Data Sufficiency  Quant/Math  CAT 2016
Question 4 the day:
March 04, 2005
The question for the day is a data sufficiency question.
 In a data sufficiency question you will be given a question that will be followed by two statements. You are expected to answer if the information provided in the two statements is sufficient to answer the given question.
Please be careful to read the instructions before the data sufficiency questions. These instructions have changed from CAT to CAT. CAT 2003 (Re test) had a different set as compared to the ones seen in the previous three or four Common Admission Tests.
Directions
 This data sufficiency problem consists of a question and two statements, labeled (A) and (B), in which certain data are given. You have to decide whether the data given in the statements are sufficient for answering the question. Using the data given in the statements, plus your knowledge of mathematics and everyday facts (such as the number of days in a leap year or the meaning of the word counterclockwise), you must indicate whether 

(1) The question can be answered using either statement (A) alone but not statement (B) or statement (B) alone but not statement (A).
(2) If either of the two statements individually is sufficient to answer the question
(3) If both statements (A) and (B) together are required to answer the question
(4) The question cannot be answer despite using the information provided in statements (A) and (B) taken together.
Question
 How long will it take for two pipes A and B to fill an empty cistern if they worked alternately for an hour each?
A. Working alone, Pipe A can fill the cistern in 40 hours
B. Pipe B is one third as efficient as Pipe A
Correct choice (3). Correct Answer  (Both the statements together are sufficient to answer the question.)
Explanatory Answer:
From statement A, we know that Pipe A can fill the tank in 40 hours. However, this information is not sufficient as we do not have the data for Pipe B. Hence, statement A alone cannot answer the given question.
From statement B, we know that Pipe B is one third as efficient as pipe A. However, we do not know the rate at which Pipe A fills the tank. Hence, we will not be able to find the rate at which Pipe B fills the cistern. Therefore, statement B alone is not sufficient to answer the question.
Now, if we combine the two statements, we know that Pipe A take 40 hours to fill the cistern.
Pipe B takes 120 hours to fill the cistern.
If they worked alternately, then either Pipe A could have started the cycle or Pipe B could have started the cycle.
If Pipe A started the sequence of filling alternately, then at the end of two hours, the two pipes together would have filled th of the tank in an hour. Or the cistern will fill in 30 hours.
If Pipe B started the sequence, then at the end of 2 hours, the two pipes together would have filled th of the tank in an hour. Or the cistern will fill in 30 hours.
As the answer obtained irrespective of which pipe started the sequence is the same, the correct answer is (3)  i.e., both the statement are required to answer the question.
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