If x = -1 and n is the sum of the first 100 prime numbers, what is the

Question

If x = -1 and n is the sum of the first 100 prime numbers, what is the value of  x^n + x^{n+1}+x^{n+2} ?

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

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AbhinavShah14 · Answer

For this answer we don't need to know the first 100 prime number, neither the sum of it. We just need to know that 2, the only prime number that is an even number. Now the sum of an even and an odd number is an odd number.

So  x^n  where  x  is -1 &  n  is the sum of the first 100 prime numbers, which is an odd number, the answer will be -1. As -1^to any odd number is -1.

When  x^n^+1 ,  n  becomes an even number (odd + odd = even), the answer will be 1, as -1^any even number is 1.

Again  x^n^+2 , the answer will be  -1 .

So the sum of -1+1-1 =  -1 (B)

Catman · Answer

x^n+x^{n+1}+x^{n+2}
x^n(1+x+x^2)
x^n(1-1+1)
x^n
-1^n

Out of the first 100 prime numbers only "2" is the even prime number, rest 99 are odd prime number. 
Sum of 1 Prime Even Number +99 Odd Prime Number = Odd Number
 -1^{odd} 
 x^n+x^{n+1}+x^{n+2}  = -1

KESHU99W · Answer

but 100 prime number will be even becase 99 odd will give you Even number and even + even is even

Bunuel · Answer

Yes, the sum of the first 100 prime numbers will be odd, so n will be odd. So, we'd have:

x^n + x^{n+1}+x^{n+2}=

=(-1)^{odd} + (-1)^{even}+(-1)^{odd}=

=(-1) + 1 + (-1)= -1

Answer: B,

Hope it helps.

Trisha241 · Answer

There are 25 prime numbers less than 100.

2+3+5+7+11+13+17+19+23+29+31+37+41+43+47+53+59+61+67+71+73+79+83+89+97 = 1060

Sum of all these numbers is 1060 and hence an even number.

Bunuel · Answer

n is the sum of the first 100 prime numbers, not the sum of the primes less than 100.

If x = -1 and n is the sum of the first 100 prime numbers, what is the

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GMAT Problem Solving (PS) Questions

If x = -1 and n is the sum of the first 100 prime numbers, what is the

Prep Toolkit

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