TANCET 2011 Data Sufficiency Qn 1 - Speed Distance Time

Directions

The following problem has a question and two statements which are 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 on mathematics and every day facts, choose:

(1)    If you can get the answer from (1) ALONE but not from (2) alone
(2)    If you can get the answer from (2) ALONE but not from (1) alone
(3)    If you can get the answer from BOTH (1) and (2) TOGETHER, but not from (1) alone or (2) alone
(4)    If EITHER statement (1) ALONE or statement (2) ALONE suffices
(5)    If you CANNOT get the answer from statements (1) and (2) TOGETHER, but need even more data

Question

Plane X files at r miles per hour from A to B. Plane Y files at S miles per hour from B to A. Both planes take off at the same time. Which plane files at a faster rate? Town C is between A and B.
(1)    C is closer to A than it is to B
(2)    Plane X flies over C before plane Y

Correct Answer – Choice 5. Data is INSUFFICIENT

Explanatory answer

Information given in the question stem
1.    Plane X and Plane Y take off at the same time.
2.    Town C is between A and B.

Statement 1: C is closer to A than it is to B

This statement is not helpful in determining which of the two planes is faster unless we know that the two planes met at C. That is not stated in the statement or the question stem.

Statement 1 is INSUFFICIENT. 

Statement 2: Plane X flies over C before Plane Y

This statement alone is not sufficient to determine which of the planes is faster unless we know where C is located.

Statement 2 is INSUFFICIENT.

Combining the two statements, we know that C closer to A. X flies over C before Y.

Because C is closer to A, even if X is as fast as Y or even if it is slower than Y, X could have flown over C earlier than Y.

On the contrary if the statement had mentioned that Y flew over C before X and C is closer to A than to B, we could have inferred that Y was faster than X.

Even after using the two statements we cannot infer which plane is faster.

Choice 5 is the correct answer.

Speed Distance Time : TANCET Quant

Speed Distance Time is one of the topics from which you should expect a question either in the quantitative reasoning section or in the data sufficiency section of the TANCET MBA.

Here is a relatively easy quantitative reasoning question from this topic

Question

It takes Kiran 50 minutes lesser to cover a distance if she travels three times as fast as she does now. How long will she take to cover the distance if she travels twice as fast as she does now?
1. 50 minutes
2. 75 minutes
3. 150 minutes
4. 100 minutes
5. 37.5 minutes

Correct Answer : Choice 5. 37.5 minutes

Explanatory Answer

Let Kiran's present speed be S km/min. And let her take t minutes to reach her destination.

If Kiran travels three times as fast as she does now i.e., at 3S, she will cover the same distance in 1/3 of the time i.e., in t/3 minutes.

So, she is saving (t - t/3) minutes = 2t/3 minutes.
The question states that she is saving 50 minutes.
Therefore, 2t/3 = 50
or t = 75 minutes.

If she travels at S km/min, she will reach her destination in 75 minutes.

So, if she travels at 2S km/min, she will take half that time = 75/2 minutes = 37.5 minutes.

Speed Distance Time Question TANCET

Speed, Distance and Time is an important topic from a TANCET quant perspective. You could expect to get one to two questions from this topic.

The core concept in this topic is the relation between these three parameters
Distance = speed * time.

The second point to keep in mind while solving questions from this topic is to check if the units of the three parameters match.
i.e., if distance is measured in kilometres and time in hours, speed should be in km/hr. Alternatively, if speed is in kilometres and time in minute, speed should be in km/min.

Here is an easy to moderate level difficulty question in this topic.

A bus travels at 40 kmph for the first 100 kms, 60 kmph for the next 100 kms and 48 kmph for the final 200 kms, what is the average speed over the total distance?
1. 48 kmph
2. 50 kmph
3. 49 kmph
4. 52 kmph
5. 50.4kmph

The concept tested in this question is that of average speeds.

The answer to this question is 48 kmph.

Explanatory Answer

Average speed for the first 200kms = 2ab/(a + b) = 2 * 40 * 60/(40 + 60) = 48 kmph.

Bus travels equal distances at two different speeds, average speed = 2ab/(a + b)

Now, if we break the overall journey into two stretches of 200 kms each, the bus travels the first 200kms at 48kmph, and the second at 48 kmph. Overall, average speed = 48 kmph.
Correct answer (1)

Alternatively, you could find out the total time taken to cover the entire distance of 400 kms

Time taken for the first 100 kms = 100 / 40 = 10/4 hours

Time taken for the second 100 kms = 100/60 = 10/6 hours

Time taken for the last 200 kms = 200/48 = 50/12.

Adding up all three, we get 10/4 + 10/6 + 50/12 = 100/12 hours.

Average speed = total distance / total time

= 400 /(100/12) = 4800/100 = 48 kmph

For additional questions on Speed, Distance and Time, click here

Speed Time Distance : TANCET Math

Speed, Time and Distance is an interesting topic from which you could expect to get one question in the math section and probably a question in the data sufficiency section of the TANCET MBA test.

The concept is extremely simple : Distance = Speed * Time
The place where you need to be careful is to make sure that the units that you use for the different quantities have integrity i.e., if the unit for speed used is km/hr, then you should use hour as the unit for time.

Here is a simple question in speed time distance.
Question
Traveling at 4/5ths of her usual speed, Sonal reached office 20 minutes late. How long did she take today?
1. 60 minutes
2. 80 minutes
3. 100 minutes
4. 64 minutes
5. 96 minutes

Explanatory Answer
She travels at 4/5th of her usual speed.
Let her usual speed be 's' km/min. So, today she travels at 4/5s.
Let the usual time she takes be 't' minutes. So, today she will take (t + 20) minutes.
As the distance traveled in both the cases is the same, we can equate them
i.e., st = 4/5s (t + 20)
dividing both sides by 's' we get t = 4/5(t + 20)
or 5t = 4t + 80
or t = 80 minutes.
t is the usual time take.
The time taken today is t + 20 = 100 minutes.

Note: 1. We used km/min as the unit for speed as the unit of time given in the question is in minutes.
2. we did not stop at finding the value of 't'. The question was about finding the time taken today = t + 20.

You can get additional questions on speed time and distance at this link.