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If x is an integer, is x^3 divisible by 7

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abhinav008
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If x is an integer, is x^3 divisible by 7 [#permalink] New post   Updated on: 05 Jul 2015, 08:24
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If x is an integer, is x^3 divisible by 7

(1) x^2 is divisible by 7
(2) x^4 is divisible by 7
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D

Originally posted by abhinav008 on 04 Jul 2015, 07:24.
Last edited by Bunuel on 05 Jul 2015, 08:24, edited 5 times in total.
Edited the question.
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Re: If x is an integer, is x^3 divisible by 7 [#permalink] New post   04 Jul 2015, 08:10
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abhinav008 wrote:
If x is an integer , is \(x^3\) divisible by 7
i) \(x^2\) is divisible by 7
ii) \(x^4\) is divisible by 7

Not sure about statement 2 . How to approach !!



hi,

ts given x is an integer
and 7 is a prime number so if any positive integer power of x is div by 7, all positive integer power of x will be div by 7..
ans is D..
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Re: If x is an integer, is x^3 divisible by 7 [#permalink] New post   04 Jul 2015, 10:41
chetan2u wrote:
abhinav008 wrote:
If x is an integer , is \(x^3\) divisible by 7
i) \(x^2\) is divisible by 7
ii) \(x^4\) is divisible by 7

Not sure about statement 2 . How to approach !!



hi,
you say that you have made the Q and in the same breath, you say you are not sure about statement two?

anyway,

its given x is an integer
and 7 is a prime number so if any positive integer power of x is div by 7, all positive integer power of x will be div by 7..
ans is D..


Thanks for the reply . You mentioned 7 is a prime number. So what if I change 7 to 4 . Is x^3 divisible by 4 if x^4 is divisible by 4.
I am not sure but I think answer will still be same. Correct me if I am wrong .
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Re: If x is an integer, is x^3 divisible by 7 [#permalink] New post   05 Jul 2015, 02:18
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Hi
Yes in this case. But say you ask is x^2 div by 8, if x^3 is div by 8.
In this case it will not be yes. If x=2, answer will be NO.
If x=4 ans will be yes. It will be insuff.
Therefore it is important that you factor down the divisor and check the possibility of x in its prime factor form being div by it.
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Re: If x is an integer, is x^3 divisible by 7 [#permalink] New post   05 Jul 2015, 08:25
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abhinav008 wrote:
If x is an integer, is x^3 divisible by 7

(1) x^2 is divisible by 7
(2) x^4 is divisible by 7


Similar question to practice: if-x-is-an-integer-is-x-3-divisible-by-165973.html
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Re: If x is an integer, is x^3 divisible by 7 [#permalink] New post   07 Jul 2015, 15:13
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abhinav008 wrote:
If x is an integer, is x^3 divisible by 7

(1) x^2 is divisible by 7
(2) x^4 is divisible by 7


Given : x is an Integer

Question : Is x^3 divisible by 7?

Statement 1: x^2 is divisible by 7
Since x is an Integer so x^2 will be a perfect square which is divisible by 7, therefore
x also must be a multiple of 7
SUFFICIENT

Statement 2: x^4 is divisible by 7
Since x is an Integer so x^4 will be square of a perfect square which is divisible by 7, therefore
x also must be a multiple of 7
SUFFICIENT

Answer: option D
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Re: If x is an integer, is x^3 divisible by 7 [#permalink] New post   08 Jul 2022, 06:20
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Re: If x is an integer, is x^3 divisible by 7 [#permalink]
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