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Sequence Problem

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by soni_pallavi » Sat Nov 17, 2012 5:33 am
Q1) A special sequence of numbers is written as 2,9,28,65,126...Find the ratio of the 7th term to the 15th term??

a)1/4
b)1/2
c)129/422
d)43/422
e)43/129

Answer D
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by Brent@GMATPrepNow » Sat Nov 17, 2012 8:19 am
soni_pallavi wrote:Q1) A special sequence of numbers is written as 2,9,28,65,126...Find the ratio of the 7th term to the 15th term??

a)1/4
b)1/2
c)129/422
d)43/422
e)43/129

Answer D

I've never seen a GMAT question involving a sequence without any information regarding its pattern, and I'm pretty sure that I never will. The reason for this is that can be more than one way to describe the pattern within any sequence of numbers.
As such, I believe the question is out of scope.

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Brent
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by soni_pallavi » Sat Nov 17, 2012 8:30 am
Thanks Brent.

This question was on a mock test I took. There must have been some error.
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by Brent@GMATPrepNow » Sat Nov 17, 2012 8:32 am
soni_pallavi wrote:Thanks Brent.

This question was on a mock test I took. There must have been some error.
On an official (GMATPrep) mock test?
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by soni_pallavi » Sat Nov 17, 2012 12:23 pm
No not on a GMAT Prep Official test...:)
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by GMATGuruNY » Sat Nov 17, 2012 2:16 pm
soni_pallavi wrote:Q1) A special sequence of numbers is written as 2,9,28,65,126...Find the ratio of the 7th term to the 15th term??

a)1/4
b)1/2
c)129/422
d)43/422
e)43/129

Answer D
The formula for the sequence seems to be:
S(n) = n³ + 1.
To illustrate:
S(1) = 1³ + 1 = 2.
S(2) = 2³ + 1 = 9.
And so on.

Thus: S(7) = 7³ + 1 and S(15) = 15³ + 1.

A helpful identity:
a³ + b³ = (a+b)(a²-ab+b²)

Thus:
S(7) / S(15) =

= (7³ + 1³)/(15³ + 1³)

= (7+1)(7² - 7*1 + 1²) / (15+1)(15² - 15*1 + 1²)

= 8*43 / 16*211

= 43/422.

The correct answer is D.

I agree that this question is beyond the scope of the GMAT.
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by soni_pallavi » Sat Nov 17, 2012 11:26 pm
Thanks Mitch...this helped!!
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