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When positive integer n is divided by 3, the remainder is 2;

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When positive integer n is divided by 3, the remainder is 2; [#permalink] New post 06 Dec 2005, 13:09
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When positive integer n is divided by 3, the remainder is 2; and when positive integer t is divided by 5, the remainder is 3. What is the remainder when the product nt is divided by 15?

1) n-2 is divisible by 5
2) t is divisible by 3

Explanations please!
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 [#permalink] New post 06 Dec 2005, 18:32
C.
Combining statements, n/15=q and t/15=15q then n*t/15=15q

So, n*(t+2)=15q+2 remainder is 2.
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 [#permalink] New post 10 Dec 2005, 05:58
When you combine 1 and 2,

t=18
n=17 gives a nt/15 remainder of 6
But n=32 gives a n/15 remainder of 11. insuff

I pick E.
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Re: GMATPrep Question - DS [#permalink] New post 10 Dec 2005, 06:33
yb wrote:
When positive integer n is divided by 3, the remainder is 2; and when positive integer t is divided by 5, the remainder is 3. What is the remainder when the product nt is divided by 15?

1) n-2 is divisible by 5
2) t is divisible by 3

Explanations please!


n= 3k+2 (k is integer) and t= 5m+3 (m is integer)

1. n-2 is divisible by 5 , n-2= 3k ----> 3k is divisible by 5 -----> 3k is divisible by 15 ----> n-2 is divisible by 15
nt= (n-2)*t+2t -----> the remainder then nt is divided by 15 is determined by 2t ( becaue (n-2) is divisible by 15 ---> (n-2)*t is divisible by 15)
2t = 2*(5m+3) = 10m + 6
m=1 --> 2t=16 ---> the remainder is 1
m=0 ----> 2t= 6 ----> the remainder is 6
-----> stmt 1 is insuff

2. t is divisible by 3 ----> 5m+3 is divisible by 3 ----> 5m is divisible by 3 ----> 5m is divisible by 15 -----> 5m+3 divided by 15 has remainder of 3 ----> t divided by 15 has remainder of 3 ----> t= 15v + 3 ( v is integer)

nt= (3k+2) ( 15v+3) = 45kv + 9k +30v + 6 ----> the remainder is determined by 9k+6
k=0 ----> the remainder is 6
k= 1 ----> the remainder is 0
----> stmt 2 is insuff

Combine 1 and 2
nt= (n-2)t + 2t
(n-2)t is divisible by 15 as proved above ---> the remainder is determined by 2t
2t= 2* ( 15v+3)= 30 v +6 ----> 2t divided by 15 has remainder of 6
-----> nt is divided by 15 has remainder of 6 ---->suff

C it is.
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 [#permalink] New post 10 Dec 2005, 13:24
rianah100 wrote:
When you combine 1 and 2,

t=18
n=17 gives a nt/15 remainder of 6
But n=32 gives a n/15 remainder of 11. insuff

I pick E.

Here is what I did wrong
But n=32 gives a n/15 remainder of 6. suff
  [#permalink] 10 Dec 2005, 13:24
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When positive integer n is divided by 3, the remainder is 2;

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