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?

Correct Option: (d) 4

We are given two four-digit numbers A3BC and DE2F where each letter represents a different digit greater than 3 (i.e., digits can be 4, 5, 6, 7, 8, 9). Their sum is given as 15902. Let's set up the addition: A3BC + DE2F = 15902. Looking at the units column: C + F = 12 (since the sum ends in 2, and C, F > 3, maximum sum is 9 + 8 = 17, so C + F = 12 with a carry of 1). Looking at the tens column: B + 2 + 1 (carry) = 10 (ends in 0, carry 1). So B + 3 = 10 => B = 7. Looking at the hundreds column: 3 + E + 1 (carry) = 9 (ends in 9, no carry). So 4 + E = 9 => E = 5. Looking at the thousands column: A + D = 15. We are given that A, B, C, D, E, F are distinct digits greater than 3. Since B = 7 and E = 5, the remaining available digits greater than 3 are 4, 6, 8, 9 (since 5 and 7 are already used). We have A + D = 15. The available pairs from {4, 6, 8, 9} that sum to 15 are 6 and 9 (6 + 9 = 15). Therefore, {{A, D}} = {6, 9}. The question asks for the difference between the values of A and D: |A - D| = |9 - 6| = 3. Wait, let's check options: (a) 1, (b) 2, (c) 3, (d) 4. Wait, let's check if A and D can be 8 and 7? But 7 is already B. What about 6 and 9? Difference is 9 - 6 = 3. Wait, let's check option (c).