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# When positive N is divided by 3, the remainder is 2; and

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Joined: 28 Feb 2007
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When positive N is divided by 3, the remainder is 2; and [#permalink]

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27 Aug 2008, 17:26
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hi folks,
I searched this question in this forum but couldn't find .
Could u plz show me fastest way to solve it. Thanks. OA is later.

Source GmatPrep:

When positive N is divided by 3, the remainder is 2; and when positive T is divided by 5the remainder is 3. What is the remainder if NT is divided by 15.

1) N-2 is divisible by 5
2) T is divisible by 3

Kudos [?]: 42 [0], given: 0

SVP
Joined: 29 Aug 2007
Posts: 2472

Kudos [?]: 843 [0], given: 19

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27 Aug 2008, 22:38
UMB wrote:
hi folks,
I searched this question in this forum but couldn't find .
Could u plz show me fastest way to solve it. Thanks. OA is later.

Source GmatPrep: When positive N is divided by 3, the remainder is 2; and when positive T is divided by 5the remainder is 3. What is the remainder if NT is divided by 15.

1) N-2 is divisible by 5
2) T is divisible by 3

N = 3k+2 where k is an integer
T = 5j+3 where j is an integer
so if NT = 15x+y, what is y?

1: N-2 = 5p where p is an integer.
or, N = 5p +2
i.e. N has the same reminder, 2, when divided by 3 or 5. so N is a multiple of 15 plus 2.
i.e N = 15s+2 where s is an integer.
but have no relation about T and 3. nsf....

2: if T = 3q, where q is an integer and reminder is 0
T = 15v + 3 where s is an integer.
but have no information about the relationship between N and 5. nsf...

from 1 and 2: NT = (15s+2)(15v+3) = 225sv + 45s + 30v + 6
all terms except the last one is not divisible by 15. so r = 6
C.
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Kudos [?]: 843 [0], given: 19

SVP
Joined: 07 Nov 2007
Posts: 1792

Kudos [?]: 1062 [0], given: 5

Location: New York

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27 Aug 2008, 22:52
GMAT TIGER wrote:
UMB wrote:
hi folks,
I searched this question in this forum but couldn't find .
Could u plz show me fastest way to solve it. Thanks. OA is later.

Source GmatPrep: When positive N is divided by 3, the remainder is 2; and when positive T is divided by 5the remainder is 3. What is the remainder if NT is divided by 15.

1) N-2 is divisible by 5
2) T is divisible by 3

N = 3k+2 where k is an integer
T = 5j+3 where j is an integer
so if NT = 15x+y, what is y?

1: N-2 = 5p where p is an integer.
or, N = 5p +2
i.e. N has the same reminder, 2, when divided by 3 or 5. so N is a multiple of 15 plus 2.
i.e N = 15s+2 where s is an integer.
but have no relation about T and 3. nsf....

2: if T = 3q, where q is an integer and reminder is 0
T = 15v + 3 where s is an integer.
but have no information about the relationship between N and 5. nsf...

from 1 and 2: NT = (15s+2)(15v+3) = 225sv + 45s + 30v + 6
all terms except the last one is not divisible by 15. so r = 6
C.

Agree with this solution.. Took >2 min.

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Kudos [?]: 1062 [0], given: 5

Re: DS: remainder   [#permalink] 27 Aug 2008, 22:52
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