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

Question

What is the value of integer x?

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

yashikaaggarwal · Answer

Statement 1: 2^x<20<3^x
Where X can be both 3&4

Such as 2^3<20<3^3
=> 8<20<27 (correct)

Or. 2^4<20<3^4
=> 16<20<81 (correct)
But we have two values.
(Insufficient)

Statement 2: 2^(x+1)<20<3^(x+1)
Where X can be both 2&3

Such as 2^(2+1)<20<3^(2+1)
=> 2^3<20<3^3
=> 8<20<27 (correct)

Or. 2^(3+1)<20<3^(3+1)
2^4<20<3^4
=> 16<20<81 (correct)
But we have two values.
(Insufficient)

Together 1&2 : X = 3&4 or 2&3 where 3 is common. Hence C is sufficient.

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GMATinsight · Answer

Answer: Option C

Please check the explanation in image and video attached

https://www.youtube.com/watch?v=C00FaqFdON8

Monodeep Dutta · Answer

St 1- X can be 3 or 4 and hold true- Insufficient

St 2- x+1 can be 3 or 4, hence x can be 2,3 hence insufficient

1+2

X can only be 3 
Ans- C

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NitishJain · Answer

IMO  C

Since we need integer values for x,

From Statement 1: x = 3 or 4 
From Statement 2: x = 2 or 3

Combining both statements x = 3

Kinshook · Answer

What is the value of integer x?

(1)  2^x < 20 < 3^x 
x = 3 or 4 
NOT SUFFICIENT

(2)  2^{(x + 1)} < 20 < 3^{(x + 1)} 
x = 2 or 3
NOT SUFFICIENT

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

IMO C

What is the value of integer x? (1) 2^x < 20 < 3^x (2) 2^(x + 1) < 20

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