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by sanju09 » Tue Jul 27, 2010 4:54 am
Ratio of sum of first 'n' integers to that of next 'n' integers is 3/8. What is the ratio of sum of squares of first 'n' integers to that of next 'n' integers?
A. 5
B. 10
C. 1/7
D. 1/6
E. 1/5


[spoiler]Options do not follow an order here. Can this be a GMAT question, overall?

Source: writegmat.com[/spoiler]
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by kmittal82 » Tue Jul 27, 2010 5:43 am
The question doesn't explicitly specify a few details like:

Is this a sum of positive integers?
Is the difference between the integers in the series constant?

Assuming the series starts from 1
Sum of a series of n terms = (first term + last term)*n/2

Sum of first n integers = (1+n)*n/2
Sum of next n integers = (n+1+2n)*n/2

Thus, we have (n+1)/(3n+1) = 3/8 => n = 5

So you need to find sum of square of first 5 integers = 1 + 4 + 9+ 16 + 25 = 55
Sum of squares of next 5 integers = 36 + 49 + 64 + 81 + 100 = 330

Ratio is 55/330 = 1/6

Hence (D)

I'm not sure if this could be a GMAT question, although I have yet to see questions which utilize any "sum of a series with n terms" type arithmetic.
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