What is the largest two digit number which when divided by 6 and 7 gives remainder 3 and 4 respectively?

As we know that the largest two-digit number is 99.

As per the question, the number should be divided by 6 and 7 respectively. So the LCM of (6, 7) is 42.

99 can be written as $$42\times\ 2+15$$

So the number which follows both the conditions is $$42\times\ 2-3$$ = 84-3 = 81

Now if 81 is divided by 6 and 7 respectively, then gives the remainder 3 and 4 respectively.

We can also solve this question by checking each of the options one by one.