Cryptarithm AB x CD = DEF, DEF + GHI = 975
Question
AB and CD are 2-digit numbers. Multiplying AB with CD results in a 3-digit number DEF. Adding DEF to another 3-digit number GHI results in 975. Further A, B, C, D, E, F, G, H, I are distinct digits. If E = 0, F = 8 then what is A + B + C equal to ?
Options
6
7
8
9
Explanation
We are given that E = 0 and F = 8, so the product DEF = D08[cite: 4402, 4467]. Substitute this into the second cryptarithm addition equation: D08 + GHI = 975 [cite: 4400, 4466]
Evaluate the column addition from right to left:
The digits used so far are \{0, 6, 7, 8\}. The remaining open digits are \{1, 2, 3, 4, 5, 9\}. Since D + G = 9, the only available pair from our remaining pool is (4, 5) or (5, 4). Thus, D can only be 4 or 5.
Now evaluate the multiplication: AB × CD = D08[cite: 4398, 4399, 4465].
This configuration works perfectly and uses the distinct digits A=1, B=2, C=3, D=4, G=5, H=6, I=7, E=0, F=8. All 9 digits are completely distinct[cite: 4401, 4466]. Calculate the required sum: A + B + C = 1 + 2 + 3 = 6.
Answer: (a).
Question details
Year
2023
Paper
CSAT
Question
Q76
Section
Logical & Analytical Reasoning
Sub-topic
Cryptarithmetic
Type
Coding-decoding
Difficulty
Hard
Source hint
Cryptarithmetic puzzle
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