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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]

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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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13 May 2008, 06:58
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?

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.
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13 May 2008, 10:58
GMATBLACKBELT wrote:
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?

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?
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13 May 2008, 11:01
ManhattanGMAT has one, http://www.manhattangmat.com/forums/post10151.html

But even it seems to long...unless someone has a faster way than this.
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13 May 2008, 12:47
chineseburned wrote:
GMATBLACKBELT wrote:
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?

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
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13 May 2008, 13:40
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?

1) n-2 is divisible by 5
2) t is divisible by 3
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13 May 2008, 15:33
ok t cannot =3

3/5 does not equal x Remainder 3.

am i wrong here?

but it still seems to be C.
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19 May 2008, 05:45
From the question stem:

Possible value of n = 2, 5, 8, 11, 14, 17, 20, 23, 26, 29, 32,... ----------I
Possible valud of t = 3, 8, 13, 18, 23, 28, 33, 38, 43.... ----------II

1) n-2 is divisible by 5; So use (I) to get filtered value of n
n = 2, 17, 32,...
not sufficient

2) t is divisible by 3; from (II) get the new filtered value of t
t = 3, 18, 33, ...
not sufficient

Together:
the remainder could be 6 [2*3/15] or 2[17*18/15] or 1[17*3/15]

E.

***EDITED****
Must have been high on something... Yeah reminder is 6 all the way. So, agree with the C gang!

Last edited by mbawaters on 19 May 2008, 10:57, edited 1 time in total.
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19 May 2008, 08:32
Yes i get C

N=3K+2 possible values 2, 5, 8, 11, 14, 17, 20, 24
T=5K+3 possible values 3, 8, 13, 18, 23,

1) says n-2=5K..n can be 2, 17
2+3=5/15 remainder =5
17+13=30 remiander=0
Insuff

2) T is multiple of 3..t can be 3, 18..

3+14=17/15 remainder =2.. 18+24=42/15 remainder=12..insuff

together..n=2 t=3 remainder 5... n=2, t=18 remainder 5..n=17 t=18 remainder=5..

i wonder if there is a shortcut to this..
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19 May 2008, 09:38
gmatnub wrote:
is it E?

Remainder is 6

Haha, I was on crack, I meant C.

BTW freshina, the remainder is 6 instead of 5
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29 May 2008, 03:34
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?

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
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29 May 2008, 04:53
C has to be the answer.

Without look at the hints the possible values for:
n= 2,5,8,11,14,17,20,23...................
t=3,8,13,18,23...................

From hint 1

possible values of n= 17,32,47.....
t= 3,8, 13, 18

17X3/15= 6 (as rdr.)
17X8/15= 1 (rdr.)

Thus insuff.

From Hint 2

Possible values of t= 3,18,33.......
n=2,5,8,11,14,17,20,23.....
thus
18X5/15=0 (rdr)
18X11=198/15= 3 (rdr)
Thus insuff.

Combing Hint 1 and Hint 2
Possible value of n=17,32,47.....
Possible value of t= 3,18,33......

any two combos wud give 6 as a rdr

thus C.
Re: GMATPrep DS   [#permalink] 29 May 2008, 04:53
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