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Data sufficiency question: divisibility and primes (medium)

Expert replies
by coolgirl26 » Tue Mar 03, 2009 1:31 pm
Hi everyone. I am having trouble understanding this question.

Question:
is N/14 an integer?

1) N is divisible by 28

2) N is divisible by 70


The answer is : each statement alone is sufficient but I am having trouble understanding why.


My understanding of the question is N/14 will be an integer if N= 14, -14, 28 etc.

So if I go to 1) If N is divisible by 28 that means that N must be a multiple of 28 or -28 etc.
which should be sufficient

2) N is divisible by 70
The problem is that if N is divisible by 70, can the answer not be a multiple of 70= 70, 140, etc.

I know that 140 / 70 = 2
and n = 140/14= 10 and gives you a definte answer
but what about when
you divide 70/70=1 and plug into the original question

70/14 not an integer

My problem is I am having trouble understanding what it that needs to be specifically done..Maybe I'm overlooking into the problem..

If someone can help me, that would be great..!!!
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Source: — Data Sufficiency |

by bzji » Tue Mar 03, 2009 2:07 pm
70/14 = 5...integer.....therefore #2 satisfies the condition the same reason #1 satisfies
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by coolgirl26 » Tue Mar 03, 2009 2:31 pm
thank you so much

now that i think about it pretty funny and its worthwhile memorizing the times tables!!!

Thank you
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by Jeff@TargetTestPrep » Tue Dec 19, 2017 9:31 am
coolgirl26 wrote:Is N/14 an integer?

1) N is divisible by 28

2) N is divisible by 70
We need to determine whether n/14 = integer.

Statement One Alone:

n is divisible by 28.

Since 14 is a factor of 28, n will always be divisible by 14. Statement one alone is sufficient to answer the question.

Statement Two Alone:

n is divisible by 70.

Since 14 is a factor of 70, n will always be divisible by 14. Statement two alone is sufficient to answer the question.

Answer: D

Jeffrey Miller
Head of GMAT Instruction
[email protected]

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by ceilidh.erickson » Tue Dec 19, 2017 11:40 am
When rephrasing divisibility questions, it's always helpful to break integers down into PRIME factors.

Is N/14 an integer => is N divisible by 14?
14 has prime factors of 2 and 7. Thus, any integer that is divisible by both 2 and 7 MUST be divisible by 14.

Target question: does N have prime factors of both 2 and 7?

1) N is divisible by 28
28 is divisible by both 2 and 7, so it must be divisible by 14. Sufficient.

2) N is divisible by 70
70 is also divisible by both 2 and 7, so it must be divisible by 14. Sufficient.
Ceilidh Erickson
EdM in Mind, Brain, and Education
Harvard Graduate School of Education
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