Multiple choice

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. X can complete a job in 10 days and X, Y and Z together can complete the same job in 5 days. Y can complete the same job in how many day? (1) Z can complete the same job in 30 days. (2) Y is 2 time efficient than Z.

  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

Let R_x, R_y, R_z be the rates. We know R_x = 1/10 and R_x + R_y + R_z = 1/5. Thus, R_y + R_z = 1/10. Statement (1) gives R_z = 1/30, allowing us to find R_y. Statement (2) gives R_y = 2 * R_z, which combined with R_y + R_z = 1/10 also allows us to find R_y. Both statements are sufficient independently.

AI explanation

The combined rate of X, Y, and Z is 1/5, and X's rate is 1/10, so the combined equation for Y and Z is 1/Y + 1/Z = 1/10. Statement 1 provides Z's rate as 1/30, allowing you to solve for Y directly by substituting the value into the equation. Statement 2 provides the ratio of Y's efficiency to Z's efficiency as 2 to 1, meaning Y takes half the time Z takes, which allows you to substitute Y as Z/2 and solve for the exact days. Since you can find Y's time by substituting the data from either statement into the main equation, each statement alone is sufficient.

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