Multiple choice

Passage

Directions: This data sufficiency problem consists of a question and two statements labelled (1) and (2). You have to decide whether the data given in the statements is sufficient for answering the question.

Rahim can complete 40% of the work in 16 days, Karim can complete 60% of the same work in 12 days and Abdul can complete the whole work in X days. Find the value of X. (i) The efficiency of Abdul is the average of the efficiency of Rahim and Karim together. (ii) The Abdul is twice as efficient than Rahim.

  1. Statement (1) alone is sufficient, but statement (2) alone is not sufficient.

  2. Statement (2) alone is sufficient, but statement (1) alone is not sufficient.

  3. Both statements (1) and (2) together are sufficient, but neither of them alone is sufficient.

  4. Each statement alone is sufficient.

  5. Both statements (1) and (2) together are not sufficient.
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Rahim: 40% in 16 days -> 100% in 40 days. Karim: 60% in 12 days -> 100% in 20 days. Efficiencies are 1/40 and 1/20. Statement (1): Abdul's efficiency = (1/40 + 1/20)/2 = (3/40)/2 = 3/80. X = 80/3. Statement (2): Abdul is twice as efficient as Rahim (1/40), so Abdul = 2/40 = 1/20. X = 20. Both statements are sufficient individually.

AI explanation

From the given data, Rahim's rate is 40/100 / 16 = 1/40 and Karim's rate is 60/100 / 12 = 1/20. Statement 1 notes Abdul's efficiency is the average of Rahim and Karim, so Abdul's rate is (1/40 + 1/20)/2 = 3/80, giving X = 80/3 days. Statement 2 says Abdul is twice as efficient as Rahim, so Abdul's rate is 2 * 1/40 = 1/20, giving X = 20. Since X can be found using either statement independently, each statement alone is sufficient.

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