25.If x, y, and n are positive integers, is (x/y)^n greater than 1,000 ?
(1) x=y^3 and n > y.
(2) x > 5y and n > x.
(1) x=y^3 and n > y.
(2) x > 5y and n > x.
IMO B
OA please
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Source: Beat The GMAT — Data Sufficiency |
A
x=y^3 and n > y
= (x/y)^n
= y^2n
and n>y
so we can not get any relation for relating it to 1000
B
x > 5y
we need to check for
(x/y)^n = (x/y)^n
(x/y)^n < (5y/y)^n
(x/y)^n < 5^n
now as x and y are +ve integers
so min y can be 1
hence min x has to be 6
and if n > x
so n will certainly be greater than 6
and we all know 5 to the power a no greater than 6 will certainly be greater than 1000
hence B is sufficient
Hope this helps!!!
x=y^3 and n > y
= (x/y)^n
= y^2n
and n>y
so we can not get any relation for relating it to 1000
B
x > 5y
we need to check for
(x/y)^n = (x/y)^n
(x/y)^n < (5y/y)^n
(x/y)^n < 5^n
now as x and y are +ve integers
so min y can be 1
hence min x has to be 6
and if n > x
so n will certainly be greater than 6
and we all know 5 to the power a no greater than 6 will certainly be greater than 1000
hence B is sufficient
Hope this helps!!!
