If x and y are positive integers, is 4^x – 7^y

Question

If x and y are positive integers, is  4^x – 7^y < 0 ?

(1)  16^{x + 1} < 49^y

(2)  x > y

KrishnanTN · Answer

Is 4^X < 7^y ? 1) Since 4 < 7 and x and y are positive, X +1 < y. This can answer the question. 2) x> y —> sufficient. HENCE D Posted from my mobile device

sanikale · Answer

We need to establish if: 4^x < 7^Y
(1) when simplified gives us 4^(X+1)<7^y —> 4 x 4^x is less than 7^y. If that is the case, Then 4^x is definitely less than 7^y therefore
(1) is sufficient

(2) while this might seem tempting, a simple trial and error will help to prove this insufficient - where x=2 and y=1, 4^x >7^Y. However,when x=4 and 4=3, 7^y > 4^x. Therefore there is no definite answer. (2) is insufficient.

Ans is (A)

Posted from my mobile device

chetan2u · Answer

If x and y are positive integers, is  4^x – 7^y < 0 ?

OR Is  4^x-7^y ?

(1)  16^{x + 1} < 49^y…………….4^{2(x+1)}<7^{2y} 
As the numbers are positive integers on both sides, we can take square root of the inequality. 
 4^{x+1}<7^y……….4^x<4^{x+1}<7^y 
Sufficient

(2)  x > y 
If x and y are 2 and 1 or 10 and 1, answer is No. 
If x and y are large integers with a difference of just 1, answer is Yes. 
 4^{4}=64……..7^{3}=343 
Insufficient

A

TarunKumar1234 · Answer

If x and y are positive integers, is 4^x – 7^y < 0 ? Stat1: 16^{x + 1} < 49^y or, 4^{2(x+1)} < 7^{2y} , as x and y are positive integers, so, 2(x+1) < 2y or, y-x > 1, so the given equation will be true always. Sufficient Stat2: x > y There can be two conditions here, either x = 2 and y =1 then, 4^x – 7^y > 0 and, if x = 200 and y =1 then, 4^x – 7^y < 0 . Not sufficient So, I think A.

Crytiocanalyst · Answer

(1)  16^{x + 1} < 49^y 
since these are positive numbers we can take root therefore 
4*4^x+1 <4*x < 7*y 
Which is clearly sufficient

(2)  x > y

when x=1 and y=2 eqn is satisfied

however x=100 and y=2 it's not sufficient

Therefore IMO A

parasma · Answer

As per statement 1 =

4^x < 7^y/4 so clearly 4^x < 7^y

Statement 1 is sufficient.

Statement 2=
X>Y

x=2, Y=1 Yes
X=4, Y=3 No
Statement 2 is insufficient.

Answer is A.

If x and y are positive integers, is 4^x – 7^y < 0?

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

GMAT Data Sufficiency (DS) Questions