In the infinite sequence S, where S1 = 25, S2 = 125, S3 = 225, ..., Sk = 100*(k-1) + 25, is odd integer x a divisor of every member of S?

(1) For all values of k ≥ 3, x is a divisor of Sk.

(2) x is a divisor of 500.

here it goes--

S1= 25 then its divisors can be - 1,5,25
s2= 125 then its divisors can be - 1,5,25,125
s3 = 225 then its divisors can be - 1,3,5,9,25
s4= 325 then its divisors can be - 1,5,25,13
s5= 425 then its divisors can be - 1,5,25,17
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statement 1 says x can be 1,5,25 ( since its common in all Sk) since these( 1,5,25) are divisors of every member of S this answers our question.
Statement 2 - x can be 1,2,4,5,25,125 hence not sufficient.

IMO- A

@ force5: just one small question:
from stat 1 we know x can be 1,5,25 (odd and factors of S) but we cannot identify one odd integer (as the Q asks)
also from stat 1 we know 13,17 (odd and NOT divisors of S)
hence should we not mark it as INSUFFICIENT since we have multiple values of X that satisfy the solution in first case?

force5 wrote:

In the infinite sequence S, where S1 = 25, S2 = 125, S3 = 225, ..., Sk = 100*(k-1) + 25, is odd integer x a divisor of every member of S?

(1) For all values of k ≥ 3, x is a divisor of Sk.

(2) x is a divisor of 500.

here it goes--

S1= 25 then its divisors can be - 1,5,25
s2= 125 then its divisors can be - 1,5,25,125
s3 = 225 then its divisors can be - 1,3,5,9,25
s4= 325 then its divisors can be - 1,5,25,13
s5= 425 then its divisors can be - 1,5,25,17
. .
. .
. .
. .
. .
statement 1 says x can be 1,5,25 ( since its common in all Sk) since these( 1,5,25) are divisors of every member of S this answers our question.
Statement 2 - x can be 1,2,4,5,25,125 hence not sufficient.

IMO- A

srcc25anu wrote:@ force5: just one small question:
from stat 1 we know x can be 1,5,25 (odd and factors of S) but we cannot identify one odd integer (as the Q asks)
also from stat 1 we know 13,17 (odd and NOT divisors of S)
hence should we not mark it as INSUFFICIENT since we have multiple values of X that satisfy the solution in first case?

Be careful here...

You are correct, statement A does not narrow down x to a specific value. However the question doesn't ask for a value of x, its a yes/no question. This should be triggered by "..., is odd integer x...". A is sufficient since x is restricted to a set that must be a divisor of each member of S so the answer to the target question is yes.

Yes well said Idoolitt. If the question was asking the value of that odd divisor then the answer would have been E. however the question just asks you

is odd integer x a divisor of every member of S?

and the answer to this question is YES...





hope it helps....