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. Find the number of days in which Rahim can complete a piece of work. (1) Rahim and Sunil together can complete the same piece in 72/7 days. (2) Rahim is 33.33% more efficient than Sunil.

  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. Both the statement alone is sufficient.

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

Statement (1) gives the combined rate of work. Statement (2) provides the ratio of their efficiencies. To find the individual time, you need both the combined rate and the relative efficiency to set up a system of equations.

AI explanation

Statement 1 provides the combined rate of Rahim and Sunil as 7/72, yielding the equation 1/Rahim + 1/Sunil = 7/72. Statement 2 establishes an efficiency ratio, meaning Rahim completes 4/3 of the work Sunil completes in the same time, so Rahim takes 3/4 of the time Sunil takes, giving the relationship Rahim = 0.75 * Sunil. You cannot solve for the individual time with only one equation from Statement 1, nor can you find an absolute number of days with only the ratio from Statement 2. By substituting the value from Statement 2 into the equation from Statement 1, you can solve for Rahim's exact time, proving both statements together are sufficient.

Keep practicing — related questions