Multiple choice

The following questions are accompanied by three statements I, II and III. You have to determine which statement(s) is/are necessary/sufficient to answer the question? In how many days could each A, B and C do the work by himself? Statement I: A and B together can finish the work in 12 days. While B and C together can finish in 15 days. Statement II: C alone can finish the work in 40 days. Statement III: B alone can finish the work in 20 days.

  1. Only I or II or III

  2. Only I and either II or III

  3. Only II and III

  4. All are necessary

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

From I: A + B = 1/12 and B + C = 1/15. This gives A - C = 1/12 - 1/15 = 1/60. Statement II: C = 1/40. Substituting in I: B = 1/15 - 1/40 = 1/24, then A = 1/12 - 1/24 = 1/24. Statement III: B = 1/20. Substituting in I: A = 1/12 - 1/20 = 1/30, then C = 1/15 - 1/20 = 1/60. Either II or III combined with I is sufficient.

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