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divisibility

by mehrasa » Mon Sep 26, 2011 12:10 am
is x divisible by 8?

1)x is divisible by 24
2)x is divisible by 16


[spoiler]OA: A[/spoiler]
my Q is that how we can prove B is not sufficient
bcuz 16 have four (2) while for divisibility of 8 we need three (2).. why we can not determine that x is divisible by 8.. can sum1 explain for me theoretically...
Last edited by mehrasa on Mon Sep 26, 2011 2:17 am, edited 1 time in total.
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by shankar.ashwin » Mon Sep 26, 2011 12:59 am
What? 48 is ofcourse divisible by 8.

Should be D IMO


mehrasa wrote:is x divisible by 8?

1)x is divisible by 24
2)x is divisible by 16


[spoiler]OA: A[/spoiler]
my Q is that how we can prove B is not sufficient
bcuz 16 have four (2) while for divisibility of 8 we need three (2).. why we can not determine that x is divisible by 8.. can sum1 explain for me theoretically...
i know its example is 48 which is divisible by 16 but not 8
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by mehrasa » Mon Sep 26, 2011 1:49 am
to me also the answer is D bcuz as i said 16 have four (2) and 8 needs three (2)... I taught maybe I,m wrong

shankar.ashwin wrote:What? 48 is ofcourse divisible by 8.

Should be D IMO


mehrasa wrote:is x divisible by 8?

1)x is divisible by 24
2)x is divisible by 16


[spoiler]OA: A[/spoiler]
my Q is that how we can prove B is not sufficient
bcuz 16 have four (2) while for divisibility of 8 we need three (2).. why we can not determine that x is divisible by 8.. can sum1 explain for me theoretically...
i know its example is 48 which is divisible by 16 but not 8
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by mehrasa » Mon Sep 26, 2011 1:50 am
to me also the answer is D bcuz as i said 16 have four (2) and 8 needs three (2)... I taught maybe I,m wrong

shankar.ashwin wrote:What? 48 is ofcourse divisible by 8.

Should be D IMO


mehrasa wrote:is x divisible by 8?

1)x is divisible by 24
2)x is divisible by 16


[spoiler]OA: A[/spoiler]
my Q is that how we can prove B is not sufficient
bcuz 16 have four (2) while for divisibility of 8 we need three (2).. why we can not determine that x is divisible by 8.. can sum1 explain for me theoretically...
i know its example is 48 which is divisible by 16 but not 8
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by shankar.ashwin » Mon Sep 26, 2011 1:56 am
Having greater Nos. of 2's is Okay, only when you have lesser No's of 2's the number would not be divisible..

IF the question was;

Is x divisible by 16?

A) X is divisible by 8
B) X is divisible by 32

In this case it would be B (Because A has lesser Nos of 2's)
mehrasa wrote:to me also the answer is D bcuz as i said 16 have four (2) and 8 needs three (2)... I taught maybe I,m wrong
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by Brent@GMATPrepNow » Mon Sep 26, 2011 5:00 am
mehrasa wrote:is x divisible by 8?
1)x is divisible by 24
2)x is divisible by 16
[spoiler]OA: A[/spoiler]
A lot of integer property questions can be solved using prime factorization.
For divisibility questions, we can say:
If N is divisible by k, then k is "hiding" within the prime factorization of N
Examples:
24 is divisible by 3 <--> 24 = 2x2x2x3
70 is divisible by 5 <--> 70 = 2x5x7
330 is divisible by 6 <--> 330 = 2x3x5x11

So, if x is divisible by 8, then we know an 8 is hiding in the prime factorization of x.
In other words x = (2)(2)(2)(?)(?)... [notice that we may or may not have primes other than the three 2's in the factorization. All we can be certain of is that there are three 2's (8) within the prime factorization]

Okay, with all of that, we can first take the target question "Is x divisible by 8?" and reword it as "Is 8 hiding in the prime factorization of x"

Statement 1: x is divisible by 24
In other words, 24 is hiding in the prime factorization of x
So, we can say that x = (2)(2)(2)(3)(?)(?)...
From here we can see that 8 is hiding in the prime factorization of x (in the form of three 2's)
So, statement 1 is sufficient.

Statement 1: x is divisible by 16
In other words, 16 is hiding in the prime factorization of x
So, we can say that x = (2)(2)(2)(2)(?)(?)...
From here we can see that 8 is hiding in the prime factorization of x (in the form of three 2's)
So, statement 2 is sufficient, and the answer is D

Cheers,
Brent
Brent Hanneson - Creator of GMATPrepNow.com
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