In the sum A + 1A + 5A + AA + A1 = 1AA for which digit does the symbol A stand?

The given sum is A + 1A + 5A + AA + A1 = 1AA. We can express each term using place values, where A represents a single digit: A = A 1A = 10 + A 5A = 50 + A AA = 10A + A = 11A A1 = 10A + 1 1AA = 100 + 10A + A = 100 + 11A Substitute these into the equation: A + (10 + A) + (50 + A) + (11A) + (10A + 1) = 100 + 11A Combine the 'A' terms on the left side: A + A + A + 11A + 10A = 24A Combine the constant terms on the left side: 10 + 50 + 1 = 61 So the equation simplifies to: 24A + 61 = 100 + 11A Now, solve for A: Subtract 11A from both sides: 24A - 11A + 61 = 100 13A + 61 = 100 Subtract 61 from both sides: 13A = 100 - 61 13A = 39 Divide by 13: A = 39 / 13 A = 3 Alternatively, we can look at the units digits of the sum. Units digits on the left side: A + A + A + A + 1 = 4A + 1 Units digit on the right side: A This means the units digit of (4A + 1) must be A. Let's test the options: A) If A = 2: 4(2) + 1 = 9. The units digit is 9, not 2. B) If A = 3: 4(3) + 1 = 13. The units digit is 3, which matches A. C) If A = 4: 4(4) + 1 = 17. The units digit is 7, not 4. D) If A = 5: 4(5) + 1 = 21. The units digit is 1, not 5. Only A=3 satisfies this condition. Thus, the symbol A stands for the digit 3. The final answer is B