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

Statement can be written as IS 4^x< 3^y?
A. y = 2x so is 4^x< 9^x. True for positive integer x. SUFFICIENT.
B. y=4. INSUFFICIENT.

Answer A.

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

(1) y = 2x
(2) y = 4


In general, if one con is number and the other con is ratio, it is most likely that ratio is an answer.
Since con 1) is ratio, substitute 1). Then, it becomes (4^x)(1/3)^2x=(4^x)(1/9)^x=(4/9)^x<1, which is always yes and sufficient.
Therefore, the answer is A.


 from con 1) and con 2), if one of the conditions is given by numbers and the other is given by ratio (percent,fraction), then the condition with ratio (percent,fraction) value has higher chance of being the answer.

Solution:
Pre Analysis:

• x and y are positive integers
• We are asked if \((4^x)*(\frac{1}{3})^y < 1\) or \(\frac{4^x}{3^y}<1\) or \(4^x<3^y\)

Statement 1: y = 2x

• We have \(4^x<3^y\)
  \(⇒4^x<3^{2x}\)
  \(⇒2^{2x}<3^{2x}\)
• Since x is a positive integer, \(2^{2x}<3^{2x}\) is always true
• Thus, statement 1 alone is sufficient and we can eliminate options B, C and E

Statement 2: y = 4

• This statement doesn't tell me anything about x
• Thus, statement 2 alone is not sufficient

Hence the right answer is Option A