Question: 2N Divided by D

Comment on 2N Divided by D

Awesome website for GRE

How to reach the solution from the first approach?
greenlight-admin's picture

Great question.
We have...

28 + N
28 + 2N
28 + 3N
28 + 4N

15 + D
15 + 2D
15 + 3D

Let's test the answer choices.

A) 41
If D = 41, then one possible value of N = 28 + D = 28 + 41 = 69
So, N = 69
This means that 2N = 2(69) = 138
IMPORTANT: Is it possible to plug in D = 41 into one of the options for 2N so that we get 138?

You bet. If we take the option 2N = 15 + 3D, we get:
138 = 15 + 3(41)

Perfect! Since D = 41 is possible, we can stop checking answer choices.

How to think this way in exam? Will we get such tough questions on the day of exam?
greenlight-admin's picture

Since the GRE is computer adaptive, you will see difficult questions like this on the second quant section IF you do well on the first quant section.

Thanks Brent. :)

Hi Brent,
I have some problem understanding this approach, could plz let me know if I can work around this way:

I put the value of D in equation
i.e N = q.41 + 28 or N = 69 , q=1
and solving for R,
then : 2*69/41 gives a reminder 15 with quotient 3.

Let me know I have assumed in the first equation since I have used the quotient as 1, is it valid to assume that

greenlight-admin's picture

Testing the answer choices works here.
Nice work!

Is this the official GRE question?
very trickly.
greenlight-admin's picture

It's not an official GRE question, but it's within the scope of the GRE. So, you could see a question like this on test day.

This question I've approached a bit differently.
I simply made the supposition that N=28, so that it yields back 28 remainder.
Following this, to be able to find what D is, I simply multiplied 28*2 and then subtracted 15, to find what the right Divisor.

greenlight-admin's picture

Beautiful logic - great work!!!

Is this a valid approach?
NX+28=D, 2NX+15=D
2(NX+28)=2D ==> 2NX+56=2D

(2NX+56=2D)-(2NX-15=D)==> 56-15=D D=41
greenlight-admin's picture

You actually got a little bit lucky with that solution. Here's why:

The remainder property (aka "Rebuilding the Dividend") goes like this:
If N ÷ D = Q with remainder R, then N = QD + R

For example, 17 ÷ 3 = 5 with remainder 2
This means we can also write: 17 = (5)(3) + 2

You wrote: NX + 28 = D, which is the same as: D = NX + 28
This equation suggests that, D ÷ N = X with remainder 28.
However, this is not what the question tells us.
The question tells us that N ÷ D = X with remainder 28

From this point, it's just lucky that everything worked out.


I find a quick approach:
If 28 is the remainder, then the minimum value of N is 28. So, 2N = 56. Now, the remainder is 15. In this case, the value of D is 56-15 = 41.
greenlight-admin's picture

Nice work!

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