Data Sufficiency

If x & y are positive integers, is 4^x(1/3)^y < 1?

1. y = 2x
2. y = 4

OA is A. Request some explanation for the answer.

Hi Viren,

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Now the solution !

If x & y are positive integers, is 4^x(1/3)^y < 1?
Assumption : The expression 4^x(1/3)^y is same as (4^x)*((1/3)^y)

1. y = 2x

(4^x)*((1/3)^y) = (4^x)*((1/3)^2x) = (4^x)*((1/9)^x) = (4/9)^x
x > 0 and x is an integer.So the value of x > 1
we know that 0< a^n < 1, If 0< a < 1 and n > 0
So, (4/9)^x is always < 1

Sufficient!

2. y = 4

(4^x)*((1/3)^4)

If x = 1 then the value of the expression (4^x)*((1/3)^4) < 1
If x = 4 then the value of the expression (4^x)*((1/3)^4) > 1

We cannot answer the question.Hence, Insufficient

Answer A

Viren1808 wrote:If x & y are positive integers, is 4^x(1/3)^y < 1?

1. y = 2x
2. y = 4

OA is A. Request some explanation for the answer.

1) given y = 2x
need to find whether 4^x(1/3)^y < 1=>
4^x<3^y
4^x<3^(2x)
4^x<9^x
since x is a +ve integer always 4^x<9^x. hence sufficient.

2) since we dont know about x, this is insufficient.

user123321

simplifying the original statement "is 4^x(1/3)^y < 1? "
we need to find is 4^x<3^y ?

statement1. if y=2x, for every positive integer value of x, 4^x will always be less than 3^y: Sufficient
Statement2: does not talk about x. not enough. Insufficient.