Num Properties Concept Query - instructors!?

[san2009]

say, you know that n divided by 3 gives you remainder 2
and you also know that n divided by 5 gives you remainder 2
THEN, what is the remainder when n is divided by 15?
Please provide detailed explanation.

Here is how far i got

n = 3A + 2
n = 5B + 2

But how do you combine the two statements to figure out what the remainder when n is divided by 15 is??

Thanks!

[kvcpk]

say, you know that n divided by 3 gives you remainder 2
and you also know that n divided by 5 gives you remainder 2
THEN, what is the remainder when n is divided by 15?
Please provide detailed explanation.

Here is how far i got

n = 3A + 2
n = 5B + 2

But how do you combine the two statements to figure out what the remainder when n is divided by 15 is??

Thanks!

n = 3A + 2 Multiply both sides by 5
n = 5B + 2 Multiply both sides by 3

5n = 15A + 10
3n = 15B +6
By subtracting,
2n = 15(A-B) +4
n = 15(A-B)/2 +2

Hence Whenever A-B is even, you will have a reminder of 2.

Another way to approach this is:
Find the LCM of 3 and 5 = 15
Now, add 2 to it.
17 -> when divided by 3 gives reminder 2 and also when divided by 5 gives reminder 2.
Similarly for other multiples of 15, you get 32, 47 etc..

Hope this helps!!

[Stuart@KaplanGMAT]

say, you know that n divided by 3 gives you remainder 2
and you also know that n divided by 5 gives you remainder 2
THEN, what is the remainder when n is divided by 15?
Please provide detailed explanation.

Here is how far i got

n = 3A + 2
n = 5B + 2

But how do you combine the two statements to figure out what the remainder when n is divided by 15 is??

Thanks!

Hi,

I'd approach this logically rather than algebraically.

Since 3 and 5 have no common factors, the only way that n/3 and n/5 could have the same remainder is if n cycles in 15s - in other words, 3 and 5 only intersect every 15 integers, so n must be a (multiple of 15) + 2.

Since n is a (multiple of 15) + 2, n/15 has remainder 2.

[san2009]

Stuart - sorry, but i don't quite understand. can you please elaborate?

[san2009]

never mind. got it. thanks