Let A3BC and DE2F be four-digit numbers where each letter represents

Let A3BC and DE2F be four-digit numbers where each letter represents a different digit greater than 3. If the sum of the numbers is 15902, then what is the difference between the values of A and D?

Answer: C

Explanation

As per the given condition in the question, each letter represents a different digit greater than 3.

So, you can replace the letters with 4, 5, 6, 7, 8, or 9.

A3BC + DE2F = 15902

Step 1: Unit digit

If you add C and F, then you should get 12. Only then you can get 2 at the unit place in the sum.

So, C, F can be (4, 8) or (5, 7)

Step 2: Tens digit

We got a carry of 1 from 12. Now, we know that the tens digit of the sum, 15902 is 0.

So, B + 2 = 9

B = 7

Hence, C, F cannot be (5, 7). They must be (4, 8).

Step 3: Hundreds digit

We got a carry of 1 from 10. Now, we know that the hundreds digit of the sum, 15902 is 9.

So, E + 3 = 8

E = 8 - 3 = 5

Hence, we found that B =7, C = 4/8, E = 5 and F = 4/8

So, A/D = 6/9

So, difference between A and D = 9 - 6 = 3

Exam Year: 2020