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

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abrutlag
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What is the value of x? (1) 2^x < 20 [#permalink] New post   05 Jul 2020, 10:50
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What is the value of x?

(1) \(2^x < 20 < 3^x\)
(2) \(2^{(x + 1)} < 20 < 3^{(x + 1)}\)
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E
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gurmukh
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Re: What is the value of x? (1) 2^x < 20 [#permalink] New post   05 Jul 2020, 11:21
From statement 1
X=3 and 4
Insufficient
From statement 2
X =2 and 3
Insufficient
Together
X=3
Sufficient
Answer is C

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IanStewart
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Re: What is the value of x? (1) 2^x < 20 [#permalink] New post   06 Jul 2020, 04:51
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abrutlag wrote:
What is the value of x?

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


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).
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Re: What is the value of x? (1) 2^x < 20 [#permalink] New post   06 Jul 2020, 04:57
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IanStewart wrote:
abrutlag wrote:
What is the value of x?

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


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).


Yes. Edited the OA. Re-posted question where x is an integer here: https://gmatclub.com/forum/what-is-the- ... 28425.html
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Re: What is the value of x? (1) 2^x < 20 [#permalink] New post   06 Jul 2020, 07:08
abrutlag wrote:
What is the value of x?

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


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
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Re: What is the value of x? (1) 2^x < 20 [#permalink] New post   08 Jul 2020, 13:40
nkme2007 wrote:
abrutlag wrote:
What is the value of x?

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


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


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.
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Re: What is the value of x? (1) 2^x < 20 [#permalink] New post   08 Jul 2020, 13:42
Bunuel wrote:
IanStewart wrote:
abrutlag wrote:
What is the value of x?

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


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).


Yes. Edited the OA. Re-posted question where x is an integer here:


Apologies, the question should specify that x is an integer. Thank you for reposting.
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indugopal1991
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Re: What is the value of x? (1) 2^x < 20 [#permalink] New post   09 Jul 2020, 08:35
When we take the values of X as 1 or 2, Do the values satisfy the statements?
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IanStewart
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Re: What is the value of x? (1) 2^x < 20 [#permalink] New post   09 Jul 2020, 10:21
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indugopal1991 wrote:
When we take the values of X as 1 or 2, Do the values satisfy the statements?


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.
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What is the value of x? (1) 2^x < 20 [#permalink] New post   09 Jul 2020, 10:30
abrutlag wrote:
What is the value of x?

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


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
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What is the value of x? (1) 2^x < 20 [#permalink]
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