Question

Some equations are solved on a certain basis. Find \(13 \times 13 = \,?\) given: \(5 \times 8 = 28,\; 3 \times 7 = 12,\; 8 \times 6 = 35.\)

• A. 169
• B. 130
• C. 140
• D. 144

Hint:

Test simple transforms like \((a-1)(b-1)\) or \((a+1)(b+1)\) on all examples to uncover the rule.

Answer 1

The Correct Option is D

Rule: \(a \times b \;\mapsto\; (a-1)(b-1)\). \[ 5\times 8 \Rightarrow 4\cdot 7=28,\quad 3\times 7 \Rightarrow 2\cdot 6=12,\quad 8\times 6 \Rightarrow 7\cdot 5=35. \] Therefore, \[ 13\times 13 \Rightarrow 12\cdot 12=144. \] \[ \boxed{144} \]