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# An integer n, when divided by 3 has a remainder of 2

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Senior Manager
Joined: 11 Feb 2007
Posts: 350

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An integer n, when divided by 3 has a remainder of 2 [#permalink]

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20 Mar 2007, 00:41
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An integer n, when divided by 3 has a remainder of 2. An integer t, when divided by 5, has a remainder of 3. What is the remainder when n*t is divided by 15?

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

OPEN DISCUSSION OF THIS QUESTION IS HERE: when-positive-integer-n-is-divided-by-3-the-remainder-is-86155.html

Last edited by ricokevin on 20 Mar 2007, 01:19, edited 1 time in total.

Kudos [?]: 186 [0], given: 0

Senior Manager
Joined: 20 Feb 2007
Posts: 256

Kudos [?]: 63 [0], given: 0

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20 Mar 2007, 01:09

I could find some method but not quick enough...

Last edited by Summer3 on 20 Mar 2007, 01:21, edited 1 time in total.

Kudos [?]: 63 [0], given: 0

Senior Manager
Joined: 11 Feb 2007
Posts: 350

Kudos [?]: 186 [0], given: 0

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20 Mar 2007, 01:18
Summer3 wrote:

I have added the OA. Highlight to see.

Kudos [?]: 186 [0], given: 0

Senior Manager
Joined: 20 Feb 2007
Posts: 256

Kudos [?]: 63 [0], given: 0

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20 Mar 2007, 01:29
Yeah, first I did it wrong way...so I got wrong answer but I did it again and got C.

This is what I did:

n = 3q + 2 (q = quotient) then I drew a table (i) for q and n...
t = 5q + 3 again I drew a table(ii) for q and t too

(1) (n-2 / 5) = int ....I checked from the table (i) and found n = 17 fit here..
but from table (ii) any value of t can be taken and remainder will be different..INSUFF

(2) t/3 = int .....from table (ii) t = 18 fits here...but n from table (i) can be any value so different remainders...INSUFF

Taking both (1) and (2) together:
n = 17 and t = 18......we can get the answer...SUFF

Kudos [?]: 63 [0], given: 0

Senior Manager
Joined: 20 Feb 2007
Posts: 256

Kudos [?]: 63 [0], given: 0

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20 Mar 2007, 01:39
And yes, I rechecked the C by taking another value for n and t, too...e.g. n = 32 from table (i) and t = 63 or even same 18....remainder was same

Kudos [?]: 63 [0], given: 0

20 Mar 2007, 01:39
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