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If a, b, and n are positive integers, is n odd? 15 Feb 2021, 09:45
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54% (01:48) correct 46% (01:52) wrong based on 163 sessions

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If a, b, and n are positive integers, is n odd?


(1) \(a^n - b^n \) is divisible by \(a - b\)

(2) \(a^n + b^n\) is not divisible by \(a + b\)


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If a, b, and n are positive integers, is n odd? 15 Feb 2021, 10:13
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Bunuel
If a, b, and n are positive integers, is n odd?


(1) \(a^n - b^n \) is divisible by \(a - b\)

(2) \(a^n + b^n\) is not divisible by \(a + b\)


Are You Up For the Challenge: 700 Level Questions: 700 Level Questions
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Something that will be very useful in such questions
1) \(a^n-b^n \) is divisible by both a-b and a+b if n is even..
2) \(a^n-b^n \) is divisible by a-b if n is odd.
3) \(a^n+b^n \) is divisible by a+b if n is odd...

(1) \(a^n - b^n \) is divisible by \(a - b\)
Case (1) and (2) are possible.
So n can be even or odd.

(2) \(a^n + b^n\) is not divisible by \(a + b\)
But if n is odd, case (3) tells us that it should be divisible by a+b
Hence n is not odd
Sufficient

B

You can also take a=2 and b=3, and n as 1 and 2 to check the options.
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If a, b, and n are positive integers, is n odd? 27 May 2021, 22:25
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chetan2u
Bunuel
If a, b, and n are positive integers, is n odd?


(1) \(a^n - b^n \) is divisible by \(a - b\)

(2) \(a^n + b^n\) is not divisible by \(a + b\)


Are You Up For the Challenge: 700 Level Questions: 700 Level Questions


Something that will be very useful in such questions
1) \(a^n-b^n \) is divisible by both a-b and a+b if n is even..
2) \(a^n-b^n \) is divisible by a-b if n is odd.
3) \(a^n+b^n \) is divisible by a+b if n is odd...

(1) \(a^n - b^n \) is divisible by \(a - b\)
Case (1) and (2) are possible.
So n can be even or odd.

(2) \(a^n + b^n\) is not divisible by \(a + b\)
But if n is odd, case (3) tells us that it should be divisible by a+b
Hence n is not odd
Sufficient

B

You can also take a=2 and b=3, and n as 1 and 2 to check the options.
Show more

Hi chetan2u since it is not mentioned that a and b are distinct integers.
so for the case of \(a^n+b^n \) can be divisible by a+ b when n is even.
if a=b=5 the 5^2+5^2 is 50 and a+b is 10.

is this thought process correct?
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If a, b, and n are positive integers, is n odd? 05 Jun 2021, 20:15
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apurv09
chetan2u
Bunuel
If a, b, and n are positive integers, is n odd?


(1) \(a^n - b^n \) is divisible by \(a - b\)

(2) \(a^n + b^n\) is not divisible by \(a + b\)


Are You Up For the Challenge: 700 Level Questions: 700 Level Questions


Something that will be very useful in such questions
1) \(a^n-b^n \) is divisible by both a-b and a+b if n is even..
2) \(a^n-b^n \) is divisible by a-b if n is odd.
3) \(a^n+b^n \) is divisible by a+b if n is odd...

(1) \(a^n - b^n \) is divisible by \(a - b\)
Case (1) and (2) are possible.
So n can be even or odd.

(2) \(a^n + b^n\) is not divisible by \(a + b\)
But if n is odd, case (3) tells us that it should be divisible by a+b
Hence n is not odd
Sufficient

B

You can also take a=2 and b=3, and n as 1 and 2 to check the options.

Hi chetan2u since it is not mentioned that a and b are distinct integers.
so for the case of \(a^n+b^n \) can be divisible by a+ b when n is even.
if a=b=5 the 5^2+5^2 is 50 and a+b is 10.

is this thought process correct?
Show more

Hi,
If you are taking the two numbers to be same, they will be divisible irrespective of the value of n.
\(a^n+b^n=a^n+a^n=2*a^n\)
And a+b=2a

2a^n will always be divisible by 2a irrespective of the value of n.
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If a, b, and n are positive integers, is n odd? 02 Jan 2024, 14:25
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