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

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After the first term, each term in a sequence is five times [#permalink] New post 27 Oct 2010, 17:44
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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, 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.
[Reveal] Spoiler: OA

Last edited by Bunuel on 08 Dec 2014, 03:16, edited 2 times in total.
corrected the language
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Re: After the first term, each term in a sequence is five times [#permalink] New post 27 Oct 2010, 18:02
You should make clear the question whether:

1. What is the value of the 4 term minus the second?
2. Is the value of the 4term minus the second an integer?

if 2 is correct, A is sufficient
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Re: After the first term, each term in a sequence is five times [#permalink] New post 27 Oct 2010, 23:29
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So the first term is x
Every subsequent term is obtained by multiplying by (5/2)
Fourth term is (125/8)x and second term is (5/2)x
Difference is (105/8)x

The way to satisfy this being an integer is to ensure that x is divisible by 8.

(1) x is a multiple of 12 ... Insufficient : May not be divisible by 8. Eg. x=36
(2) x is a multiple of 56 ... Sufficient ! ... will always be divisible by 8

Answer : (b)
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Re: After the first term, each term in a sequence is five times [#permalink] New post 07 Dec 2014, 20:06
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Re: After the first term, each term in a sequence is five times   [#permalink] 07 Dec 2014, 20:06
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After the first term, each term in a sequence is five times

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