alleryCode ABCD uses distinct digits 1–6. C=2D and A+C=B+D. The two-digit numbers AB and CD differ by 24, with AB larger. Find A×C+B×D.
A13
B11
C15
D17
Answer & Solution
Correct answer: A. 13
Putting C=2D gives B=A+D. Then AB−CD=11A−20D=24. With D=1,2,3 and distinct digits 1–6, only A=4,D=1 works. The code is 4521 and A×C+B×D=8+5=13.
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