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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, 12:35

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
_________________

I'd love to hear any feedback or ways to improve my problem solving. I make a lot of silly mistakes. If you've had luck improving on stupid mistakes, I'd love to hear how you did it.

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

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01 Nov 2017, 17:03

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

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.