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

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

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New post 05 Dec 2017, 21:55
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B
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Re: If x is an integer, is x^3 divisible by 49? [#permalink]

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New post 05 Dec 2017, 22:00
IMO B

From st1 x can be any value. For example x can be 16 and it will satisfy the statement but not the question stem. If x is 56 it will satisfy both the statement as well as question stem. Hence insufficient.

From st2 we can have x as 14, 28, 42 etc. all of them are multiples of 7. So x^3 is always divisible by 49. Hence sufficient


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

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New post 06 Dec 2017, 04:07
For x^3 to be divisible by 49, it has to be a multuple of 7^2
(1) This statement gives us information that x is a multiple of 2^3, but no information about 7^2
Insufficient
(2) Aftyer prime factorization of 14=2*7 we understand that x is a multiple of 7, hence x^3 will have 3 powers of 7 and thus is divisible by 7^2.
Answer should be B
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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]

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New post 06 Dec 2017, 23:06
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.

so B is the answer

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If x is an integer, is x^3 divisible by 49?   [#permalink] 06 Dec 2017, 23:06
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If x is an integer, is x^3 divisible by 49?

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