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Interesting DS question--Please help

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Source: — Data Sufficiency |
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by [email protected] » Fri Nov 15, 2013 5:05 pm
Is the answer A?
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by [email protected] » Fri Nov 15, 2013 5:07 pm
Is the answer A?
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by vjaykumar73@ » Sat Nov 16, 2013 4:32 am
i got C
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by [email protected] » Sat Nov 16, 2013 1:51 pm
Hi All,

When DS question involve variables and really limited information, you have a really easy approach: TEST Values.

We're asked: Is MN divisible by 40? This is a YES/NO question. Notice how were are not told anything about M and N; they can be ANYTHING (positive, negative, 0, integers, fractions, etc.). Keep THAT in mind when you TEST Values.

Fact 1: M is divisible by 40

M = 40
N = 1
The answer to the question is YES

M = 40
N = .7
The answer to the question is NO
Fact 1 is INSUFFICIENT

Fact 2: N is divisible by 4
M = 40
N = 4
The answer to the question is YES

M = 1
N = 4
The answer to the question is NO
Fact 2 is INSUFFICIENT

Combined, we know that M is divisible by 40 and N is divisible by 4
So, we have (multiple of 40)(multiple of 4) ---> ALWAYS divisible by 40.
Combined, SUFFICIENT

Final Answer: C

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by David@VeritasPrep » Sun Nov 17, 2013 6:02 am
Not sure what the "prime box method" is but you should listen to Rich on this one. A problem like this comes down to number properties. Statement 1 seems to give you all the information you need. I mean, you want to know if mn is divisible by 40 and you are told that m is divisible by 40. That seems to give you your answer right there. It appears that statement 1 alone might be sufficient.

Simply run through the 4 Basic number properties to make sure that you have not forgotten to consider something:

1) positive and negative: well this is not important in this case because even if m or n is negative that does not matter. Negative 40 is divisible by 40. So put this property aside as we do not need it this time.

2) odd/ even: Of course 40 is an even number but that is not really a consideration given that M is already an even number. Put this property aside.

3) non-integers: Does it matter if N is a non-integer? YES!! That is what Rich tested above with the value of .7 for n. This is a non-integer and it can turn mn into something that is not a multiple of 40. This property makes statement 1 not-sufficient alone.

4) 0 and 1: We did not need to test this value for this question. But if we had it would not have been key to this question. Of course if n = 1 then 40*1 = 40 so that is divisible by 40. If n = 0 then 40*0 = 0 and this too is divisible by 40.

Statement 1 is not sufficient because n could be a non-integer.

Statement 2 alone has no chance of being sufficient since you are only told that n = 4.

Taken together the statements are sufficient - not because statement 2 makes n = 4 - but simply because statement 2 guarantees that n is an integer and that is all that you need to know. If m = 40 then 40 (times and integer) = a multiple of 40.


As an aside, testing values as you practice for the GMAT is a great way to teach yourself the rules of number properties. After testing values on this question you can see that a non-integer is something important to think about when testing divisibility. So in the future you can recognize this.
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by Mathsbuddy » Sun Nov 17, 2013 1:12 pm
dddanny2006 wrote:Is mn divisible by 40?
(1)m is divisible by 40
(2)n is divisible by 4


Would prefer if anyone helps me out with the Prime Box method here.
As this question stands, there's no need for any system to solve it. Look:

m = 40k where k is the other unknown factor

so mn = 40k *n = 40kn which is divisible by 40.

I hope this helps.
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