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When positive integer n is divided by 3 the remainder is 2; [#permalink]

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11 May 2008, 19:37

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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 tn is divided by 15?

1) n-2 is divisible by 5 2) t is divisible by 3
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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 tn is divided by 15?

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

E.

Try values: 17, 27, and 32 for N. And anything divisible by 3 for t. Id start w/ 3.

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 tn is divided by 15?

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

E.

Try values: 17, 27, and 32 for N. And anything divisible by 3 for t. Id start w/ 3.

27 is divisible by 3 and therefore cannot be N.

Plugging n=17 and t=3 -> tn=51 -> 51/15 -> r=6 Plugging n=32 and t=3 -> tn=96 -> 96/15 -> r=6 Plugging n=17 and t=18 -> tn=306 -> 306/15 -> r=6

OA is C.

But plugging numbers like this takes way longer than 2-3 min since you don't have many options to deal with simple numbers. Does anyone have a shorter solution?
_________________

Chinese Democracy is misunderstood...at your nearest BestBuy.

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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 tn is divided by 15?

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

E.

Try values: 17, 27, and 32 for N. And anything divisible by 3 for t. Id start w/ 3.

27 is divisible by 3 and therefore cannot be N.

Plugging n=17 and t=3 -> tn=51 -> 51/15 -> r=6 Plugging n=32 and t=3 -> tn=96 -> 96/15 -> r=6 Plugging n=17 and t=18 -> tn=306 -> 306/15 -> r=6

OA is C.

But plugging numbers like this takes way longer than 2-3 min since you don't have many options to deal with simple numbers. Does anyone have a shorter solution?

arghhh... serves me right for doing this in my head

I wonder if my approach was too basic and simple...

I plugged in n=5, t=8

Remainder of tn/15= 10

plugged in n and t into statements (1) & (2) and found both insufficient.

I still got E as the answer but is there a step I'm missing? (Even if answer is correct, if the approach is incorrect it doesnt help)

chineseburned 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 tn is divided by 15?

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 tn is divided by 15?

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

Hi,

n=3x+2-----------(1) t=5y+3-----------(2)

Statement 1: arranging (1) n-2=3x this means 3x is divisible by 5 let 3x=3*5*a=15a equation (1) is now n=15a+2 not suff

Statement 2: (2)is divisible by 3 means 5y is divisible by 3 so let 5y=3*5*b=15b

eq (2) now is t=15b+3 not suff

combining nt=15a+2*15b+3

all terms except 6 is divisible by 6 so remainder is 6