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04 May 2022, 02:30
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B
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:
54% (01:24) correct
46%
(01:13)
wrong
based on 57
sessions
History
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Not Attempted Yet
If x^n = 1, where x and n are both integers, what is the value of the x?
(1) n is a multiple of 5.
(2) n is an odd number.
(1) n is a multiple of 5.
(2) n is an odd number.
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
04 May 2022, 07:55
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Step 1: Analyse Question Stem
\(x^n\) = 1.
Both x and n are integers.
We have to find the value of x.
In the equation given in the question,
If n = 0, x = any value except zero
If n is a non-zero number, x = 1 or -1 depending on whether n is odd or even.
With this analysis in mind, it is time to analyse the statements.
Step 2: Analyse Statements Independently (And eliminate options) – AD / BCE
Statement 1: n is a multiple of 5.
If n = 5, x = 1
If n = 10, x = 1 or -1
The data in statement 1 is insufficient to find a unique value for x.
Statement 1 alone is insufficient. Answer options A and D can be eliminated.
Statement 2: n is an odd number.
Since n is odd, n is not equal to zero. Therefore, the first case mentioned in the Question analysis can be ruled out.
Also, since n is odd, the only way in which \(x^n\) = 1 is by substituting x = 1.
The data in statement 2 is sufficient to say that the unique value of x is 1.
Statement 2 alone is sufficient. Answer options C and E can be eliminated.
The correct answer option is B.
\(x^n\) = 1.
Both x and n are integers.
We have to find the value of x.
In the equation given in the question,
If n = 0, x = any value except zero
If n is a non-zero number, x = 1 or -1 depending on whether n is odd or even.
With this analysis in mind, it is time to analyse the statements.
Step 2: Analyse Statements Independently (And eliminate options) – AD / BCE
Statement 1: n is a multiple of 5.
If n = 5, x = 1
If n = 10, x = 1 or -1
The data in statement 1 is insufficient to find a unique value for x.
Statement 1 alone is insufficient. Answer options A and D can be eliminated.
Statement 2: n is an odd number.
Since n is odd, n is not equal to zero. Therefore, the first case mentioned in the Question analysis can be ruled out.
Also, since n is odd, the only way in which \(x^n\) = 1 is by substituting x = 1.
The data in statement 2 is sufficient to say that the unique value of x is 1.
Statement 2 alone is sufficient. Answer options C and E can be eliminated.
The correct answer option is B.
09 May 2022, 08:55
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Statement 1:
Take two cases as example
x=1, n=10 (10 is a multiple of 5)
So, 1^10=1, here x=1
x=-1, n=10
So, -1^10=1, here x=-1
So no certain conclusion can be madeon the value of x.
Statement 1 is not sufficient alone
Statement 2:
n is odd = 3,5,7,9......
Anything^any odd value = 1
It can only be possible if that anything is +1
Eg:
i. 79^3=some value
ii. -79^3=some negative value
iii. -1^3=-1
iv. 1^3=1
So, statement B alone is sufficient
Concept: Since, integer is given so we dont have to worry about fractions. But since positive integer is not mentioned, so we need to test for both negative and positive values
Take two cases as example
x=1, n=10 (10 is a multiple of 5)
So, 1^10=1, here x=1
x=-1, n=10
So, -1^10=1, here x=-1
So no certain conclusion can be madeon the value of x.
Statement 1 is not sufficient alone
Statement 2:
n is odd = 3,5,7,9......
Anything^any odd value = 1
It can only be possible if that anything is +1
Eg:
i. 79^3=some value
ii. -79^3=some negative value
iii. -1^3=-1
iv. 1^3=1
So, statement B alone is sufficient
Concept: Since, integer is given so we dont have to worry about fractions. But since positive integer is not mentioned, so we need to test for both negative and positive values
