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Re: If x = -1 and n is the sum of the second 101 prime numbers, what is th [#permalink]
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Given: x=-1
n = Sum of the second 101 prime nos

In the second set of 101 prime nos,
1. There are no even nos
2. Sum of any two odd nos is a Even no

Since n is the sum of 101 prime nos, n = odd

Now,
(-1)^n+(-1)^(n+1)+(-1)^(n+2)+(-1)^(n+3)

As n = odd,
n+1= Even
n+2=Odd
n+3=Even
and (-1)^odd = (-1), and (-1)^Even = +1

On Solving,
-1+1-1+1=0

Alternatively, irrespective of whether n= odd/even, ans =0
Case 1: n = odd, n+1 = Even ,n+2 = odd, n+3 = Even (-1+1-1+1 = 0)
Case 2: n = Even, n+1 = odd, n+2 = Even, n+3 = Odd (-1+1-1+1 = 0)

Ans =C = 0
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Re: If x = -1 and n is the sum of the second 101 prime numbers, what is th [#permalink]
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The answer is 0
What ever may be the value of n ( either odd or even),
the expression x^n+x^n+1+x^n+2+x^n+3 will have two even power of x and two odd powers of x. Since x is -1, the expression reduces to +1+1-1-1=0 (order can vary )
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Re: If x = -1 and n is the sum of the second 101 prime numbers, what is th [#permalink]
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Expert Reply
Bunuel wrote:

Math Revolution and GMAT Club Contest Starts!



QUESTION #13:

If x=-1 and n is the sum of the second 101 prime numbers, what is the value of \(x^n + x^{(n+1)} + x^{(n+2)} + x^{(n+3)}\)?

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


Check conditions below:



Math Revolution and GMAT Club Contest

The Contest Starts November 28th in Quant Forum


We are happy to announce a Math Revolution and GMAT Club Contest

For the following four (!) weekends we'll be publishing 4 FRESH math questions per weekend (2 on Saturday and 2 on Sunday).

To participate, you will have to reply with your best answer/solution to the new questions that will be posted on Saturday and Sunday at 9 AM Pacific.
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NOTE: Test Prep Experts and Tutors are asked not to participate. We would like to have the members maximize their learning and problem solving process.

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MATH REVOLUTION OFFICIAL SOLUTION:

The sum of the second 101 prime numbers is the sum of the all prime numbers from the second prime number to the next 101 prime numbers. Except 2, every prime number is an odd number. So, n=3+5+…………..+prime=odd.

Then, \(x^n + x^{(n+1)} + x^{(n+2)} + x^{(n+3)}=(-1)^{odd}+(-1)^{even}+(-1)^{odd}+(-1)^{even}=(-1)+1+(-1)+1=0\), and the correct answer is C.
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Re: If x = -1 and n is the sum of the second 101 prime numbers, what is th [#permalink]
Probably a stupid question: What does "second" mean here? I got the question right but just by plugging in -1 due to gutfeeling :)
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Re: If x = -1 and n is the sum of the second 101 prime numbers, what is th [#permalink]
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expertesp wrote:
Probably a stupid question: What does "second" mean here? I got the question right but just by plugging in -1 due to gutfeeling :)


Agree the wording could be clearer.

The sum of the second 101 prime numbers is the sum of the all prime numbers from the second prime number to the next 101 prime numbers. Except 2, every prime number is an odd number. So, n=3+5+…………..+prime=odd.
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Re: If x = -1 and n is the sum of the second 101 prime numbers, what is th [#permalink]
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Re: If x = -1 and n is the sum of the second 101 prime numbers, what is th [#permalink]
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