What is the value of x? (1) 2^x

Question

What is the value of x?

(1)  2^x < 20 < 3^x 
(2)  2^{(x + 1)} < 20 < 3^{(x + 1)}

gurmukh · Answer

From statement 1
X=3 and 4
Insufficient
From statement 2 
X =2 and 3
Insufficient
Together 
X=3
Sufficient
Answer is C

Posted from my mobile device

IanStewart · Answer

What is the source? The answer is E, not C.

If x needs to be an integer, then using both Statements, x must be 3. But we don't know x is an integer here, and you'll find that any value of x between roughly 2.73 and 3.31 will work in both Statements (to find those bounds I had to use logarithms, which you don't need on the GMAT).

Bunuel · Answer

Yes. Edited the OA. Re-posted question where x is an integer here: https://gmatclub.com/forum/what-is-the- ... 28425.html

nkme2007 · Answer

From Statement 1: x can be 3, 2 or 1 
So, INSUFFICIENT

From Statement 2, x can be 2 or 1
So, INSUFFICIENT

From Statement 1 and 2, x can be 2 or 1
So, INSUFFICIENT

Answer: E

abrutlag · Answer

Statement 1 lets x be 3 or 2. x can't be 1 because 20 is not between 2^1 and 3^1 (2 and 3).

Statement 2 lets x be 2 or 1.

The only overlap is x=2.

abrutlag · Answer

Apologies, the question should specify that x is an integer. Thank you for reposting.

indugopal1991 · Answer

When we take the values of X as 1 or 2, Do the values satisfy the statements?

IanStewart · Answer

x cannot equal 1 using either Statement, and cannot equal 2 using the first Statement alone. Using both Statements, the only integer value x can have here is 3, though there are non-integer values of x close to 3 that are also possible.

Kinshook · Answer

What is the value of x?

(1)  2^x < 20 < 3^x 
Since x may not be an integer
x = 3 or 4 or any other similar value
NOT SUFFICIENT

(2)  2^{(x + 1)} < 20 < 3^{(x + 1)} 
Since x may not be an integer
x = 2 or 3 or any other similar value
NOT SUFFICIENT

(1) + (2) 
(1)  2^x < 20 < 3^x 
(2)  2^{(x + 1)} < 20 < 3^{(x + 1)} 
Since x may not be an integer
x = 3 or any other similar value
NOT SUFFICIENT

IMO E

What is the value of x? (1) 2^x < 20

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