QUESTION

CSAT

Medium

Reasoning

Prelims 2024

If the sum of the two-digit numbers AB and CD is the three-digit number 1CE, where the letters A, B, C, D, E denote distinct digits, then what is the value of A?

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Explanation

Let AB and CD represent two-digit numbers, where A and C are the tens digits and B and D are the units digits, respectively. This gives:

AB = $10A + B$
CD = $10C + D$

Their sum is a three-digit number, 1CE, where "1" is the hundreds digit:

$10A + B + 10C + D = 100 + 10C + E$

Since 1CE is a three-digit number starting with "1," and the sum of two two-digit numbers typically results in a number around 100, A must be 9 to reach the hundreds place in the sum.

Thus:

Answer: A. 9

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