Is 7^x 100 ? (1) 7^(x+2) 9,800 (2) 7^(2x) 10,000

Question

Is  7^x > 100  ?

(1)  7^{(x+2)} > 9,800

(2)  7^{(2x)} > 10,000

Are You Up For the Challenge: 700 Level Questions

BrentGMATPrepNow · Accepted Answer

Target question :    Is  7^x > 100

Statement 1 :  7^{(x+2)} > 9,800   
Rewrite as:  (7^x)(7^2) > 9,800 
In other words:  (7^x)(49) > 9,800 
Divide both sides by 49 to get:  (7^x) > 200 
Since 200 > 100, we can write:  (7^x) > 200 >100 
So, the answer to the target question is  YES, 7^x IS greater than 100 
Since we can answer the  target question  with certainty, statement 1 is SUFFICIENT

Statement 2 :  7^{(2x)} > 10,000  
Rewrite as:  (7^x)^2 > 100^2 
This means:  7^x > 100 
The answer to the target question is  YES, 7^x IS greater than 100 
Since we can answer the  target question  with certainty, statement 2 is SUFFICIENT

Answer: D

Cheers,
Brent

RELATED VIDEO 
 https://www.youtube.com/watch?v=At7a1ibdOTc

unraveled · Answer

Is  7^x > 100  ?
Since  7^3 = 343 , is x > 2 ?

(1)  7^{x+2} > 9,800 
 7^x . 7^2 > 9800 
 7^x > 200  (dividing both sides by 7^2)
x > 2

SUFFICIENT.

(2)  7^{2x} > 10,000 
Taking square root 
 7^x > 100 
x >2

SUFFICIENT.

Answer D.

harshbirsingh · Answer

Target question :    Is  7^x > 100

Statement 1 :  7^{(x+2)} > 9,800   
Rewrite as:  (7^x)(7^2) > 9,800 
In other words:  (7^x)(49) > 9,800 
Divide both sides by 49 to get:  (7^x) > 200 
Since 200 > 100, we can write:  (7^x) > 200 >100 
So, the answer to the target question is  YES, 7^x IS greater than 100 
Since we can answer the  target question  with certainty, statement 1 is SUFFICIENT

Statement 2 :  7^{(2x)} > 10,000  
Rewrite as:  (7^x)^2 > 100^2 
This means:  7^x > 100 
The answer to the target question is  YES, 7^x IS greater than 100 
Since we can answer the  target question  with certainty, statement 2 is SUFFICIENT

Answer: D

Cheers,
Brent
-------------------------------------------------

Hi  BrentGMATPrepNow ,

Square root of x^2 can be either +x or -x. On the same lines, could you please explain why we ignored the negative possibilities in statement 2? If we were to assume there are 2 possibilities - positive and negative, statement 2 would have been insufficient. Please help.

Thanks,
Harshbir

Thanks,
Harshbir

chetan2u · Answer

7^x > 100 .. (1) 7^{(x+2)} > 9,800........7^x*7^2>9800......7^x*49>9800.......7^x>200>100.......7^x>100 Yes and sufficient (2) 7^{(2x)} > 10,000....(7^x)^2>100^2........7^x>100 Yes and sufficient D harshbirsingh , on your query that 7^x<-100 should also be checked. 7^x can never be negative. Even if x is some negative quantity to the tune of say -10000000, 7^{-10000000}=\frac{1}{7^{10000000}}>0 , so 7^x<-100 is NOT valid.

BrentGMATPrepNow · Answer

Since the base, 7, is positive, we can be certain that 7^x is positive for all values of x.

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.

Is 7^x > 100 ? (1) 7^(x+2) > 9,800 (2) 7^(2x) > 10,000

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