Question: 2N Divided by D

Comment on 2N Divided by D

Could you please tell me what the difficulty is of this question? Is it more a 600+ question or a 550-600 question?
gmat-admin's picture

It's definitely a higher-level question. I'd place it at around 650 - 700

Can you please explain how to finish the first approach?
gmat-admin's picture

Hi Zoser,

I added that approach to the video to demonstrate the thought process that one should follow with math questions. That is, consider your options, try an approach and closely monitor whether you're making progress with that approach. If you're not making progress, you should abandon that approach and try something else.

In this case, it's doubtful that the first approach will take us anywhere.

I got you!


I did it this way:
Using the relationship that N divided by D gives 28 as remainder, the possible value of N are 28, QD+28, ...
Lets assume N=28
In which case 2N=56
It is given that 2N when divided by D leaves remainder 15, which means 2N-15 or 41 is completely divisible by D
Since 41 is a prime no., D has only 2 possible values- 1 & 41
And since D could not be 1, therefore D=41

Is this approach valid and will it work on other such questions as well?
gmat-admin's picture

It certainly works this time. Yes, that strategy will work on other questions with the SAME setup.

sir why can't we take 2N/D=Q(15).Anyhow we are getting the same answer in negave that is -41.
gmat-admin's picture

In the solution, I let the Q represents the quotient of the first division, and I let the K represents the quotient of the second division.

Since Q and K are both variables, I could have just as easily switched them around (as you suggest). If I had done so, the answer would still be 41.

Once we know that D(K - 2Q) = 41 (at 3:00 in the video), we can conclude that D = 1 or 41 (since D, K and Q are all INTEGERS)

Yes, D = -41 also satisfies the equation D(K - 2Q) = 41, but we're told that D, K and Q are POSITIVE integers.

ASIDE: When it comes to remainder questions on the GMAT, the question will ALWAYS specify that the numbers in the question are POSITIVE INTEGERS.

Does that help?


Hi Brent,

Can you please confirm if my approach would work every time?

I did this:

the remainder of 2n/d should be 2x the remainder of n/d. If it is not then the quotient was increased by probably 1. therefore, 28 x 2 = 56 - 15 = 41.
gmat-admin's picture

That's a great idea, but it often doesn't work.
For example, 11 divided by 7 equals 1 with REMAINDER 4, but 22 divided by 7 equals 3 with REMAINDER 1

Likewise, 11 divided by 4 equals 2 with REMAINDER 3, but 22 divided by 4 equals 5 with REMAINDER 2



Hi Brent,

I think this approach is correct enough since we're not concerned with only the remainder and not the whole number. It is true that the whole number may not be incremented by 1, but we can still correctly obtain the divisor.
In your example 11/7 = 1(4) and 22/7 =3(1). Then we can find the divisor by 4*2 - 1 = 7.
Similarly 11/4 = 2(3) and 22/4 = 5(2). Then the divisor is 2*3 - 2 = 4.
Please let me know what you think!
gmat-admin's picture

I'm not entirely sure what you are saying, when you write "...since we're NOT concerned with only the remainder and NOT the whole number." Can you elaborate on this?

Also, can you show me how this would play out in solving the original question?


Oh, yes I mistyped that and it doesn't make any sense. I mean to say that we're not concerned with the whole number and only concerned with the remainder. Example - 11/4 has the whole number 2 and remainder 3.

For the original question we have N/D has remainder 28, and then 2*N/D has remainder 15. So 2*28 - 15 = 41.
gmat-admin's picture

Yes, that appears to work.
Nice job!


if N = 28+d
and 2N =15+d
then 2(28+d)=15+d
56+2d = 15+d d= -41
why is this approach wrong??
gmat-admin's picture

You took the fact that "when N is divided by D, the remainder is 28" and concluded that N = D + 28.
This is not necessarily true.

To see where the error lies, let's examine another example.

When integer N is divided by 5, the remainder is 2
What can we conclude (with certainty) about the value of N?
Can we say that N MUST equal 5 + 2 (aka 7)?
N COULD equal 7, but N COULD also equal 12.
Or N COULD equal 2, or 17, or 22 or 27 or.....

Likewise, if we're told that "when N is divided by D, the remainder is 28," we cannot conclude that N = D + 28

Some possible values of N are: 28, 28 + D, 28 + 2D, 28 + 3D, etc
So, we can't just choose 1 of the possible values and go from there.

Does that help?


yes thanks :)

I think it is much easier to pick the numbers, but what is the limitations to that Brent? When does it start being really complicated?

In that case, it was:

Assuming N = 28 and D bigger than that. Then dividing 56 by a number that leaves 15 remainder. 41 in that case. Well, 41 is greater than 28, so it satisfies that first condition. We got our answer.

Does that always work that fine or can you think of a case where it would be more complex to pick the numbers?


gmat-admin's picture

It's hard to say when picking numbers becomes "complicated."
Just note that it is one of several strategies to consider when answering questions involving remainders.

I hope that helps.

Hey Brent!
I assumed that N=28
And then tried values for D from the options above and found that for N=28 and D=41
verifies the given
Is it ok to use numerical application to solve this question?
Thanks in advance
gmat-admin's picture

Nice solution!
When it comes to solving Integer Properties questions, it's often a good idea to consider testing values.

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