If n is a positive integer and r is the remainder when 4+7n

[troikaru]

Dear all,
I can’t understand the explanation of the "theory method#1" in this thread by RonPurewal :

remainder-gmat-prep-t5779.html

Here is the question again:

If n is a positive integer and r is the remainder when 4+7n is divided by 3, what is the value of r?

1) n+1 is divisible by 3
2) n>20


The second statement is easy. Drop it.

However I stuck with the first one.

If we write n+1=3k then n=3k-1 and then put this equation in 4+7n, therefore 4+7*(3k-1)=
4+21k-7=
21k-3=
3(7k-1).
Consequently, 4+7n is a multiple of 3, which means that the remainder always be 0.

If this works out, then the 1st statement is sufficient. However, you see that plugging the numbers less then 20, there will be different remainders. Where is logic then?

Could somebody help to understand where I go wrong? Maybe I miss something?

Thx in advance

[Ben Ku]

Hi troikaru,

I believe the original question states that r is the remainder when "4n + 7" is divided by 3, not "4 + 7n" as you posted. Hope that helps!

[jakildedhia]

FYI the question posted by troikaru is correct as even i got the same question yesterday on my prep test.

Infact it seems troikaru was on the right track but missed a couple of steps further in his solution (i.e.replacing K with actuals).

OA:A
statement one is sufficient, as the remainder will always be 1.

Hi troikaru,

I believe the original question states that r is the remainder when "4n + 7" is divided by 3, not "4 + 7n" as you posted. Hope that helps!

[dmitryknowsbest]

Hi troikaru,

Plugging in should work fine here. You just have to make sure to plug in numbers that fit the constraints. Since we know that n+1 must be a multiple of 3, we need to plug in values of n that are one less than a multiple of 3. (2, 5, 8, 11, etc.) These will all produce a multiple of 3 (as proven by the theoretical approach you ran through).

4+ 7(2) = 18
4+ 7(5) = 39
4+ 7(8) = 60
etc.

I'm not sure what you mean about plugging in values less than 20. Since we can solve with Statement 1 (and not 2), we don't need to involve the number 20 in any way.