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