Speed Data Sufficiency should be the last topic in the chapter we call Time and Speed. In this section, we will discuss the data sufficiency questions from this section. Remember that the data sufficiency test is one of the most important topics for banking eams and other similar graduate level courses. Here we will see many examples and practice questions of Speed Data Sufficiency.

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## Speed Data Sufficiency

Let us solve some questions from the section that are expected to be asked in the exam. We have divided the questions into several parts for convenience.

Directions (Questions 1 to 6): Each of the questions below consists of a statement and/or a question and two statements numbered I and II given below it. You have to decide whether the data provided in the statements is/are sufficient to answer the question. Read both the statements and:

Write the answer (a) if the data in Statement I alone are sufficient to answer the question, while the data in Statement II alone are not sufficient to answer the question.

Give the answer (b) if the data in Statement II alone are sufficient to answer the question, while the data in Statement I alone are not sufficient to answer the question.

Write the answer (c) if the data in Statement I or in Statement II alone are not sufficient to answer the question.

Give the answer (d) if the data even in both Statements I and II together are not sufficient to answer the question.

Write the answer (e) if the data in both Statements I and II together are necessary to answer the question.

### Part I

Q 1: How much time did X take to reach the destination?

I. The ratio between the speeds of X and Y is 3: 4.

II. Y takes 36 minutes to reach the same destination.

Answer: I. If Y takes 4 minutes then X takes 3 minutes.

II. If Y takes 36 minutes then X takes [3/4×36] min = 27 mi.

Thus, I and II together give the answer. Therefore correct answer is (e).

Q 2: What is the usual speed of the train? [MBA 2002]

I. The speed of the train is increased by 25 km/hr to reach the destination 150 km away in time.

II. The train is late by 30 minutes.

Answer: Let the usual speed of the train be x kmph. Time taken to cover 150 km at usual speed = 150/x hrs.

I. Time taken at increased speed = (150)/(x + 25) hrs.

II. (150/x) – (150)/(x + 25) = 30/60. In other words we have:

1/x – /(x + 25) = 1/300. Therefore we have [(x + 25) – x] × 300 = x(x + 25).

Thus we have x^{2} + 25x – 7500 = 0. Also, (x + 100)(x – 75) = 0 and x = 75. Thus, I and II together give the answer. Therefore the correct answer is (e).

### Part II

Q 3: Two towns are connected by railway. Can you find the distances between them?

I. The speed of mail train is 12 km/hr more than that of an express train.

II. A mail train takes 40 minutes less than an express train to cover the distance. [M.B.A. 2001]

Answer: Let the distance between the two stations be x km.

I. Let the speed of the express train be y km/hr. Then, the speed of the mail train = (y + 12) km/hr.

II. x/y – x/(y + 12) = 40/60. Thus, even I and II together do not give x. Therefore the correct answer is (d).

Q 4: The towns A, B and C are on a straight line. Town C is between A and B. The distance from A to B is 100 km. How far is A from C?

I. The distance from A to B is 25% more than the distance from C to B.

II. The distance from A to C is /4 of the distance from C to B.

Answer: Let A and B be the two endpoints and C be a point between them such that AC = x and CB = (100 -x) km.

I. AB = 125% of CB. In other words, we can write 100 = (125/100)×(100 – x). We can write it as (100 – x) = (100×100)/125 = 80 and x = 20 km. Therefore AC = 20 km.

Thus I alone gives the answer.

II. AC = 1/4 CB which implies that x = 1/4(100 – x). Thus we have 5x = 100 and x = 20. Therefore AC = 20 km and II alone gives the answer. Thus the correct answer is (c).

### Part III

Q 5: What is the average speed of the car over the entire distance?

I. The car covers the whole distance in four equal stretches at speeds of 10 kmph, 20 kmph, 30 kmph and 60 kmph respectively.

II. The total time taken is 36 minutes.

Answer: Let the whole distance be 4x km.

I. Total time taken = [x/10 + a20 + x/30 + x/60] = (6x + 3x + 2x + x)/60 = 12x/60 = x/5.

Therefore speed = (Distance)/(Time) = 4x/(x/5) kmph = 20 km/hr. Thus I alone is sufficient to answer the question and II alone doesn’t give the answer. Therefore the correct answer is (a).

## Practice Questions

Q 1: Directions (Questions 1 to 6): Each of the questions below consists of a statement and/or a question and two statements numbered I and II given below it. You have to decide whether the data provided in the statements is/are sufficient to answer the question. Read both the statements and:

Write the answer (a) if the data in Statement I alone are sufficient to answer the question, while the data in Statement II alone are not sufficient to answer the question.

Give the answer (b) if the data in Statement II alone are sufficient to answer the question, while the data in Statement I alone are not sufficient to answer the question.

Write the answer (c) if the data in Statement I or in Statement II alone are not sufficient to answer the question.

Give the answer (d) if the data even in both Statements I and II together are not sufficient to answer the question.

Write the answer (e) if the data in both Statements I and II together are necessary to answer the question.

Two cars pass each other in opposite direction. How long would they take to be 500 km apart?

I. The sum of their speeds is 135 km/hr.

II. The difference of their speeds is 25 km/hr. [MAT 1998]

Ans: (a)