What is the value of positive integer x? (1) x^4

Question

What is the value of positive integer x ?

(1)  x^4 < 1000

(2)  2^x < x^2

Bunuel · Accepted Answer

What is the value of positive integer x ?

Notice that we are told that x is a positive integer.

(1) \(x^4 < 1000\). x could be 1, 2, 3, 4, or 5. Not sufficient.

(2) \(2^x < x^2\). Test values:
If x = 1, then (2^x = 2) > (x^2 = 1);
If x = 2, then 2^x = 4 = x^2;
If x = 3, then (2^x = 8) < (x^2 = 9);
If x = 4, then 2^x = 16 = x^2;
If x > 4, then 2^x > x^2.

So, x can only be 3. Sufficient.

Answer: B.

clipea12 · Answer

even with testing values i got tricked and mistakenly chose C !
is there another way to solve it or at least understand that 3 is a good fit ?

Bunuel · Answer

I think it's the easiest way to solve. The key here is to see that when x is 4 or more, 2^x will be more than or equal to x^2. So, you have to test only 3 values: 1, 2, and 3.

clipea12 · Answer

Yea I got it

thank you bunuel

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.

What is the value of positive integer x? (1) x^4 < 1,000 (2) 2x < x^2

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