If x is an integer, is 3^x less than 500?

Question

(1) 4^(x–1) < 4^x – 120

(2) x^2 = 36

Bunuel · Accepted Answer

If x is an integer, is 3^x less than 500?

Since \(3^6=729>500\) and \(3^5=243<500\), then the question basically asks whether x is an integer less than 6 (5, 4, 3, 2, 1, 0, -1, ...).

(1) 4^(x–1) < 4^x – 120;

\(\frac{4^x}{4}<4^x-120\);

\(120<\frac{3}{4}*4^x\);

\(160<4^x\);

x is an integer greater than 3: 4, 5, 6, 7, ... Not sufficient.

(2) x^2 = 36 --> \(x=6\) or \(x=-6\). Not sufficient.

(1)+(2) From above \(x=6\), thus the answer to the question is NO. Sufficient.

Answer: C.

Similar questions to practice:
https://gmatclub.com/forum/is-x-10-10-1 ... 27881.html
https://gmatclub.com/forum/is-5-k-less- ... 28055.html
https://gmatclub.com/forum/if-x-is-an-i ... 06353.html
https://gmatclub.com/forum/is-4-x-5-3x- ... 86765.html
https://gmatclub.com/forum/is-5-x-134898.html
https://gmatclub.com/forum/is-3-x-134968.html

Hope it helps.

goeladit · Answer

for both the value of x in statement 2 i.e -6 and 6, statement 3x<500 is yes. Then why isnt the answer b?

I see. we are interpreting the question differently. The main statement is 3x in the question not 3 RAISED TO THE POWER X.

If 3x, in that case answer is b otherwise its c.

Bunuel · Answer

It's  3^x , NOT  3x . That's what the first post says as well as my solution above.

AmanMatta · Answer

Can you please elaborate the steps for statement 1?

Bunuel · Answer

4^{(x–1)} < 4^x – 120 ;

\frac{4^x}{4}<4^x-120 ;

Add 120 to both sides:  \frac{4^x}{4}+120<4^x ;

Subtract 4^x/4 from both sides:  20<4^x-\frac{4^x}{4} ;

120<\frac{3}{4}*4^x ;

Multiply by 4/3:  160<4^x ;

x is an integer greater than 3: 4, 5, 6, 7, ... Not sufficient.

davidbeckham · Answer

Bunuel  - can you explain to me how did 4^(x–1) become 4x/4?

Bunuel · Answer

4^{(x–1)}=4^x*4^{-1}= 4^x*\frac{1}{4}=\frac{4^x}{4}

Chanovski · Answer

3^(-6) is also less than 500 no?

Bunuel · Answer

Yes, 3^(-6) = 1/3^6, which is less than 1.

bumpbot · Answer

Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.

If x is an integer, is 3^x less than 500?

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

If x is an integer, is 3^x less than 500?

Prep Toolkit

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