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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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This topic is locked. If you want to discuss this question please repost it in the respective forum. 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) n2 is divisible by 5 2) t is divisible by 3
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Re: GMATPrep DS [#permalink]
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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) n2 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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Re: GMATPrep DS [#permalink]
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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) n2 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 23 min since you don't have many options to deal with simple numbers. Does anyone have a shorter solution?
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Re: GMATPrep DS [#permalink]
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13 May 2008, 11:01
ManhattanGMAT has one, http://www.manhattangmat.com/forums/post10151.htmlBut even it seems to long...unless someone has a faster way than this.



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Re: GMATPrep DS [#permalink]
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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) n2 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 23 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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Re: GMATPrep DS [#permalink]
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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) n2 is divisible by 5 2) t is divisible by 3



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Re: GMATPrep DS [#permalink]
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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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Re: GMATPrep DS [#permalink]
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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) n2 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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Re: GMATPrep DS [#permalink]
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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 n2=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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Re: GMATPrep DS [#permalink]
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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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Re: GMATPrep DS [#permalink]
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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) n2 is divisible by 5 2) t is divisible by 3 Hi, n=3x+2(1) t=5y+3(2) Statement 1: arranging (1) n2=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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Re: GMATPrep DS [#permalink]
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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.










