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Source: — Data Sufficiency |

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by Anurag@Gurome » Tue Nov 15, 2011 11:43 pm
Viren1808 wrote:If x & y are positive integers, is 4^x(1/3)^y < 1?

1. y = 2x
2. y = 4
Solution:
Consider first (1) alone.
It implies that the given expression is 4^x * (1/3)^2x = (4/9)^x.
If x is a positive integer, (4/9)^x is less than 1.
Hence, (1) alone is sufficient.
We next consider (2) alone.
It makes the given expression 4^x * (1/3)^4 = (4^x)/81.
If x = 2, (4^x)/81 = 16/81 < 1 and if x = 4, (4^x) = 256/81 > 1.
Hence, (2) does not give a definite answer and so is not alone sufficient.

The correct answer is (A).
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by neelgandham » Tue Nov 15, 2011 11:56 pm
Hi Viren,

Welcome to the forum! Before I answer the question, I would like to request you to conceal the answer when you post. Please use spoiler to conceal the answer. How ? see below

https://www.beatthegmat.com/new-spoilers-t5302.html

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
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by user123321 » Wed Nov 16, 2011 3:52 am
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.

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by zooki » Wed Nov 16, 2011 6:22 am
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.
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