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GMAT exam question won't leave me alone

Problem Solving — algebra and arithmetic (GMAT Focus Edition)
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by SoftwareDrone » Mon Aug 13, 2012 7:52 pm
Hey, I just passed the GMAT!! :-)) CELEBRATION!!!! :-D

However..........
There was this ONE PROBLEM that keeps eating at me!
It says let x = -1. Then it gives a formula and that formula is x to the power of n plus x to the power of (n-1) plus x to the power of (n-2). So, x^n + x^(n-1) + x^(n-2). Then it says that n is the sum of all the prime numbers up to 403. WTF?????????
How am I supposed to know that?? Not fair.
I can see that if n was odd, then the answer would be -1 and if n was even, the answer would be 1. But how do they expect me to know the sum of all the prime numbers up to 403?
If there were an even number of prime numbers, and all are odd except 2, then we would have odd + odd + even = even. If there were an odd number of prime numbers, then we would have odd + odd + odd + even = odd.
????????????????????????
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Source: — Quantitative Reasoning |

by theCEO » Wed Aug 15, 2012 4:19 pm
What was the question asking for?
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by SoftwareDrone » Wed Aug 15, 2012 5:10 pm
theCEO wrote:What was the question asking for?
Sorry about that. :-)
The question was asking the value of f(x), where f(x) = x^n + x^(n-1) + x^(n-2) where n = the sum of all of the prime numbers up to 430.
If that sum is odd, then the answer would be -1 (-1 + 1 + -1). If even, then the answer would be 1 (1 + -1 + 1). The trick is finding out whether n is odd or even.
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by dabral » Thu Aug 16, 2012 11:54 am
SoftwareDrone,

I highly doubt that on the GMAT they would expect you to know if there are an even or an odd number of prime numbers up to say 403. This would require one to know all the prime numbers from 1 to 403, and on the GMAT they only test prime numbers less than 100. I haven't seen such a question on the GMAT so far.

However, I do expect them to test the following variants:
What is the value of (-1)^n + (-1)^(n+1) + (-1)^(n+2) where n is:

Variation#1) The product of prime numbers less than 403.

Variation#2) The sum of the first 403 prime numbers. (This is different from the sum of the prime numbers less than 403)

My guess is they asked you Variation#2.

Cheers,
Dabral
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by SoftwareDrone » Thu Aug 16, 2012 11:59 am
dabral wrote:SoftwareDrone,
However, I do expect them to test the following variants:
What is the value of (-1)^n + (-1)^(n+1) + (-1)^(n+2) where n is:

Variation#2) The sum of the first 403 prime numbers. (This is different from the sum of the prime numbers less than 403)

Cheers,
Dabral
I had been thinking the same thing. This variant was probably the real question.
Thanks!
:-)
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by DFritschy » Thu Aug 16, 2012 12:16 pm
So can someone please explain the answer using the variants listed above?
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by dabral » Thu Aug 16, 2012 12:30 pm
DFritschy,

I will give you a hint:
How many of the first 403 prime numbers are odd and how many are even? What would be the sum of the resulting set of integers? Odd or Even? And why?

What is the value of (-1)^n + (-1)^(n+1) + (-1)^(n+2) where n is:

Variation#2) The sum of the first 403 prime numbers.

Dabral
Free Video Explanations: 2021 GMAT OFFICIAL GUIDE.
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