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# Remainder question

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Intern
Joined: 23 Sep 2007
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22 Jul 2008, 13:44
This topic is locked. If you want to discuss this question please re-post it in the respective forum.

I think this was solved before but I couldn't solve it. Can someone explain. Thanks

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 nt is divided by 15?

1) n – 2 is divisible by 5

2) t is divisible 3

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25 Jul 2008, 03:29
singaks wrote:
I think this was solved before but I couldn't solve it. Can someone explain. Thanks

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 nt is divided by 15?

1) n – 2 is divisible by 5

2) t is divisible 3

See, n gives a remainder of 2 with 3 thus n-2 is divisible by 3.
From 1) n-2 is divisible by 5.

Thefore the minimum value of n-2 is 15 and that of n is 17. ----------------(A)

But since the remainder is also dependent on the value of t, let us try finding out the value of t.

As per the qns:
t/5 gives a remainder of 3. Thus the values could be 3,18,33....--------------------(B)

From (A) and (B)

The remainder is 6 with any combination.

Thus from 1) one can get a definite answer

From 2) the values of t are 3, 18, 33..
the values of n are 2,5,8,11,14..

remainders from different combinations cud be: 6,0,3,12

Thus A.

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25 Jul 2008, 04:27
rahulgoyal1986 wrote:
See, n gives a remainder of 2 with 3 thus n-2 is divisible by 3.
From 1) n-2 is divisible by 5.

Thefore the minimum value of n-2 is 15 and that of n is 17. ----------------(A)

But since the remainder is also dependent on the value of t, let us try finding out the value of t.

As per the qns:
t/5 gives a remainder of 3. Thus the values could be 3,18,33....--------------------(B)

From (A) and (B)

The remainder is 6 with any combination.

Thus from 1) one can get a definite answer

From 2) the values of t are 3, 18, 33..
the values of n are 2,5,8,11,14..

remainders from different combinations cud be: 6,0,3,12

Thus A.

I don't see how you can get an answer with just (1).

We know form stem that n = 3k + 2 and t = 5p + 3, with k and p non-negative integers

Then nt = 15pk + 9k + 10p + 6

(1) tells us that 3k is divisible by 5 and therefore we know k is divisible by 5 since 3 is not.

We can then say that 15pk + 9k is divisible by 15, but we don't know anything about 10p (remainder by 15 could be 5 or 10, we don't know)

==> (1) is insufficient

(2) tells us that 5p + 3 is divisible by 3, so 5p is divisible by 3 and therefore we know p is divisible by 3 since 5 is not.

We can then say that 15pk + 10p is divisible by 15, but we don't know anything about 9k (remainder by 15 could be 9 or 3, 12, ... , we don't know)

==> (2) is insufficient

(1) & (2) tell us that 15pk + 9k + 10p is divisible by 15 and therefore the remainder of nt by 15 is 6

==> (1) & (2) is sufficient

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25 Jul 2008, 07:07
Oski wrote:
rahulgoyal1986 wrote:
See, n gives a remainder of 2 with 3 thus n-2 is divisible by 3.
From 1) n-2 is divisible by 5.

Thefore the minimum value of n-2 is 15 and that of n is 17. ----------------(A)

But since the remainder is also dependent on the value of t, let us try finding out the value of t.

As per the qns:
t/5 gives a remainder of 3. Thus the values could be 3,18,33....--------------------(B)

From (A) and (B)

The remainder is 6 with any combination.

Thus from 1) one can get a definite answer

From 2) the values of t are 3, 18, 33..
the values of n are 2,5,8,11,14..

remainders from different combinations cud be: 6,0,3,12

Thus A.

I don't see how you can get an answer with just (1).

We know form stem that n = 3k + 2 and t = 5p + 3, with k and p non-negative integers

Then nt = 15pk + 9k + 10p + 6

(1) tells us that 3k is divisible by 5 and therefore we know k is divisible by 5 since 3 is not.

We can then say that 15pk + 9k is divisible by 15, but we don't know anything about 10p (remainder by 15 could be 5 or 10, we don't know)

==> (1) is insufficient

(2) tells us that 5p + 3 is divisible by 3, so 5p is divisible by 3 and therefore we know p is divisible by 3 since 5 is not.

We can then say that 15pk + 10p is divisible by 15, but we don't know anything about 9k (remainder by 15 could be 9 or 3, 12, ... , we don't know)

==> (2) is insufficient

(1) & (2) tell us that 15pk + 9k + 10p is divisible by 15 and therefore the remainder of nt by 15 is 6

==> (1) & (2) is sufficient

I could find errors in my approach. Thanks Oski.

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Re: Remainder question   [#permalink] 25 Jul 2008, 07:07
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# Remainder question

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