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Data Sufficiency - CAT 2013
Question 4 the day:
April 10, 2002
- 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
- Leaving home and travelling at 3/4ths of my usual speed, I reached office late today. What is the usual time that I take to reach office? (Assume that each day I take the same route to the office)
(A) It took me 15 more minutes to reach office today.
(B) The distance between my office and home is 12 kms.
Correct Answer - (1)
Solution:
Statement (A) alone is sufficient to answer the question. Statement (B) alone is not sufficient to answer the question. Hence the correct answer is (1).
The distance between my home and office is the same irrespective of the speed I travel at.
Let the usual speed at which I travel be S km/min. Therefore, the speed at which I travelled today = (3/4)S.
Let 't' be the usual time in minutes that I take to travel to my office.
From Statement (A) we know that I took 15 more minutes today, the time taken today = t + 15.
We know that Distance = Speed * Time
As the distance is the same on both the occassions,
St = (3/4)S * (t+15)
==> t = (3/4)(t + 15). Cross multiplying 4 on to the other side we get,
==> 4t = 3t + 45
==> t = 45 minutes. The usual time that I take to reach office is 45 minutes. Statement (A) alone is sufficient to answer the question.
Statement (B) provides the information about the distance between my home and office, which will not be of use in finding out the usual time that it takes. Hence Statement (B) alone is not sufficient.
Therefore, the correct answer is (1).
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