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After the first term, each term in a sequence is five t

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After the first term, each term in a sequence is five t

by varun289 » Thu Dec 13, 2012 9:17 am
209. After the first term, each term in a sequence is five times greater than half the preceding term. If x is the first term of the sequence, and x does not equal zero, what is the value of the fourth term minus the second term an integer?
(1) x is a multiple of 12.
(2) x is a multiple of 56.
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by eaakbari » Thu Dec 13, 2012 10:29 am
IMO B

This is a geometric progression

with a = x

& d = 5/2

t(4) = x * (5/2)^3

t(2) = x * (5/2)^1

Difference = x * (5/2) [ (5/2)^2 - 1]

= x * (5/2) [ 21/4]

For the difference to be an integer x has to be divisible by 8.

I) x cannot be conclusively div by 8. Hence Insuff

II) x has to be div by 8. Hence Suff

Answer = B
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