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If x is an integer, is x^3 divisible by 49 ? (1) x is

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guygmat
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If x is an integer, is x^3 divisible by 49 ? (1) x is [#permalink] New post   20 Jun 2011, 21:07
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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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Re: If x is an integer, is x^3 divisible by 49 ? (1) x is [#permalink] New post   20 Jun 2011, 22:22
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guygmat wrote:
If x is an integer, is x3 divisible by 49 ?

(1) x is divisible by 8.

(2) x is divisible by 14.


St1: X divisible by 8 .. not sufificent .
8^3/49 is not an integer.

St2: X is divisible by 14.
any multiple of 14 will give u atleast one 7
49 gives us two 7's

s0 14^X( for any multiple of 14) , where X>1, it will always give two 7's

thus its always an interger when divided by 49.

hence B
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sameershintrein
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Re: If x is an integer, is x^3 divisible by 49 ? (1) x is [#permalink] New post   21 Jun 2011, 08:45
I did not get how the answer is B for this question.
Lets consider (2) x is divisible by 14.
Lets consider x=70 (Its divisible by 14) but 70*3 is not completely divisible by 49 so should answer be 'E' ?
Please clarify ...
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Re: If x is an integer, is x^3 divisible by 49 ? (1) x is [#permalink] New post   21 Jun 2011, 08:51
sameershintrein wrote:
I did not get how the answer is B for this question.
Lets consider (2) x is divisible by 14.
Lets consider x=70 (Its divisible by 14) but 70*3 is not completely divisible by 49 so should answer be 'E' ?
Please clarify ...


its not 70*3 it shud be 70^3.
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Re: If x is an integer, is x^3 divisible by 49 ? (1) x is [#permalink] New post   21 Jun 2011, 13:23
did not get how the answer is B for this question.
Lets consider (2) x is divisible by 14.
Lets consider x=70 (Its divisible by 14) but 70*3 is not completely divisible by 49 so should answer be 'E' ?
Please clarify ...


If you know x is divisible by 14 you know that x's prime factors must AT LEAST have a 7 and a 2.

No matter what the value for x will be, if you square x it means that x.x is divisible by 14(14) twice. So that gives us atleast two 7's and two 2's.. 2x7=49 which makes it sufficient.
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Re: If x is an integer, is x^3 divisible by 49 ? (1) x is [#permalink] New post   22 Jun 2011, 06:39
same doubt as above post
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Re: If x is an integer, is x^3 divisible by 49 ? (1) x is [#permalink] New post   22 Jun 2011, 06:48
guygmat wrote:
If x is an integer, is x3 divisible by 49 ?

(1) x is divisible by 8.

(2) x is divisible by 14.


Please avoid the ambiguity by using proper math symbol. I have seen many people making the same mistake when representing the exponents.

The correct version of the question above should be:
*************************************************
If x is an integer, is x^3 divisible by 49 ?

(1) x is divisible by 8.

(2) x is divisible by 14.
*******************************************

Better use the m tag:
********************************************
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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Re: If x is an integer, is x^3 divisible by 49 ? (1) x is [#permalink] New post   22 Jun 2011, 10:21
We need: to be divisible by 49, X3 needs to have atleast two 7s.

Stmt 1: X is divisible by 8. IE it's a multiple of 8. No 7. Insufficient.
Stmt 2: X is divisible by 14. IE it has 7 and 2 as its factors. X3 will have atleast three 7s. This satisfies our need.

Hence B it is.
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Re: If x is an integer, is x^3 divisible by 49 ? (1) x is [#permalink] New post   22 Jun 2011, 19:08
1. not sufficient

as we dont know whether x has factor 7 in it or not.

if x has a factor 7 , then x^3 is divisible by 49 else no

2. sufficient

as we know x has a 7 , x^3 has 7^3 as a factor

hence x^3 is divisble by 49.

Answer is B.
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Re: If x is an integer, is x^3 divisible by 49 ? (1) x is [#permalink] New post   23 Jun 2011, 03:19
a 0 and 8 gives different values for 49. Hence not sufficient.

b 0 and 14^3 = 7^3 * 2^3
sufficient.

B it is.
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Re: If x is an integer, is x^3 divisible by 49 ? (1) x is [#permalink] New post   30 Jun 2011, 09:35
Dont u think that ans has to be D ..
option 1 :: x is divisible by 8
means x can be 8,16, 24 etc ..
In any of the case x^3 will not be divisible by 49 ..Means ans is NO ..thus sufficient .
Does it makes any sense ?
pls share yr views .
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Re: If x is an integer, is x^3 divisible by 49 ? (1) x is [#permalink] New post   05 Jul 2011, 07:18
guygmat wrote:
If \(x\)is an integer, is \(x^3\) divisible by \(49\)?

(1) \(x\)is divisible by \(8\).

(2) \(x\)is divisible by \(14\).



a Simple B for me

reason already explained by fellow users :) :)
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Re: If x is an integer, is x^3 divisible by 49 ? (1) x is [#permalink] New post   05 Jul 2011, 08:40
stmnt 1) x contains atleast three 2s, may or may not contain 7- not sufficient- A/D out
stmnt 2) x contains atleast one 2 and one 7. x^3 will contain atleast 3 two's and 3 seven's. this will be divisible by 7. B is the answer.



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Re: If x is an integer, is x^3 divisible by 49 ? (1) x is [#permalink]
05 Jul 2011, 08:40
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