Multiple choice

Directions: The question below consists of two statements labelled (I) and (II). You have to decide whether the data provided in the statements is sufficient to answer the question. Two taps P and Q together take 3 min 36 sec to fill a tank. How many minutes does a drain pipe R take to empty the tank when it is full? (I) P and R can fill the tank in 9 min. (II) Q alone takes 9 min to fill the tank. Mark your answer as:

  1. If the question can be solved using only one of the statements

  2. If the question can be solved using either of the statements

  3. If the question can be solved using both the statements but not either alone

  4. If the question cannot be solved using the given statements
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Let the tank capacity be 1 unit. P+Q fill at 1/3.6 = 5/18 units/min. Statement (II) says Q fills at 1/9 units/min, so P fills at 5/18 - 2/18 = 3/18 = 1/6 units/min. Statement (I) says P-R fills at 1/9 units/min, so R empties at 1/6 - 1/9 = 1/18 units/min. Both statements are required to find R's rate.

AI explanation

Taps P and Q together take 3 minutes and 36 seconds, which is 3.6 minutes, making their combined rate 5/18 of the tank per minute. Statement I provides the combined rate of P and R, but lacks information about Q, while statement II provides the filling rate of Q but lacks information about R. Using both statements, we can first determine the rate of P by subtracting Q's rate from the combined P and Q rate, and then use that to find R's rate from the P and R combined rate. Since both statements are required to find the individual rates of P and Q needed to deduce the rate of R, the question can be solved using both statements together but not by either alone.

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