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Data Sufficiency - CAT 2013
Question 4 the day:
May 24, 2002
The question for the day is a data sufficiency question.
In this question, there is a question statement which is followed by two statements. You have to decide whether the data provided in the two statements is sufficient for answering the question.
- Mark 1
- If the question can be answered by using one of the statements alone, but cannot be answered by using the other statement alone.
- Mark 2
- If the question can be answered by using either statement alone.
- Mark 3
- If the question can be answered by using both statements together, but cannot be answered by using either statement alone.
- Mark 4
- If the question cannot be answered even by using both the statements together.
- Question
- What was the speed at which I traveled from the office to the CAT class today?
(A) Today, I was traveling at 4/5th of my usual speed.
(B) Today, it took me 10 more minutes to reach the class.
Correct Answer - (4)
Solution
Let the usual speed at which I travel to the class be ‘S’ km/min. And let the usual time that it takes me to reach the class from office be ‘t’ minutes. Therefore, the distance between my office and the classes is S*t km. (Distance = speed * time)
Statement A: Today, I am traveling at 4/5th of my usual speed. Therefore, today’s speed = 4S/5. We know the distance between my office and the class is St and statement A does not provide sufficient data to find out what ‘S’. Therefore, statement A alone is not sufficient. Hence we can eliminate (2) as an answer choice. The answer has to be (1) or (3) or (4).
Statement B: It took me 10 more minutes to reach the class. Therefore, the time taken today = (t + 10). We know that the distance between my office and class is St and the time taken today is (t+10). Statement B alone has not provided sufficient information to find out S or 4S/5. Hence it is also not sufficient. So the answer choice is neither (1) nor (2). It has to be either (3) or (4).
Combining Statement A and Statement B, we get
The speed today is 4S/5 and the time taken today is (t + 10) minutes.
The distance between the office and the class will be the same irrespective of the speed at which I travel and the consequent time it takes.
Therefore, St = (4S/5)(t + 10).
=> t = 4/5 (t + 10) => 5t = 4t + 40 or t = 40 minutes. So the usual time it takes is 40 minutes and the time it took today is 50 minutes. From Statement A and Statement B, we know the usual time and the time it took today. But there is no way to find out the speed without knowing the distance between the office and the class.
Hence, the data provided by the two statements is not sufficient to answer the question - “the speed at which I traveled today to the class”. Therefore, the correct answer is (4).
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