Question: 2N Divided by D

Comment on 2N Divided by D

Awesome website for GRE

Awesome website for GRE

How to reach the solution

How to reach the solution from the first approach?

Great question.

Great question.
We have...

SOME POSSIBLE VALUES OF N:
28
28 + N
28 + 2N
28 + 3N
28 + 4N
etc

SOME POSSIBLE VALUES OF 2N:
15
15 + D
15 + 2D
15 + 3D
etc

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

How to think this way in exam? Will we get such tough questions on the day of exam?

Since the GRE is computer

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,

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

Thanks

Testing the answer choices works here.
Nice work!

Is this the official GRE

Is this the official GRE question?
very trickly.

It's not an official GRE

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

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.

Beautiful logic - great work!

Beautiful logic - great work!!!

Is this a valid approach?

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

You actually got a little bit

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.

Cheers,
Brent

I find a quick approach:

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.

Nice work!