num properties

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rnaah: Junior | Next Rank: 30 Posts; Posts: 24; Joined: Thu Jul 15, 2010 9:45 am; Thanked: 1 times

by rnaah » Tue Oct 25, 2011 11:30 pm

The remainder when n is divided by 3 is 2 and the remainder when t is divided by 5 is 3. What is the remainder when nt is divided by 15?

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

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Source: Beat The GMAT — Problem Solving | Tue Oct 25, 2011 11:30 pm

neelgandham: Community Manager; Posts: 1060; Joined: Fri May 13, 2011 6:46 amFollowed by: 52 members; Location: Utrecht, The Netherlands; Thanked: 318 times

by neelgandham » Wed Oct 26, 2011 3:01 am

Answer : C - Explanation to follow !

Note: Oops typo! Edited now

Last edited by neelgandham on Wed Oct 26, 2011 4:13 am, edited 1 time in total.

Anil Gandham
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MartinK: Junior | Next Rank: 30 Posts; Posts: 22; Joined: Wed Mar 09, 2011 12:38 am; Location: Slovakia; Thanked: 3 times

by MartinK » Wed Oct 26, 2011 4:11 am

n=Qx3+2 Q>=0, n={2,5,8,11,14,17,20,23,26,29,32,...}, n=2+(N-1)3
t=Zx5+3 Z>=0, z={3,8,13,18,23,28,33,...}, t=3+(N-1)5

1.)n-2 is divisible by 5
- n={2,17,32,47,62,...}, n=2+(N-1)15
- we do not know anynothing NEW about t
- so let try to multiply few options from n and t

17x3=51 => 51/15=3x15+6, remainder is 6
17x8=136 => 136/15=9x15+1, remainder is 1

INSUFFICIENT

2.)t is divisible by 3
- t={3,18,33,48,...}, t=3+(N-1)15
- we do not know anything NEW about n
- so let try to multiply few options from n and t

2x3=6 => 6/15=0x15+6
3*18=54 => 54/15=3x15+9

INSUFFICIENT

1+2)
- n={2,17,32,47,62,...}
- t={3,18,33,48,...}
- so let try to multiply few options from n and t

17*3=51 => 51/15=3x15+6
17*33=561 => 561/15=37*15+6

C - SUFFICIENT

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user123321: Master | Next Rank: 500 Posts; Posts: 385; Joined: Fri Sep 23, 2011 9:02 pmFollowed by: 6 members; Thanked: 62 times

by user123321 » Wed Oct 26, 2011 4:14 am

rnaah wrote:The remainder when n is divided by 3 is 2 and the remainder when t is divided by 5 is 3. What is the remainder when nt is divided by 15?

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

should be C
based on given info...

n = 3p + 2, t = 5k + 3
so remainder to be found when nt/15

1) n-2 = 5q
n=5q+2
but from given data, when combined with above
n = 15q + 2
still we cannot say anything about the remainder when nt = (15q + 2)(5k+3) is divided by 15 because 5k+3 term in the product might give 2 or 5 or 8

2) t = 3m
but from given data, when combined with above
t = 15m + 3
still we cannot say anything about the remainder when nt = (3p + 2)(15m + 3) is divided by 15 because first term in the product gives 3 or 8 or 13

combining above two...
then nt = (15q + 2)(15m + 3), which is clearly divisble by 15 with remainder 2*3 = 6

hence C
while solving you can eliminate 10% of the steps by doing most steps mentally

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GMATGuruNY: GMAT Instructor; Posts: 15539; Joined: Tue May 25, 2010 12:04 pmFollowed by: 1906 members; Location: New York, NY; Thanked: 13060 times; GMAT Score:790

by GMATGuruNY » Wed Oct 26, 2011 4:50 am

rnaah wrote:The remainder when n is divided by 3 is 2 and the remainder when t is divided by 5 is 3. What is the remainder when nt is divided by 15?

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

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GmatKiss: Legendary Member; Posts: 2789; Joined: Tue Jul 26, 2011 12:19 amFollowed by: 43 members; Location: Chennai, India; Thanked: 206 times; GMAT Score:640

by GmatKiss » Wed Oct 26, 2011 7:53 am

IMO: C

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