-1)^{2n}(3 - 2)}?

A. 2
B. 4
C. 6
D. 8
E. 10
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Re: m is an even integer, and n is an odd integer. What is (-1)mn (-1)m-n {(-1)2m-1(3 + 2) - (-1)2n(3 - 2)}?

by GMATinsight » Fri Jul 03, 2020 4:14 am
Max@Math Revolution wrote: ↑
Fri Jul 03, 2020 1:49 am
 [GMAT math practice question]

m is an even integer, and n is an odd integer. What is (-1)^{mn} (-1)^{m-n} {(-1)^{2m-1}(3 + 2) - (-1)^{2n}(3 - 2)}?

A. 2
B. 4
C. 6
D. 8
E. 10
(-1)^Even = +1
(-1)^odd = -1

m = even, n = odd
i.e m+n or m-n = Odd
and m*n = Even

(-1)^{mn} (-1)^{m-n} {(-1)^{2m-1}(3 + 2) - (-1)^{2n}(3 - 2)} = (+1)*(-1)*{(-1)*5 - (+1)*1} = 6

Answer: Option C

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Re: m is an even integer, and n is an odd integer. What is (-1)mn (-1)m-n {(-1)2m-1(3 + 2) - (-1)2n(3 - 2)}?

by Max@Math Revolution » Sun Jul 05, 2020 6:11 pm
=>

(-1)^mn (-1)^(m-n)(-1)^(2m-1)(3+2) -(-1)^2n(3-2)
= (-1)^(even·odd) (-1)^(even-odd) (-1)^(2·even-1)(5) - (-1)^(2·odd)(1)
= (-1)^even (-1)^odd (-1)^odd(5) - (-1)^even(1)
= 1·(-1)·(-1)·5 - 1·1
= 5 - 1
= 4.


Therefore, B is the correct answer.
Answer: B
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