Multiple choice

In how many days could each A, B, and C do the work by himself? (I) A and B together can finish the work in 12 days. While B and C together can finish in 15 days. (II) C alone can finish the work in 40 days. (III) B alone can finish the work in 20 days.

  1. Only I and II

  2. Only I and III

  3. Only I and either II or III

  4. All I, II and III

  5. None of these
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

From Statement I: A+B=12 days and B+C=15 days. Combining these gives their rates. Statement II (C=40 days) or Statement III (B=20 days) each provide the third value needed. Using I+II: With C=40, from B+C=15 we get B's rate, then from A+B=12 we get A's rate. Using I+III: With B=20, from A+B=12 we get A, then from B+C=15 we get C. Either pair gives all three values. I+II is sufficient, I+III is sufficient, and the question asks which combination works.

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