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?

(A) Y= 2X

(B) Y = 4

tkirk32 · Answer

A = insufficient

0 and positive numbers are fine. But the equation is greater then 1 if x and y are negative.

B = insufficient

X could = a HUGE number or a very small number

A and B = Sufficient

If Y = 4 then x must equal 2. Only one solution.

sparky · Answer

A. 1)(4/9)^X < 1 if X >1 suff

2) is insuff since X can vary

rthothad · Answer

I will go with A
Statement 1: (2/3)^2x < 1 for any positive integer
Statement 2: Depending on x's value it could be either.

TooLegitToQuit · Answer

The OA is A. 

I was confused because I read first statement as X = 2Y... doh~

ywilfred · Answer

A) If x = 1, y = 2, then 4(1/9) < 1
 If x = 2, y = 4, then 16(1/81) < 1

A is sufficient

B) is not sufficient since no information about x is given.

Ans: A

WinWinMBA · Answer

The question stem specifically states that both X and Y are positive integers. So you cannot use negative numbers as examples.

A is thus sufficient because you'll always get fractions with values < 1.

Test using Y= 1,2,3,4...etc to see it.

gmat2me2 · Answer

Sparky that was good way to approach this problem.....

Yes it is A

AJB77 · Answer

S1 4^X * (1/3)^2X = 2^2X / 3^2X = (2/3)^2X which is < 1 when X is a positive integer. So Strike out B,C,E S2 4^X * 1/3^4 = 4^X/81.This is < 1 if 1 <= X <= 3 and > 1 if X > 3 Strike out D Answer is A

mandy · Answer

got C
st1 Y=2X does not give any value for x and y
insufficient

St2 y=4 DOES Not tell much except 1/3^4 = 1/81
that a may be answer depending on x
hence insufficient

TOgether yes we know Y= 4 AND Y/2 = x hence x=2
HENCE we can plug back the x and y values to answer the question
:wink:

mandy · Answer

it seems I am wrong can anyone explain me why the first statement is sufficient thanks

gumbico · Answer

ywilfred's explanation covers what I did but here's just detailed breakdown:

-from the stem, we know X and Y are positive so we only need to test pos numbers

(A) Y= 2X 

-from this, we know Y is twice X. I used (x=1,y=2) and(x=2,y=4). You can select any number so long as it fits (A). (x=5,y=10) etc. But small numbers are easier to work with.

 

Now the only possible choices are A and D.

(B) Y=4

-this says nothing about X so it's insufficient 

Answer is A.

The logic you are following (two unknowns require two equations) doesn't apply here because we're not asked to find a specific value for either X or Y. We only need to know if 

(4^X) (1/3)^Y < 1

And from (A), we know that the left side of this inequality will always be less than 1.

IF X and Y are positive integers, is (4^X) (1/3)^Y < 1?

Prep Toolkit

Top 5 GMAT Debrief Videos

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards