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24 Jan 2023, 03:22
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C
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
45%
(medium)
Question Stats:
55% (01:43) correct
45%
(01:49)
wrong
based on 44
sessions
History
Date
Time
Result
Not Attempted Yet
n is positive integer. What is the value of x?
(1) 9^n = 10,000*x.
(2) 1/10 < x < 1.
(1) 9^n = 10,000*x.
(2) 1/10 < x < 1.
Pure algebraic questions like this one are no longer part of the GMAT Data Sufficiency syllabus.
For relevant Data Sufficiency questions, please check the Data Sufficiency forum:
Data Sufficiency Forum
Data Sufficiency Forum
14 Feb 2023, 10:49
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Given that n is positive integer and we need to find the value of x
STAT 1: 9^n = 10,000*x
There are many values of x which satisfy this equation and will result in multiple values of positive n
=> Ex: x = \(\frac{9}{10,000}\) => \(9^n\) = 10,000*\(\frac{9}{10,000}\) = 9 => n = 1
=> Ex: x = \(\frac{9^2}{10,000}\) => \(9^n\) = 10,000*\(\frac{9^2}{10,000}\) = 9^2 => n = 2
=> NOT SUFFICIENT
STAT 2: 1/10 < x < 1
=> 0.1 < x < 1
Alone, it is not sufficient because we do not have any relationship between n and x
=> NOT SUFFICIENT
Taking BOTH Statements TOGETHER we get
9^n = 10,000*x = \(10^4\) * x and 0.1 < x < 1
=> x can be \(\frac{9^4}{10^4}\) (~0.64) as other values of x which will give n as integer will not lie in 0.1 < x < 1 range
=> 9^n = 10,000*x = 9^n = 10,000*\(\frac{9^4}{10^4}\) = \(9^4\)
=> n = 4
=> SUFFICIENT
So, Answer will be C
Hope it helps!
Watch the following video to learn the Basics of Exponents
STAT 1: 9^n = 10,000*x
There are many values of x which satisfy this equation and will result in multiple values of positive n
=> Ex: x = \(\frac{9}{10,000}\) => \(9^n\) = 10,000*\(\frac{9}{10,000}\) = 9 => n = 1
=> Ex: x = \(\frac{9^2}{10,000}\) => \(9^n\) = 10,000*\(\frac{9^2}{10,000}\) = 9^2 => n = 2
=> NOT SUFFICIENT
STAT 2: 1/10 < x < 1
=> 0.1 < x < 1
Alone, it is not sufficient because we do not have any relationship between n and x
=> NOT SUFFICIENT
Taking BOTH Statements TOGETHER we get
9^n = 10,000*x = \(10^4\) * x and 0.1 < x < 1
=> x can be \(\frac{9^4}{10^4}\) (~0.64) as other values of x which will give n as integer will not lie in 0.1 < x < 1 range
=> 9^n = 10,000*x = 9^n = 10,000*\(\frac{9^4}{10^4}\) = \(9^4\)
=> n = 4
=> SUFFICIENT
So, Answer will be C
Hope it helps!
Watch the following video to learn the Basics of Exponents
14 Feb 2023, 23:23
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Bunuel
Solution:
Pre Analysis:
- Given n is a positive integer
- We are asked the value of x
Statement 1: \(9^n = 10,000*x\)
- \(⇒x=\frac{9^n}{10000}\)
- We cannot get the value of \(x=\frac{9^n}{10000}\) without knowing the value of n
- Thus, statement 1 alone is not sufficient and we can eliminate options A and D
Statement 2: \(\frac{1}{10} < x < 1\)
- We cannot get the value of x from this range
- Thus, statement 2 alone is also not sufficient
Combining:
- From statement 1, we have \(x=\frac{9^n}{10000}\)
- From statement 2, we have \(\frac{1}{10} < x < 1\)
\(⇒\frac{1}{10} < \frac{9^n}{10000} < 1\)
\(⇒1000<9^n<10000\) - The only positive integral value of n which will satisfy the above range is \(n=4\)
- So, the value of \(x=\frac{9^4}{10000}\)
Hence the right answer is Option C
