Num Properties Concept Query - instructors!?

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Num Properties Concept Query - instructors!?

by san2009 » Sun Aug 08, 2010 2:47 am
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!
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by kvcpk » Sun Aug 08, 2010 3:03 am
san2009 wrote: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!!

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by Stuart@KaplanGMAT » Sun Aug 08, 2010 7:42 pm
san2009 wrote: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.
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by san2009 » Wed Aug 11, 2010 1:58 am
Stuart - sorry, but i don't quite understand. can you please elaborate?

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by san2009 » Wed Aug 11, 2010 1:59 am
never mind. got it. thanks :)