Question

If AB + XY = 1XP, where A # () and all the letters
signify different digits from 0 to 9, then the value
of A is
(a) 6
(b) 7
(c) 9
(d) 8​

Answer 1

Answer:

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Answer 2

Answer:

So they're digits, i.e:

(10A + B) + (10X + Y) = 100 + 10X + P

10A + B + Y = 100 + P

B + Y will be at most 17 (9 + 8), which means it can contribute at most 10 to the 10s column. Since, on the RHS, we have no 10s, either A = 0, or A = 9, and B + Y >= 10. But A is not 0. Not only that, A is provably not 0, since if A = 0, there is no way to match to the 100 on the RHS of the equation. Hence A = 9:

90 + B + Y = 100 + P

B + Y = 10 + P

This is about as far as we can conceivably go. We know that neither B, Y, P, nor X can be 9, otherwise we get a repeat. Then, B + Y is at most 15, which means that P is at most 5. It also means that B and Y can't be below 2, since B and Y are both below 8, and to make the sum greater than or equal to 10 with one being less than 2, we need the other greater than 8.

To summarize:

A = 9

10 <= B + Y <= 15

0 <= P <= 5

2 <= B <= 8

2 <= Y <= 8