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

Question

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

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

sunaimshadmani · Answer

Statement 1 tells that y=2x.
So (2)^2x * (1/3)^2x = (2/3)^2x.
This is always less than 1 for any +ve Integer x. 
Sufficient.

Statement 2 is clearly insufficient.
Answer should be A.

gmat6nplus1 · Answer

statement 1: y=2x. the ratio between y and x is 2:1. Since x and y are positive integers, we are always going to obtain a proper fraction, which is smaller than 1.

statement 2: insufficient.

Answer A.

82vkgmat · Answer

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.

MathRevolution · Answer

Forget conventional ways of solving math questions. In DS, Variable approach is the easiest and quickest way to find the answer without actually solving the problem. Remember equal number of variables and independent equations ensures a solution.

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.

SaquibHGMATWhiz · 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

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

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GMAT Data Sufficiency (DS) Questions

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

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