TANCET 2014 DS Question 62: Speed Time
Directions
The question is followed by two statements labeled (1) and (2) 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 problem plus your knowledge of mathematics and everyday facts, choose the answer as:
 Choice 1 if statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.
 Choice 2 if statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.
 Choice 3 if both the statements (1) and (2) TOGETHER are sufficient, but NEITHER statement alone is sufficient.
 Choice 4 if each statement ALONE is sufficient.
 Choice 5 if statements (1) and (2) TOGETHER are not sufficient, and additional data is needed.
Question
2. Basic ratio proportion concepts 2 concepts
A car drives along a straight road from Sankarankoil to Coimbatore, going through Madurai along the way. What is the total distance travelled by the car from Sankarankoil to Coimbatore?
 Statement 1: The distance from Sankarankoil to Madurai is 3/5 of the entire distance.
 Statement 2: The distance from Madurai to Coimbatore is 12 km.
Correct Answer Choice (3). Both statements are needed to answer the question.
Explanatory Answer  step by step

What do we know from the Question Stem?
Before evaluating the two statements, answer the following questions to gain clarity.
What kind of an answer will the question fetch?
The question is "What is the total distance travelled by the car?"
The answer should be a number followed by a unit of distance. Say, 52 miles or 28 km.
When is the data sufficient?
If we are able to come up with a unique value for the distance travelled by the car, the data is sufficient.
Either if we are not able to come up with a unique answer (i.e., if we get more than one value) or if the data is not enough to find the exact distance between Coimbator and Sankaran Koil, the data is NOT sufficient.
What else is know from the question?
The question states that "the car travelled via Madurai".

Statement (1) ALONE
The distance from Sankarankoil to Madurai is 3/5 of the entire distance.
Sankarankoil to Madurai is 3/5th of the total distance.
Without knowing the distance between Sankarankoil and Madurai, we cannot equate the proportion to the actual distance and compute the total distance.
For instance, if the distance between Sankarankoil and Madurai is 300 km, the total distance will be 500 km. Conversely, if the distance between Sankarankoil and Madurai is 600 km, the total distance will be 1000 km.
The bottomline is that we cannot find the total distance from the information given in statement (1).
Statement (1) ALONE is NOT sufficient.
The moment we realize that statement (1) is NOT sufficient, we can eliminate choices 1 and 4.
We can narrow down our choices to 2, 3 and 5.

Statement (2) ALONE
The distance from Madurai to Coimbatore is 12 km.
Remember: When you are evaluating statement (2) ALONE, please do not recall information that you read in statement (1). It might even be a good practice to cover statement (1).
We know the distance for one part of the journey  between Madurai and Coimbatore.
However, from statement (2) we do not know the distance for the other part  distance between Sankarankoil and Madurai.
We are not able to determine the total distance using statement (2) alone.
Statement (2) ALONE is NOT sufficient.
We can eliminate choice 2.
The answer narrows down to 3 or 5.

Combine the statements
1. The distance from Sankarankoil to Madurai is 3/5 of the entire distance.
+2. The distance from Madurai to Coimbatore is 12 km.
From statement (1) we can deduce that the distance between Madurai and Coimbatore is 2/5th of the total distance.
From statement (2) we know that the distance between Madurai and Coimbatore is 12 km.
Equating the two we will be able to get a unique answer for the total distance.
Note: You do not have to find the distance in a data sufficiency question . You just need to be sure that you can find a unique answer.
Nevertheless, let us find the distance before wrapping the question
If the total distance is x, then \\frac { 2 }{ 5 } x =12 \\)
Or x = \\frac { 12\times 5 }{ 2 } \\) = 30 km.
Using statements (1) and (2) TOGETHER, we could find a unique answer.
Hence, the correct answer is Choice 3. Both statements are needed to answer the question.
Video Explanation
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 Number Theory
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