Operators □, ◇ and → are defined by: a□b = (a−b)/(a+b); a◇b = (a+b)/(a−b); a→b = ab.
Find the value of (66 □ 6) → (66 ◇ 6).
Options:
(A) −2
(B) −1
(C) 1
(D) 2
Official Answer Key:
C
Step-by-Step Solution & Explanation
First evaluate the two bracketed terms using the given definitions:
66 □ 6 = (66−6)/(66+6) = 60/72 = 5/6.
66 ◇ 6 = (66+6)/(66−6) = 72/60 = 6/5.
Now apply a→b = ab on these results: (5/6) → (6/5) = (5/6)×(6/5) = 1. Note that ◇ is exactly the reciprocal of □ for the same operand pair, so their product under → always equals 1 — recognising this shortcut avoids arithmetic errors. Hence (C) is correct.
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