Deducing logical conclusions from categorical syllogisms with negative premises
Question
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?
Options
9
8
7
Cannot be determined due to insufficient data
Explanation
Analyze the bounds of the cryptarithm addition: AB + CD = 1CE. Since we are adding two 2-digit numbers, their maximum possible mathematical sum is 99 + 98 = 197. This immediately forces the hundreds place of our result to be 1, which is already printed.
Now look at the tens column: A + C plus any potential carry-over from the units column (B+D) must equal a value that ends in C and generates a carry of 1 to the hundreds place. Algebraically: 10 × 1 + C = A + C + carry \implies 10 = A + carry.
Since the maximum carry from a single-column addition of two digits is 1, ⟨MATH⟩A⟨/MATH⟩ must be either 9 (with a carry of 1) or 10 (impossible). Thus, A is forced to equal 9.
Answer: (a).
Question details
Year
2024
Paper
CSAT
Question
Q48
Section
Logical & Analytical Reasoning
Sub-topic
Syllogism
Type
Statement-based
Difficulty
Medium
Source hint
Syllogism statements and conclusions
Same sub-topic — other years
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