Data Sufficiency For IBPS RRB Exam, Check All Questions

Data Sufficiency For IBPS RRB Exam: Data sufficiency problems are an essential part of the Reasoning section. It contains a question followed by statements with clues to answer it. These clues might look confusing but act as keys to answering the questions. These problems are not traditional questions but questions where candidates find the answer directly. It tests candidates’ tenacity or his/her power of judgment, where they must ascertain or conclude whether the given statements provide enough information to solve the question. These types of questions appear frequently in multiple government exams, including the IBPS RRB Exam. Candidates can prepare effectively for upcoming government exams by understanding the patterns of questions asked in Data Sufficiency. Read on to clear any doubts on this topic.

In this article, we’ll take a deep dive into the key concepts of the Data Sufficiency Logical Reasoning section. We’ll explore solved examples, practice questions, and valuable tips and tricks needed to successfully and quickly tackle the Data Sufficiency for IBPS RRB exam.

What is Data Sufficiency?

Data Sufficiency part of the Reasoning sections requires the ability to check or test the given information in option form. You’ll have to decide whether the information or options are enough to answer a question or not. Data Sufficiency-type questions will test your ability to relate provided information to come to a conclusion or reach a decision. In short, it tests your decision-making power logically. It might throw at your questions from any of the topics of reasoning or quantitative aptitude and examine your analytical skills through it. 

These questions cover varied topics like sequence, coding-decoding, ranking, and puzzle tests. There are multiple statements following the questions or problem. These statements, which are usually 5 in number, provide information to solve the question and get the right answer. You must, therefore, determine which statement(s) are sufficient for answering. In short, these statements will help you arrive at the right answer. Therefore, your power of decision-making is important for solving these types of questions.

Types of Data Sufficiency

Data Sufficiency questions are a common feature of the reasoning sections in almost all the government competitive exams. This part tests the candidate’s ability to decide or establish whether the given statements have enough information to answer the question or not. Check out the table below to learn about the different types of Data Sufficiency questions you might encounter, together with a brief description of each type.

Type of Data Sufficiency	Description
Blood Relation	Questions involve determining the relationship between two people. Candidates must use the given statements.
Order & Ranking	Questions involve determining the order or ranking of people. Candidates must analyze the provided data.
Coding Decoding	Questions involve deciphering coded words or letters. Candidates need to find the logic applied in the coding process.
Direction & Distance	Questions involve determining directions or distances. Candidates must use the movement or location data provided.
Seating Arrangement	Questions involve finding the arrangement of people. This can be in linear or circular setups based on the information.
Floor Puzzle	Questions involve determining which floor people live on. This can be in one or multiple buildings based on the provided data.
Scheduling	Questions involve determining schedules based on data. The data can be related to months, years, or specific dates.

Data Sufficiency Practice Questions & Answers

It is essential to practice the maximum number of questions on Data Sufficiency for IBPS RRB Exam, to successfully tackle them in the exam. This is the reason why we have brought you the best examples of their solutions and the Hindi versions of them as well. Practice these questions and others and take mock tests to check the speed and accuracy needed to master Data Sufficiency for IBPS RRB Exam.

Question 1: Rajiv and Puneet started travelling towards each other from point A and point B, respectively at the same time. Find the speed of Puneet.

Statement I: Distance between point A and point B is 396 km.

Statement II: Ratio of speed of Rajiv to speed of Puneet is 6:5, respectively.

Statement III: Rajiv takes 3 hours to reach point B after meeting Puneet.

A) Data in statement I and II together are necessary to answer the question.

B) Data in statement I and III together are necessary to answer the question.

C) Data in statement II and III together are necessary to answer the question.

D) Data in statements I, II and III together are necessary to answer the question.

E) Data in statements I, II and III together are not sufficient to answer the question.

Question 2: The question consists of two statements numbered “I and II” given below it. You have to decide whether the data provided in the statements are sufficient to answer the question.

Three pipes, A, B and C are attached to a tank. Pipe A and B together can fill the tank in 40 minutes, while pipe B and C together can fill the tank in 50 minutes. If all the pipes are opened for 4 minutes and then pipe A and C are closed, find the time taken to empty the tank.

Statement I: Pipe A is 20% more efficient than pipe C. 

Statement II: Pipe A, B and C together can fill the tank in 20 minutes.

A) 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.

B) 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.

C) The data either in statement I alone or in statement II alone are sufficient to answer the question.

D) The data given in both statements I and II together are not sufficient to answer the question.

E) The data in both statements I and II together are necessary to answer the question.

Question 3: The question consists of two statements numbered “I and II” given below it. You have to decide whether the data provided in the statements are sufficient to answer the question.

Dheeraj and Samay are travelling to point B from point A by bus and car, respectively. Find the speed of the bus.

Statement I: Distance between point A and point B is 320 km. Bus takes 160 more minutes than car to reach point B.

Statement II: Speed of bus is two-third of speed of car.

A) 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.

B) 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.

C) The data either in statement I alone or in statement II alone are sufficient to answer the question.

D) The data given in both statements I and II together are not sufficient to answer the question.

E) The data in both statements I and II together are necessary to answer the question.

Question 4: The question consists of two statements numbered “I and II” given below it. You have to decide whether the data provided in the statements are sufficient to answer the question.

What is the length of the train X?

Statement I: Two trains X and Y cross each other while travelling in the opposite direction towards each other, and while travelling in same direction in 10 seconds and 25 seconds, respectively. Length of train Y is 80 metres.

Statement II: Speed of train X is 35 km/h and the speed of train Y is less than that of X.

A) 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.

B) 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.

C) The data either in statement I alone or in statement II alone are sufficient to answer the question.

D) The data given in both statements I and II together are not sufficient to answer the question.

E) The data in both statements I and II together are necessary to answer the question.

Question 5: The question consists of two statements numbered “I and II” given below it. You have to decide whether the data provided in the statements are sufficient to answer the question.

Find the time taken by a boat to cover a distance of 250 km in still water.

Statement I: The boat can cover a distance of 135 km upstream and 195 km downstream in 6 hours.

Statement II: The boat can travel 90 km upstream and 130 km in downstream in 4 hours.

A) 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.

B) 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.

C) The data either in statement I alone or in statement II alone are sufficient to answer the question.

D) The data given in both statements I and II together are not sufficient to answer the question.

E) The data in both statements I and II together are necessary to answer the question.

Question 6: The question consists of two statements numbered “I and II” given below it. You have to decide whether the data provided in the statements are sufficient to answer the question.

A mixture contains milk and water in the ratio of 12:11 respectively. Find the quantity of water in the mixture.

Statement I: 20% of mixture is replaced with same quantity of water then the ratio of milk to water becomes 48:67.

Statement II: If 125 ml of water is added in the mixture, the ratio of milk to water becomes 3:4.

A) 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.

B) 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.

C) The data either in statement I alone or in statement II alone are sufficient to answer the question.

D) The data given in both statements I and II together are not sufficient to answer the question.

E) The data in both statements I and II together are necessary to answer the question.

ANSWER KEYS and SOLUTIONS:

1) – D)

2) – C)

3) – E)

4) – E)

5) – D)

6) – B)

Solution 1: D)

Statement I:

Distance between point A and point B is 396 km.

So, statement I alone is not sufficient to answer the question.

Statement II:

Let, speed of Rajiv and Puneet be 6x km/h and 5x km/h, respectively.

So, statement II alone is not sufficient to answer the question.

Statement III:

Rajiv takes 3 hours to reach point B after meeting Puneet.

So, statement III alone is not sufficient to answer the question.

Statement I and statement II:

Distance between point A and point B is 396 km.

Let, speed of Rajiv and Puneet be 6x km/h and 5x km/h, respectively.

So, Statement I and statement II together is not sufficient to answer the question.

Statement I and statement III:

Distance between point A and point B = 396 km

Let, distance travelled by Puneet to meet Rajiv = ‘y’ km

And, distance travelled by Rajiv to meet Puneet = ‘396 – y’ km

Speed of Rajiv = y/3 km/h

So, Statement I and statement III together is not sufficient to answer the question.

Statement II and statement III:

Let, speed of Rajiv and Puneet be 6x km/h and 5x km/h, respectively.

Ratio of time taken by Rajiv and Puneet to reach their respective destination = 5: 6

Time taken by Puneet to meet Rajiv = (6/5) × 3 = 3.6 hours

So, Statement II and statement III together is not sufficient to answer the question.

Statement I, II, and III:

Let, speed of Rajiv and Puneet be 6x km/h and 5x km/h, respectively.

Distance between point A and point B = 396 km

Ratio of time taken by Rajiv and Puneet to reach their respective destination = 5: 6

Time taken by Puneet to meet Rajiv = (6/5) × 3 = 3.6 hours

So, 6x × 3.6 + 5x × 3.6 = 396

39.6x = 396, x = 10

Speed of Puneet = 5x = 50 km/h

So, statement I, statement II and statement III together is necessary to answer the question.

Hence, option d.

Solution 2: C)

Let the capacity of the tank be LCM of (40 and 50) = 200 units

Number of units of water filled by pipe (A + B) together in one minute = 200/40 = 5 units

Number of units of water filled by pipe (B + C) together in one minute = 200/50 = 4 units

Statement I:

So, number of units of water filled by pipe (A + B + B + C) together in one minute = 5 + 4 = 9 units

Now, A + 2B + C = 9

Since, the efficiency of A is 20% more than C.

So, 1.2C + 2B + C = 9

2B + 2.2C = 9 —-(1)

And, B + C = 4 —-(2)

Solving eq. (1) and eq. (2), we get

C = 5 units and A = 6 units

So, number of units of water emptied by pipe B in one minute = 6 – 5 = 1 unit

Number of units of water filled by pipe A, B and C together in one minute = 6 + 5 – 1 = 10 units

So, number of units of water filled by pipe A, B and C together in 4 minute = 40 units

Required time taken to empty the tank = 40/1 = 40 minutes

So, statement I alone is sufficient to answer the question.

Statement II:

So, number of units of water filled by pipe (A + B + C) together in one minute = 200/20 = 10 units

Number of units of water filled by pipe A in one minute = 10 – 4 = 6 units

Number of units of water emptied by pipe B in one minute = 6 – 5 = 1 unit

So, number of units of water filled by pipe A, B and C together in 4 minute = 40 units

Required time taken to empty the tank = 40/1 = 40 minutes

So, statement II alone is sufficient to answer the question.

Hence, option c.

Solution 3: E)

Statement I:

Let, time taken by car be ‘t’ hours.

So, time taken by bus = ‘t + 160/60’ hours

And, distance between point A and point B = 320 km

So, data in statement I alone is not sufficient to answer the question.

Statement II:

Let, speed of bus and car be ‘2x’ km/h and ‘3x’ km/h respectively.

So, data in statement II alone is not sufficient to answer the question.

Combining statement I and II:

Let, speed of bus and car be ‘2x’ km/h and ‘3x’ km/h respectively.

So, 320/2x – 320/3x = 160/60

(960 – 640)/6x = 8/3

40 = 2x

So, speed of bus = 2x = 40 km/h

So, the data in both statements I and II together are necessary to answer the question.

Hence, option e.

Solution 4: E)

Let speed of train X and Y be x km/h and y km/h, respectively.

Let length of train X be ‘l’ metres.

Statement I:

According to question,

(l + 80) = 10 × (x +y)………………………………(1)

(l + 80) = 25 × (x – y)………………………………(2)

From (1) and (2)

10 × (x + y) = 25 × (x – y)

7y = 3x

Therefore, statement I alone is not sufficient to answer the question.

Statement II:

Speed of train X = 35 km/h

Therefore, statement II alone is not sufficient to answer the question.

Combining the statements, I and II,

Speed of train X = 35 km/h

So, 7y = 3 × 35

y = 15 km/h

From equation (1)

(l + 80) = 10 × (x + y)

l + 80 = 10 ×(35 + 15) × 5/18

l = 139 – 80 ~ 59 metres

Therefore, statement I and statement II together are necessary to answer the question.

Hence, option e.

Solution 5: D)

Let the speed of boat in upstream and downstream be ‘x’ km/h and ‘y’ km/h, respectively.

Statement I:

135/x + 195/y = 6

135y + 195x = 6xy……………………(1)

So, data in statement I alone is not sufficient to answer the question.

Statement II:

90/x + 130/y = 4

90y + 130x = 4xy……………………..(2)

So, data in statement II alone is not sufficient to answer the question.

Combining statement I and II we get:

Subtracting equation (1) from equation (2)

45y + 65x = 2xy

Putting value of 2xy in equation (1) we get

135y + 195x = 3 × (45y + 65x)

135y + 195x = 135y + 195x

So, we cannot determine the value of ‘x’ and ‘y’.

Hence, option d.

Solution 6: B)

Let the amount of milk and water in the mixture be 12x ml and 11x ml respectively.

Statement I:

20% of the mixture = 0.2 × (12x + 11x) = 4.6x ml

According to question;

(0.8 × 12x)/(0.8x × 11x + 4.6x) = 48/67

9.6x/13.4x = 48/67

48/67 = 48/67

So, data in statement I alone is not sufficient to answer the question.

Statement II:

12x/(11x + 125) = 3/4

16x = 11x + 125

5x = 125

x = 25

Quantity of water in the mixture = 11 × 25 = 275 ml

So, data in statement II alone is sufficient to answer the question.

Hence, option b.

Questions with Solutions in Hindi

प्रश्न 1: Rajiv और Puneet एक ही समय पर क्रमशः बिंदु A और बिंदु B से एक दुसरे की ओर यात्रा शुरू करते हैं|Puneet की गति ज्ञात करें|

Statement I: बिंदु A और बिंदु B के बीच की दुरी 396 km है|

Statement II: Rajiv और Puneet की गति का अनुपात क्रमशः 6:5 है|

Statement III: Puneet से मिलने के बाद बिंदु B पर पहुँचने में Rajiv को 3 hours का समय लगता है|

A) दोनों कथन I और II में दी गई जानकारी उत्तर देने के लिए पर्याप्त है|

B) दोनों कथन I और III में दी गई जानकारी उत्तर देने के लिए पर्याप्त है|

C) दोनों कथन II और III में दी गई जानकारी उत्तर देने के लिए पर्याप्त है|

D) सभी कथन I, II और III में दी गई जानकारी उत्तर देने के लिए पर्याप्त है|

E) सभी कथन I, II और III में दी गई जानकारी उत्तर देने के लिए पर्याप्त नहीं है|

प्रश्न 2: इस प्रश्न में दो कथन I और II दिए गए हैं|आपको यह तय करना है कि कथन में दी गई जानकारी उत्तर देने के लिए पर्याप्त है या नहीं|

तीन pipes A, B और C, एक tank से संलग्न हैं|Pipe A और B साथ में tank को 40 minutes में भरते हैं, जबकि pipe B और C साथ में tank को 50 minutes में भर सकते हैं|यदि सभी pipes को 4 minutes के लिए खोला जाता है फिर pipe A और C फिर बंद कर दिया जाता है, तो tank को खाली करने में कितना समय लगेगा?

Statement I: Pipe A pipe C से 20% अधिक कार्यकुशल है|

Statement II: Pipe A, B और C साथ में tank को 20 minutes में भर सकते हैं|

A) सिर्फ कथन I में दी गयी जानकारी प्रश्न का उत्तर देने के लिए पर्याप्त है, जबकि सिर्फ कथन II में दी गई जानकारी उत्तर देने के लिए पर्याप्त नहीं है|

B) सिर्फ कथन II में दी गयी जानकारी उत्तर देने के लिए पर्याप्त है, जबकि सिर्फ कथन I में दी गयी जानकारी उत्तर देने के लिए पर्याप्त नहीं है|

C) या तो सिर्फ कथन I या सिर्फ कथन II में दी गयी जानकारी उत्तर देने के लिए पर्याप्त है|

D) दोनों कथन I और II में दी गई संयुक्त जानकारी उत्तर देने के लिए पर्याप्त नहीं है|

E) दोनों कथन I और II में दी गई संयुक्त जानकारी उत्तर देने के लिए जरुरी है|

प्रश्न 3: इस प्रश्न में दो कथन I और II दिए गए हैं|आपको यह तय करना है कि कथन में दी गई जानकारी उत्तर देने के लिए पर्याप्त है या नहीं|

Dheeraj और Samay बिंदु A से बिंदु B तक क्रमशः bus और car से जाते हैं|Bus की गति ज्ञात करें|

Statement I: बिंदु A और बिंदु B के बीच की दुरी 320 km है|बिंदु B पर पहुँचने के लिए bus car से 160 minutes अधिक लेता है|

Statement II: Bus की गति car की गति का दो-तिहाई है|

A) सिर्फ कथन I में दी गयी जानकारी प्रश्न का उत्तर देने के लिए पर्याप्त है, जबकि सिर्फ कथन II में दी गई जानकारी उत्तर देने के लिए पर्याप्त नहीं है|

B) सिर्फ कथन II में दी गयी जानकारी उत्तर देने के लिए पर्याप्त है, जबकि सिर्फ कथन I में दी गयी जानकारी उत्तर देने के लिए पर्याप्त नहीं है|

C) या तो सिर्फ कथन I या सिर्फ कथन II में दी गयी जानकारी उत्तर देने के लिए पर्याप्त है|

D) दोनों कथन I और II में दी गई संयुक्त जानकारी उत्तर देने के लिए पर्याप्त नहीं है|

E) दोनों कथन I और II में दी गई संयुक्त जानकारी उत्तर देने के लिए जरुरी है|

प्रश्न 4: प्रश्न में नीचे दिए गए दो कथन “I और II” शामिल हैं। आपको यह तय करना होगा कि कथन में दिए गए डेटा प्रश्न का उत्तर देने के लिए पर्याप्त हैं या नहीं।

train X की लंबाई कितनी है?

कथन I: दो trains X और Y विपरीत दिशा से एक-दूसरे की ओर यात्रा करते हुए एक दुसरे को 10 seconds में पार करती है जबकि समान दिशा में चलते हुए एक दुसरे को 25 seconds में पार करती हैं। train Y की लंबाई 80 metres है।

कथन II: train X की गति 35 km/h है और train Y की गति X की तुलना में कम है।

A) कथन I में दिए गए डेटा प्रश्न का उत्तर देने के लिए पर्याप्त हैं, जबकि कथन II में दिए गए आंकड़े प्रश्न का उत्तर देने के लिए पर्याप्त नहीं हैं।

B) अकेले कथन II में डेटा प्रश्न का उत्तर देने के लिए पर्याप्त है, जबकि कथन I में डेटा प्रश्न का उत्तर देने के लिए पर्याप्त नहीं है।

C) डेटा या तो कथन I या कथन II अकेले प्रश्न का उत्तर देने के लिए पर्याप्त हैं।

D) I और II दोनों कथनों में दिए गए डेटा प्रश्न का उत्तर देने के लिए पर्याप्त नहीं हैं।

E) प्रश्न का उत्तर देने के लिए I और II दोनों कथनों का डेटा आवश्यक है।

प्रश्न 5: इस प्रश्न में दो कथन I और II दिए गए हैं|आपको यह तय करना है कि कथन में दी गई जानकारी उत्तर देने के लिए पर्याप्त है या नहीं|

शांत जल में 250km की दुरी को तय करने में एक नाव को कितना समय लगता है?

कथन I: नाव 135 km धारा विरुद्ध और 195 km धारा अनुप्रवाह को 6 hours में तय करती है|

कथन II: नाव 90 km धारा विरुद्ध और 130km धारा अनुप्रवाह को 4 hours में तय करती है|

A) सिर्फ कथन I में दी गयी जानकारी प्रश्न का उत्तर देने के लिए पर्याप्त है, जबकि सिर्फ कथन II में दी गई जानकारी उत्तर देने के लिए पर्याप्त नहीं है|

B) सिर्फ कथन II में दी गयी जानकारी प्रश्न का उत्तर देने के लिए पर्याप्त है, जबकि सिर्फ कथन I में दी गई जानकारी उत्तर देने के लिए पर्याप्त नहीं है|

C) या तो सिर्फ कथन I या सिर्फ कथन II में दी गयी जानकारी उत्तर देने के लिए पर्याप्त है|

D) दोनों कथन I और II में दी गई संयुक्त जानकारी उत्तर देने के लिए पर्याप्त नहीं है|

E) दोनों कथन I और II में दी गई संयुक्त जानकारी उत्तर देने के लिए आवश्यक है|

प्रश्न 6: इस प्रश्न में दो कथन I और II दिए गए हैं|आपको यह तय करना है कि कथन में दी गई जानकारी उत्तर देने के लिए पर्याप्त है या नहीं|

एक मिश्रण में दूध और पानी का अनुपात क्रमशः 12:11 है|मिश्रण में पानी की मात्रा ज्ञात करें|

कथन I: 20% मिश्रण को पानी की समान मात्रा से प्रतिस्थापित किया जाता है तो दूध और पानी का अनुपात 48:67 हो जाता है|

कथन II: यदि मिश्रण में 125ml पानी मिलाया जाता है, तो दूध और पानी का अनुपात 3:4 हो जाता है|

A) सिर्फ कथन I में दी गयी जानकारी प्रश्न का उत्तर देने के लिए पर्याप्त है, जबकि सिर्फ कथन II में दी गई जानकारी उत्तर देने के लिए पर्याप्त नहीं है|

B) सिर्फ कथन II में दी गयी जानकारी प्रश्न का उत्तर देने के लिए पर्याप्त है, जबकि सिर्फ कथन I में दी गई जानकारी उत्तर देने के लिए पर्याप्त नहीं है|

C) या तो सिर्फ कथन I या सिर्फ कथन II में दी गयी जानकारी उत्तर देने के लिए पर्याप्त है|

D) दोनों कथन I और II में दी गई संयुक्त जानकारी उत्तर देने के लिए पर्याप्त नहीं है|

E) दोनों कथन I और II में दी गई संयुक्त जानकारी उत्तर देने के लिए आवश्यक है|

ANSWER KEYS and SOLUTIONS:

1) – D)

2) – C)

3) – E)

4) – E)

5) – D)

6) – B)

Solution 1: D)

Statement I:

Distance between point A and point B is 396 km.

So, statement I alone is not sufficient to answer the question.

Statement II:

Let, speed of Rajiv and Puneet be 6x km/h and 5x km/h, respectively.

So, statement II alone is not sufficient to answer the question.

Statement III:

Rajiv takes 3 hours to reach point B after meeting Puneet.

So, statement III alone is not sufficient to answer the question.

Statement I and statement II:

Distance between point A and point B is 396 km.

Let, speed of Rajiv and Puneet be 6x km/h and 5x km/h, respectively.

So, Statement I and statement II together is not sufficient to answer the question.

Statement I and statement III:

Distance between point A and point B = 396 km

Let, distance travelled by Puneet to meet Rajiv = ‘y’ km

And, distance travelled by Rajiv to meet Puneet = ‘396 – y’ km

Speed of Rajiv = y/3 km/h

So, Statement I and statement III together is not sufficient to answer the question.

Statement II and statement III:

Let, speed of Rajiv and Puneet be 6x km/h and 5x km/h, respectively.

Ratio of time taken by Rajiv and Puneet to reach their respective destination = 5: 6

Time taken by Puneet to meet Rajiv = (6/5) × 3 = 3.6 hours

So, Statement II and statement III together is not sufficient to answer the question.

Statement I, II, and III:

Let, speed of Rajiv and Puneet be 6x km/h and 5x km/h, respectively.

Distance between point A and point B = 396 km

Ratio of time taken by Rajiv and Puneet to reach their respective destination = 5: 6

Time taken by Puneet to meet Rajiv = (6/5) × 3 = 3.6 hours

So, 6x × 3.6 + 5x × 3.6 = 396

39.6x = 396, x = 10

Speed of Puneet = 5x = 50 km/h

So, statement I, statement II and statement III together is necessary to answer the question.

Hence, option d.

Solution 2: C)

Let the capacity of the tank be LCM of (40 and 50) = 200 units

Number of units of water filled by pipe (A + B) together in one minute = 200/40 = 5 units

Number of units of water filled by pipe (B + C) together in one minute = 200/50 = 4 units

Statement I:

So, number of units of water filled by pipe (A + B + B + C) together in one minute = 5 + 4 = 9 units

Now, A + 2B + C = 9

Since, the efficiency of A is 20% more than C.

So, 1.2C + 2B + C = 9

2B + 2.2C = 9 —-(1)

And, B + C = 4 —-(2)

Solving eq. (1) and eq. (2), we get

C = 5 units and A = 6 units

So, number of units of water emptied by pipe B in one minute = 6 – 5 = 1 unit

Number of units of water filled by pipe A, B and C together in one minute = 6 + 5 – 1 = 10 units

So, number of units of water filled by pipe A, B and C together in 4 minute = 40 units

Required time taken to empty the tank = 40/1 = 40 minutes

So, statement I alone is sufficient to answer the question.

Statement II:

So, number of units of water filled by pipe (A + B + C) together in one minute = 200/20 = 10 units

Number of units of water filled by pipe A in one minute = 10 – 4 = 6 units

Number of units of water emptied by pipe B in one minute = 6 – 5 = 1 unit

So, number of units of water filled by pipe A, B and C together in 4 minute = 40 units

Required time taken to empty the tank = 40/1 = 40 minutes

So, statement II alone is sufficient to answer the question.

Hence, option c.

Solution 3: E)

Statement I:

Let, time taken by car be ‘t’ hours.

So, time taken by bus = ‘t + 160/60’ hours

And, distance between point A and point B = 320 km

So, data in statement I alone is not sufficient to answer the question.

Statement II:

Let, speed of bus and car be ‘2x’ km/h and ‘3x’ km/h respectively.

So, data in statement II alone is not sufficient to answer the question.

Combining statement I and II:

Let, speed of bus and car be ‘2x’ km/h and ‘3x’ km/h respectively.

So, 320/2x – 320/3x = 160/60

(960 – 640)/6x = 8/3

40 = 2x

So, speed of bus = 2x = 40 km/h

So, the data in both statements I and II together are necessary to answer the question.

Hence, option e.

Solution 4: E)

Let speed of train X and Y be x km/h and y km/h, respectively.

Let length of train X be ‘l’ metres.

Statement I:

According to question,

(l + 80) = 10 × (x +y)………………………………(1)

(l + 80) = 25 × (x – y)………………………………(2)

From (1) and (2)

10 × (x + y) = 25 × (x – y)

7y = 3x

Therefore, statement I alone is not sufficient to answer the question.

Statement II:

Speed of train X = 35 km/h

Therefore, statement II alone is not sufficient to answer the question.

Combining statements, I and II,

Speed of train X = 35 km/h

So, 7y = 3 × 35

y = 15 km/h

From equation (1)

(l + 80) = 10 × (x + y)

l + 80 = 10 ×(35 + 15) × 5/18

l = 139 – 80 ~ 59 metres

Therefore, statement I and statement II together are necessary to answer the question.

Hence, option e.

Solution 5: D)

Let the speed of boat in upstream and downstream be ‘x’ km/h and ‘y’ km/h, respectively.

Statement I:

135/x + 195/y = 6

135y + 195x = 6xy……………………(1)

So, data in statement I alone is not sufficient to answer the question.

Statement II:

90/x + 130/y = 4

90y + 130x = 4xy……………………..(2)

So, data in statement II alone is not sufficient to answer the question.

Combining statement I and II we get:

Subtracting equation (1) from equation (2)

45y + 65x = 2xy

Putting value of 2xy in equation (1) we get

135y + 195x = 3 × (45y + 65x)

135y + 195x = 135y + 195x

So, we cannot determine the value of ‘x’ and ‘y’.

Hence, option d.

Solution 6: B)

Let the amount of milk and water in the mixture be 12x ml and 11x ml respectively.

Statement I:

20% of the mixture = 0.2 × (12x + 11x) = 4.6x ml

According to question;

(0.8 × 12x)/(0.8x × 11x + 4.6x) = 48/67

9.6x/13.4x = 48/67

48/67 = 48/67

So, data in statement I alone is not sufficient to answer the question.

Statement II:

12x/(11x + 125) = 3/4

16x = 11x + 125

5x = 125

x = 25

Quantity of water in the mixture = 11 × 25 = 275 ml

So, data in statement II alone is sufficient to answer the question.

Hence, option b.

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