IMO C.

The two solutions posted were saying the value of the remainder to be 6 but since it is a DS question we need not find the value.

Here is my approach.

Given in the question stem,

n - 2 is divisible by 3 since n is divisible by 3 leaving a remainder 2. -which means n-2 has atleast 3 as a factor ---fact 1

t - 3 is divisible by 5 since t is divisible by 5 leaving a remainder 3 - which mean t-3 has atleast 5 as a factor. ---fact 2

From stmt 1, it is said that n-2 is divisible by 5. Which means n-2 has atleast 5 as a factor. And from fact 1, we know that 3 is factor of n-2. So we can conclude that n-2 has atleast 3 and 5 as factors or in other words

n-2 = 15k where k is an interger. ==> n = 15k + 2 -----Eq 1

No additional information abt t. Hence insufficient.

From stmt 2, t is a divisible by 3, then t-3 is also divisible by 3. from fact 2, we know that t-3 has 5 also a factor. So we can conclude that t-3 has atleast 3 and 5 as factor or in other words,

t-3 = 15l where l is an integer ==> t = 15l + 3 -----Eq 2.

No additional information abt n is given. Hence insufficient

Now combine both the statements, we know that

n = 15k + 2

t = 15l + 3.

Rule to remember -

Arithmatic on remainders when divisiors are same states that when a and b are the remainders when x and y are divided by asome number n, then remainder left when product xy is divided by n is nothing but the product of the remainders a and b. Here n and k are numbers divided by 15 leaving remainders 2 and 3. So we can easily apply the above rule to find the remainder when product nt is divided by 15.

So ans is C.