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# If x=-1 and n is the sum of all prime numbers less than 100,

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Math Revolution GMAT Instructor
Joined: 16 Aug 2015
Posts: 4920
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If x=-1 and n is the sum of all prime numbers less than 100, [#permalink]

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31 Oct 2017, 00:59
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Question Stats:

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[GMAT math practice question]

If x=-1 and n is the sum of all prime numbers less than 100, what is the value of $$x^n+x^{n+1}+x^{n+2}+x^{n+3}+x^{n+4}+x^{n+5}$$?

A. -2
B. -1
C. 0
D. 1
E. 2
[Reveal] Spoiler: OA

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Re: If x=-1 and n is the sum of all prime numbers less than 100, [#permalink]

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31 Oct 2017, 01:05
Option C

When n is odd, first, third, fifth terms are odd. Hence these terms add up to -3 and the remaining terms add to +3. Hence total value is 0.

When n is even the case is reverse. Again 0

Hence the value of n doesn’t matter.

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Re: If x=-1 and n is the sum of all prime numbers less than 100, [#permalink]

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31 Oct 2017, 01:05
MathRevolution wrote:
[GMAT math practice question]

If x=-1 and n is the sum of all prime numbers less than 100, what is the value of $$x^n+x^{n+1}+x^{n+2}+x^{n+3}+x^{n+4}+x^{n+5}$$?

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

Similar question: https://gmatclub.com/forum/if-x-1-and-n ... 32331.html
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Re: If x=-1 and n is the sum of all prime numbers less than 100, [#permalink]

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31 Oct 2017, 11:35
MathRevolution wrote:
[GMAT math practice question]

If x=-1 and n is the sum of all prime numbers less than 100, what is the value of $$x^n+x^{n+1}+x^{n+2}+x^{n+3}+x^{n+4}+x^{n+5}$$?

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

I got C, thought it took me to long at 2:58. About 90 secs in I realized that the sum of all primes under 100 is going to be even. Odd+odd...+odd+even=even. Therefore, the sequence of the exponents will be even, odd, even, odd, even, odd. So 1+-1+1+-1+1+-1=0
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Re: If x=-1 and n is the sum of all prime numbers less than 100, [#permalink]

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01 Nov 2017, 16:03
there is no need to find whether n is even or odd.
this question involves n, n+1, n+2, n+3, n+4, n+5. Either n is odd or even, we have 3 even and 3 odd. So
Question reduces to 3( (-1)^e +(-1)^o ) = 3(1-1) = 0. Hence Answer is C.

PS: those who want to know whether n is even or odd. As we know we have 25 prime numbers less than 100, out of which smallest prime no, is 2. So n= e+ 24*o = e+e = e. Hence, n = even
Math Revolution GMAT Instructor
Joined: 16 Aug 2015
Posts: 4920
GPA: 3.82
Re: If x=-1 and n is the sum of all prime numbers less than 100, [#permalink]

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02 Nov 2017, 00:09
=>

Whatever the value of n is, $$(-1)^n+(-1)^{n+1}+(-1)^{n+2}+(-1)^{n+3}+(-1)^{n+4}+(-1)^{n+5} = 0$$, since two consecutive integer n and n+1 always have an odd integer and an even integer, and so $$(-1)^n+(-1)^{n+1}$$ = 0.

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Re: If x=-1 and n is the sum of all prime numbers less than 100,   [#permalink] 02 Nov 2017, 00:09
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