Multiple choice

Passage

Directions: The following question is accompanied by three statements, (A) or (I), (B) or (II) and (C) or (III). Determine the statement(s) sufficient/necessary to answer the question.

X, Y and Z together can complete a work in 15 days. How long will it take for Y alone to complete the same job? A. X is 50% more efficient than Y. B. X and Y together can complete the work in 25 days. C. X and Z together can complete the work in 30 days.

  1. Either A and B together or C alone is sufficient.

  2. All A, B and C are not sufficient.

  3. Only A and B are sufficient.

  4. Only A and C are sufficient.

  5. Only C is sufficient.
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

X+Y+Z = 1/15. A: X=1.5Y. B: X+Y=1/25. C: X+Z=1/30. Using A and B: 1.5Y+Y = 1/25 -> 2.5Y = 1/25 -> Y = 1/62.5. Using C: Since X+Y+Z=1/15 and X+Z=1/30, Y = 1/15 - 1/30 = 1/30. Both paths lead to a unique value for Y.

AI explanation

From the question, X, Y, and Z together complete the work in 15 days, meaning their combined daily rate is 1/15 of the work. Statement C provides the rate for X and Z together as 1/30 of the work per day. Subtracting the rate in C from the combined rate of all three gives Y's rate of 1/30, making C alone sufficient. Additionally, using statement B (X and Y equal 1/25) with statement A (X is 1.5 times Y), you can solve for Y's individual rate, meaning either A and B together or C alone is sufficient.

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