Is 3^x 100? (1) 3^√x = 9 (2) 1/3^x 0.01

Question

Is  3^x > 100 ?

(1)  3^{\sqrt{x}} = 9

(2)  \frac{1}{3^x} > 0.01

TarunKumar1234 · Answer

Is 3^x >100? Stat1: 3 ^\sqrt{ x} =9 or, x = 4, so, 3^4 <100. Sufficient Stat2: \frac{1}{3^x} >0.01 or, 3^x <100. Sufficient So, I think D.

sumitkrocks · Answer

3^x > 100

3^4 = 81
3^5 = 243
x has to be b/w 4 and 4 for 3 x  to be greater than 100

Now let us analyze

Statement 1: 3^(x/2)=9
x=4 
Hence, Sufficient

Statement 2: 1/3^x > 1/100
Take reciprocals

3^x < 100

Hence, Sufficient

D is the answer

GMATinsight · Answer

Question: Is  3^x > 100 ?

3^1 = 3 
 3^2 = 9 
 3^3 = 27 
  3^4 = 81  
  3^5 = 243

i.e.   Question REPHRASED: Is  x > 4 ?

Statement 1 :  3^{\sqrt{x}} = 9

i.e.  3^{\sqrt{x}} = 3^2 
i.e.  √x = 2 
i.e.  x = 4  i.e. answer to the question is  DEFINITELY 'NO"

SUFFICIENT

Statement 2 :  \frac{1}{3^x} > 0.01

i.e.  \frac{1}{3^x} > \frac{1}{100}

i.e.  3^x < 100  which is exactly opposite to the given question Stem
i.e. answer to the question is  DEFINITELY 'NO"

SUFFICIENT

Answer: Option D

Is 3^x > 100? (1) 3^√x = 9 (2) 1/3^x > 0.01