2022 · Q14
Let a, b, c, d be positive integers. If (1)/(a + (1)/(b +(1)/(c + (1)/(d))))= (17)/(60) then what is the product of a, b, c, d?
Elementary MathematicsNumber System
- A24
- B51
- C68
- D102
Explanation
Invert the continued fraction step by step: 60/17 = 3+9/17 gives a = 3; 17/9 = 1+8/9 gives b = 1; 9/8 = 1+1/8 gives c = 1 and d = 8. The product abcd = 3x1x1x8 = 24 (direct substitution confirms the identity). Key disputed: a widely circulated third-party Set-A key lists B, but the continued-fraction expansion uniquely gives 24. Hence the keyed option is A.