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# If x is an integer, is x^3 divisible by 49?

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Re: If x is an integer, is x^3 divisible by 49? [#permalink]
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Bunuel wrote:
If x is an integer, is x^3 divisible by 49?

(1) x is divisible by 8.

(2) x is divisible by 14.

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If x is an integer, is x^3 divisible by 49? [#permalink]
If x is an integer, is x^3 divisible by 49?

(1) x is divisible by 8.

(2) x is divisible by 14.

we have to get the definite yes /no for the answer.

to prove (x^3/49) is an integer we need to have at least one 7 as a factor of x

let us consider the statements
1. x is divisible by 8.

ex: case 1: 16 is divisible by 8 but it does not have any factor as 7 so (x^3/49) ----> (16^3/49) will never be an integer
case 2: 56 is divisible by 8 and it does have 7 as a factor so (x^3/49) ----> (56^3/49) will be an integer

so as per statement 1 we don't have a definite yes/no answer, so it is not sufficient.

2. x is divisible by 14.

since every number divisible by 14 will have at least one 7 as its factor so (x^3/49) ----> (14^3/49) will be an integer in every possible case

so statement 2 is sufficient.