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Source: — Data Sufficiency |

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by Brent@GMATPrepNow » Fri Nov 15, 2013 10:24 am
dddanny2006 wrote:Is m divisible by 8?

(1) mn is divisible by 8
(2) n is divisible by 4
IMPORTANT: Most (possibly all) GMAT divisibility questions of this nature restrict the variables to integer values. So, I think that this question would likely tell us that m and n are integers. Having said that, the correct answer is E either way.

Target question: Is m divisible by 8?

We'll jump straight to . . .

Statements 1 and 2 combined
There are several values of m and n that satisfy both statements. Here are two:
Case a: m = 8 and n = 4, in which case m is divisible by 8
Case b: m = 2 and n = 4, in which case m is not divisible by 8
Since we cannot answer the target question with certainty, the combined statements are NOT SUFFICIENT

Answer = E

Cheers,
Brent
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by dddanny2006 » Fri Nov 15, 2013 10:26 am
Brent,
Why didnt we pay attention to st1 and st2 individually?Can you please use the prime box method here.

Thanks
Brent@GMATPrepNow wrote:
dddanny2006 wrote:

Is m divisible by 8?

(1) mn is divisible by 8
(2) n is divisible by 4
IMPORTANT: Most (possibly all) GMAT divisibility questions of this nature restrict the variables to integer values. So, I think that this question would likely tell us that m and n are integers. Having said that, the correct answer is E either way.

Target question: Is m divisible by 8?

We'll jump straight to . . .

Statements 1 and 2 combined
There are several values of m and n that satisfy both statements. Here are two:
Case a: m = 8 and n = 4, in which case m is divisible by 8
Case b: m = 2 and n = 4, in which case m is not divisible by 8
Since we cannot answer the target question with certainty, the combined statements are NOT SUFFICIENT

Answer = E

Cheers,
Brent
Last edited by dddanny2006 on Fri Nov 15, 2013 10:29 am, edited 1 time in total.
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by theCodeToGMAT » Fri Nov 15, 2013 10:28 am
TO find: m/8? ==> we need three "2"s

IMP: we don't knw whether "m" is INT

Statement 1:
mn is divisible by 8
mn/2*2*2
Maybe, n is divisible by "n" and "m" is not at all INT
or, maybe m is divisible by "8"
INSUFFICIENT

Statement 2:
n/4
We have no info about "m"
INSUFFICIENT

Combining...
n--> INT ==> n/4 ---> we got two "2"s
mn/2*2*2 ==> (m/2)(n/4) --> that means m & n are INT
we can say m is divisible by "2" but cant say whether divisible by "8"
INSUFFICIENT

Answer [spoiler]{E}[/spoiler]
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by Brent@GMATPrepNow » Fri Nov 15, 2013 10:33 am
dddanny2006 wrote:Brent,
Why didnt we pay attention to st1 and st2 individually?
Good question.
In situations in which the statements appear to provide insufficient information, I might jump straight to looking for counter-examples that satisfy both statements.

Notice that I could have addressed each statement individually using the same counter-examples I used for the two statements combined.

Statement 1: mn is divisible by 8
There are several values of m and n that satisfy this condition. Here are two:
Case a: m = 8 and n = 4, in which case m is divisible by 8
Case b: m = 2 and n = 4, in which case m is not divisible by 8
Since we cannot answer the target question with certainty, statement 1 is NOT SUFFICIENT


Statement 2: n is divisible by 4
There are several values of m and n that satisfy this condition. Here are two:
Case a: m = 8 and n = 4, in which case m is divisible by 8
Case b: m = 2 and n = 4, in which case m is not divisible by 8
Since we cannot answer the target question with certainty, statement 2 is NOT SUFFICIENT

Cheers,
Brent
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by Uva@90 » Fri Nov 15, 2013 10:39 am
dddanny2006 wrote:Is m divisible by 8?
(1)mn is divisible by 8
(2)n is divisible by 4
Hi Dddanny2006,
Question Ask is M/8 = Integer(Yes/No Type)

Statement 1: mn is divisible by 8

m*n/8 = Integer

Lets take sample values,
m = 1 n = 8
1*8/8 = Integer
Here m /8 is not = Integer ==> NO
m=8,n=2
8*8/8 = Integer
here M/8 = 8/8 = Integer ==>Yes

Hence Insufficient.

Statement 2:n is divisible by 4
It says-> N/4 = Integer
Nothing said about m
Hence Insufficient.

1+2:

From 1 we get ==>m*n/8 = Integer
From 2 we get ==>N/4 = Integer
Lets us take some sample values,
we know n is a multiple of 4

So let n = 4 and m = 2

2*4/8 = Integer
2/8 is not an integer
No

N= 4 and M = 8
8*4/8 = Integer
Here 8/8 is an integer
Yes
Since we get contradicting answer

Answer is E

Regards,
Uva.
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by dddanny2006 » Fri Nov 15, 2013 12:41 pm
Brent,
Could you please solve this question using the Prime boxes method.Please!!

Is mn divisible by 40?
(1)m is divisible by 40
(2)n is divisible by 4

Target-Are there three 2's and one 5 hiding in the prime factorization of mn?

Statement 1
Since 40 = (2)(2)(2)(5), statement 1 tells us that there are 3 2's and one 5 hiding in the prime factorization of m.

So, we can be certain that there are at least 3 2's and one 5 hiding in the prime factorization of mn.

Can we then conclude that there MUST be three 3 2's and one 5 hiding in the prime factorization of mn ?

We know nothing about n as yet from statement 1,,Is statement one sufficient?

What if I rephrase statement 1 as (1)m is divisible by 10

Since 10 = (2)(5), statement 1 tells us that there is one 2 and one 5 hiding in the prime factorization of m.

So, we can be certain that there is atleast one 2 and one 5 hiding in the prime factorization of mn.

Can we then conclude that there MUST be three 3 2's and one 5 hiding in the prime factorization of mn ?No.We may have 3 2's and a 5 or we may not have.If we do have them,where are the remaining 2 2's and a 5 going to come from? Is n going to bring them?Or is it m that will bring them if at all they do come?

For statement 1,Manhattan says prime box for 10 will consist of a 2,5,.....? Are those remaining 2's and 5 going to emerge out of those "dots....?" that I've bolded if at all they emerge?Or is it n that will get these for us.

I have not gone into statement 2 here because it's a similar case.However I do want to know,where the 2 2's and the 5 going to come from.

Thanks

Brent@GMATPrepNow wrote:
dddanny2006 wrote:Is m divisible by 8?

(1) mn is divisible by 8
(2) n is divisible by 4
IMPORTANT: Most (possibly all) GMAT divisibility questions of this nature restrict the variables to integer values. So, I think that this question would likely tell us that m and n are integers. Having said that, the correct answer is E either way.

Target question: Is m divisible by 8?

We'll jump straight to . . .

Statements 1 and 2 combined
There are several values of m and n that satisfy both statements. Here are two:
Case a: m = 8 and n = 4, in which case m is divisible by 8
Case b: m = 2 and n = 4, in which case m is not divisible by 8
Since we cannot answer the target question with certainty, the combined statements are NOT SUFFICIENT

Answer = E

Cheers,
Brent
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