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# If m=-1 and n = 1^2 + 2^2 + … + 10^2,

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Math Revolution GMAT Instructor
Joined: 16 Aug 2015
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If m=-1 and n = 1^2 + 2^2 + … + 10^2,  [#permalink]

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30 Jul 2018, 01:11
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5% (low)

Question Stats:

85% (01:35) correct 15% (01:36) wrong based on 54 sessions

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[Math Revolution GMAT math practice question]

If $$m=-1$$ and $$n = 1^2 + 2^2 + … + 10^2$$, what is the value of $$m^n+m^{n+1}+m^{n+2}+m^{n+3}$$?

$$A. -2$$
$$B. -1$$
$$C. 0$$
$$D. 1$$
$$E. 2$$

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MathRevolution: Finish GMAT Quant Section with 10 minutes to spare
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"Only $99 for 3 month Online Course" "Free Resources-30 day online access & Diagnostic Test" "Unlimited Access to over 120 free video lessons - try it yourself"  Math Revolution Discount Codes EMPOWERgmat Discount Codes Magoosh Discount Codes Math Expert Joined: 02 Aug 2009 Posts: 6554 Re: If m=-1 and n = 1^2 + 2^2 + … + 10^2, [#permalink] ### Show Tags 30 Jul 2018, 01:45 MathRevolution wrote: [Math Revolution GMAT math practice question] If $$m=-1$$ and $$n = 1^2 + 2^2 + … + 10^2$$, what is the value of $$m^n+m^{n+1}+m^{n+2}+m^{n+3}$$? $$A. -2$$ $$B. -1$$ $$C. 0$$ $$D. 1$$ $$E. 2$$ since we are looking at BASE = -1 and n,n+1,n+2,n+3 are consecutive numbers TWO will be odd and TWO will be even -1^even is 1 and -1^odd = -1, so two 1 and two -1 sum = 0 otherwise $$n = 1^2 + 2^2 + … + 10^2$$ odd terms are - FIVE - $$1^2+3^2+5^2+7^2+9^2$$, so sum of FIVE odd is ODD and hence n is odd $$(-1)^{odd}+(-1)^{even}+(-1)^{odd}+(-1)^{even}=-1+1-1+1=0$$ c _________________ 1) Absolute modulus : http://gmatclub.com/forum/absolute-modulus-a-better-understanding-210849.html#p1622372 2)Combination of similar and dissimilar things : http://gmatclub.com/forum/topic215915.html 3) effects of arithmetic operations : https://gmatclub.com/forum/effects-of-arithmetic-operations-on-fractions-269413.html GMAT online Tutor Manager Joined: 04 Aug 2010 Posts: 237 Schools: Dartmouth College If m=-1 and n = 1^2 + 2^2 + … + 10^2, [#permalink] ### Show Tags 30 Jul 2018, 03:21 1 MathRevolution wrote: [Math Revolution GMAT math practice question] If $$m=-1$$ and $$n = 1^2 + 2^2 + … + 10^2$$, what is the value of $$m^n+m^{n+1}+m^{n+2}+m^{n+3}$$? $$A. -2$$ $$B. -1$$ $$C. 0$$ $$D. 1$$ $$E. 2$$ $$(-1)^{odd} = -1$$ $$(-1)^{even} = 1$$ The exponents for the expression in blue are 4 consecutive integers -- $$n, n+1, n+2, n+3$$ -- implying that two of the exponents will be ODD, while the other two will be EVEN. Thus, two of the terms in the blue expression must be equal to -1, while the other two must be equal to 1: $$-1 + -1 + 1 + 1 = 0$$ _________________ GMAT and GRE Tutor Over 1800 followers Click here to learn more GMATGuruNY@gmail.com New York, NY If you find one of my posts helpful, please take a moment to click on the "Kudos" icon. Available for tutoring in NYC and long-distance. For more information, please email me at GMATGuruNY@gmail.com. Math Revolution GMAT Instructor Joined: 16 Aug 2015 Posts: 6028 GMAT 1: 760 Q51 V42 GPA: 3.82 Re: If m=-1 and n = 1^2 + 2^2 + … + 10^2, [#permalink] ### Show Tags 01 Aug 2018, 02:07 => $$m^n+m^{n+1}+m^{n+2}+m^{n+3} = m^n(1+m^1+m^2+m^3) = (-1)^n(1+(-1)^1+(-1)^2+(-1)^3) = (-1)^n* 0 = 0$$ Whatever the value of n is, the answer is $$0$$. Therefore, C is the answer. Answer: C _________________ 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$99 for 3 month Online Course"
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Re: If m=-1 and n = 1^2 + 2^2 + … + 10^2, &nbs [#permalink] 01 Aug 2018, 02:07
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