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 no definite answer.

Thus A.

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

For me answer is (C).

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