# Data Sufficiency Practice Quiz

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# Data Sufficiency Practice Quiz

### Introduction

Data Sufficiency, a significant topic in Quantitative Aptitude section, consists of problems in which a question on any topic such as coding-decoding, blood relations, direction sense test, ranking and time sequence test, arithmetical reasoning etc. is given, followed by certain statements containing facts providing hints to solve the question. The candidate is required to find out which of the given statements is/are sufficient to answer the question.

The article Data Sufficiency Practice Quiz lists different types of Data Sufficiency questions along with solutions primarily useful for candidates preparing for different competitive examinations like RRB ALP/Technical Exams/Junior Engineer Recruitment Exams, SSC CGL,SSC CHSL, IBPS, SBI PO, SBI Clerks, CAT and etc.

### Quiz

Directions: (1 – 15)

Each question is followed by two statements, I and II. Answer each question using the following instructions. Mark:

A. if the question can be answered using statement I alone, but cannot be answered using statement II alone.
B. if the question can be answered using statement II alone, but cannot be answered using statement I alone.
C. if the question can be answered using both the statements together, but cannot be answered using either statement alone.
D. if the question can be answered using either statement I or II individually.
E. if the question cannot be answered even using both the statements together.

1. Is Manish taller than Chandra?

I. Suhas is of the same height as Manish and Chandra.
II. Chandra is not shorter than Suhas.

Explanation –

From statement I, we can conclude that Suhas, Manish and Chandra are of the same height. So, Manish is not taller that Chandra. Thus, only statement I is sufficient to answer the question. Statement II gives no relation between Manish and Chandra.

2. Buses are always punctual in Delhi city. How long, at the most, will Mr.Dhiren have to wait for the bus?

I. Mr Dhiren has come to the bus stand at 9 a.m.
II. There is a bus at 10 a.m. and possibly another bus even earlier

Explanation –

From both the given statements, we find that Dhiren reached the bus stand at 9 a.m. and a bus is sure to arrive at 10 a.m. So, Dhiren has to wait for at the most one hour.

3. How is Rajesh related to Anish?

I. Bikram is the brother of Anish.
II. Bikram is Rajesh’s son.

Explanation –

From both the statements together, we find that Rajesh is the father of Bikram and Bikram is the brother of Anish. So, Rajesh is the father of Anish. Thus, both the given statements are needed.

4. How is Shahrukh related to Salman?

I. Aamir ’s wife Reena is pat er nal aunt of Salman.
II. Shahrukh is the brother of a friend of Reena.

Explanation –

Clearly, both the statements together are not sufficient to answer the question.

5. Tendulkar ranks tenth in a class. How many students are there in the class?

I. His friend got 58th rank which is the last.
II. Tendulkar’s rank from the last is 49th.

Explanation –

Statement I reveals that 58th rank is the last rank in the class. This means that there are 58 students in the class. So, statement I alone is sufficient. Also, from statement II, we find that Tendulkar’s rank in the class is 10th and 49th from the last.

So, there are (10 + 49 – 1) = 58 students in the class. Thus, statement II alone also is sufficient.

6. How many pages of the book – The Man Who Saw Tomorrow did Sujit read on Sunday?

I. The book has 300 pages out of which two-thirds were read by him before Sunday.
II. Sujit read the last 40 pages of the book in the morning of Monday

Explanation –

From statements I and II, we find that Sujit read (300 x ), i.e. 200 pages before Sunday and the last 40 pages on Monday. This means that he reads (300 – (200 + 40)), i.e. 60 pages on Sunday.

7. In a certain language, ‘pit nac nit’ means ‘red pant shirt’. Which word means ‘pant’ in the language?

I. ‘nit tim nac sir’ means ‘he wore red pant’.
II. ‘nee jic pit’ means ‘shirt is dirty’.

Explanation –

Clearly, from each of the statements, we find that the code for ‘pant’ is either ‘nit’ or ‘nac’. So, none of them is sufficient to answer the question

8. I n a code, ‘lee pee tin’ means ‘always keep smiling’. What is the code for ‘smiling’.

I. ‘tin lut lee’ means ‘always keep left’.
II. ‘dee pee’ means ‘rose smiling’.

Explanation –

Comparing the information in the question with statement I, we find that ‘tin’ and ‘lee’ are the codes for ‘always’ and ‘keep’. So, ‘pee’ represents ‘smiling’.

Thus, statement I alone is sufficient.

Again, comparing the information in the question with statement II, we find that the common code word ‘pee’ stands for the common word ‘smiling’. Thus, statement II alone is also sufficient.

9. Among the five friends who is the tallest?

I. Dinesh is taller than Atul and Charles.
II. Basu is shorter than Ena but taller than Dinesh.

Explanation –

From statement I, we have: D > A, D > C.

From statement II, we have: E > B > D.

Combining the above two, we get: E > B > D >

(A and C). So, E is the tallest.

10. When is Tata’s birthday?

I. Tata’s father was born on 27th May, 1948.
II. Tata is 25 years younger than his mother

Explanation –

Clearly, even both the statements together do not reveal Tata’s birthday.

11. On what day in April is Hrithik’s birthday?

I. Hrithik was born exactly 28 years after his mother was born.
II. His mother will be 55 years 4 months and 5 days on August 18 this year.

Explanation –

Clearly, the birthday of Hrithik’s mother can be found out from statement II and then Hrithik’s birthday can be determined using the fact given in statement I.

Thus, both the statements are required.

12. At what time will the plane leave today?

I. The plane normally leaves on time.
II. The scheduled departure is at 14.30

Explanation –

Clearly, even both the statements together do not reveal the exact time of departure of the plane today.

13. On which day in January, Ronaldo left for

I. Ronaldo has so far spent 10 years in Germany.
II. Ronaldo’s friend Rivaldo left for Germany on $${15}^{th}$$ February and joined Ronaldo 20 days after Ronaldo’s arrival.Germany?

Explanation –

Clearly, even from both the given statements, we cannot conclude the exact date of Ronaldo leaving for Germany.

14. In which year was Sangita born?

I. Sangita at present is 25 years younger to her mother.
II. Sangita’s brother, who was born in year 1964, is 35 years younger to his mother.

Explanation –

From both the given statements, we find that Sangita is (35 – 25) = 10 years older than her brother, who was born in year 1964. So, Sangita was born in 1954. Thus, both the given statements are needed to answer the question

15. How many lectures were delivered in the two days’ programme?

I. 18 speakers were invited to give at least one lecture, out of which one-sixth of the speakers could not come.
II. One-third of the speakers gave two lectures each.

Explanation –

From statement I, we find that the no. of speakers who attended the programme = 18 – $$\frac{1}{6}$$ of 18 = 15.

From statement II, we find that $$\frac{1}{3}$$ x 15), i.e. five speakers gave two lectures each, But we
don’t know about number of lectures given by remaining 10 speakers. Because they can deliver one lecture each or more than two also.

Directions: (1 – 15)

Each question is followed by two statements, I and II. Answer each question using the following instructions. Mark:

A. if the question can be answered using statement I alone, but cannot be answered using statement II alone.
B. if the question can be answered using statement II alone, but cannot be answered using statement I alone.
C. if the question can be answered using both the statements together, but cannot be answered using either statement alone.
D. if the question can be answered using either statement I or II individually.
E. if the question cannot be answered even using both the statements together.

1. Who is the shortest student in the class, a boy or a girl?

I. Either Ram or Shyam is the shortest boy in the class.
II. Ram is shorter than Shyam, but taller than Sita in the class.

Explanation –

Statement I does not mention the girls at all, so it is insufficient to answer the question. Statement II does not mention anything about the height of Sita. Hence, statement II is also insufficient to answer the question. Putting the two statements together, we are able to say that Ram is the shortest boy but it is not yet comparable to the height of the shortest girl.

2. Four candidates (A, B, C and D) contested an election in year 2000. One lost his deposit. Who won?

I. C got more votes than A, but less votes than B.
II. It was not A who lost his deposit

Explanation –

From statement I, we get the order of candidates getting votes as B > C > A.

From statement II, we find that it was D who has lost his deposit (as A, B, C can’t have lost their deposit). Hence, the final order of candidates becomes B > C > A > D. Hence, B has got the maximum number of votes.

3. Do the cars P and Q travel along the same route for at least part of their journeys?

I. P goes from A to C via B.
II. Q goes from A to D via B.

Explanation –

Combining both statements, both cars P and Q travel from A to B. But we don’t know the number of roads connecting A and B. Hence, the question cannot be answered.

4. Has any one of them seen the picture twice?

I. A few of them saw the picture twice.
II. Most of them saw the picture only once.

Explanation –

From statement I, we infer that a small number of people saw the picture twice. So, from statement I alone, we get the answer ‘yes’. Statement II alone is insufficient to answer the question.

5. P is the only son of Q. Was P admitted?

I. Only the children of workers were admitted.
II. Q was not a worker.

Explanation –

The father of P was not a worker. But the mother of P might be a worker. No information in this regard is available either from the given statements or from the introductory part. So, this question cannot be answered.

6. How is A related to D?

I. A is the son of B.
II. D is the daughter-in-law of B.

Explanation –

Statements I and II taken alone are not sufficient to answer the question. Even when considered together, the two statements are not sufficient to answer the question, as D could be either the wife or sister-in-law of A.

7. What is Ram’s date of birth?

I. Ram is exactly 2 years elder to Gaurav who was born on 22-7-1982.
II. Ram was born in year 1988.

Explanation –

From statement I, it is clear that Ram’s date of birth is 22-7-1980. Hence, statement I is sufficient to answer the question. From statement II, though we get the year in which Ram was born, we cannot find out his date of birth.

8. How many Sundays were there in the month of March of a particular year ‘k’?

I. 10th February of that year ‘k’ was a Saturday.
II. Year ‘k’ was a leap year.

Explanation –

We get from statement I that 11th February was a Sunday. Hence, 18th and 25th February were also Sundays. The next Sunday can be looked upon as ‘32nd February’ [which is 3rd March for a leap year, as mentioned in statement II].

Since statement II mentions that year ‘k’ is a leap year, 3rd, 10th, 17th, 24th and 31st March are Sundays, giving us 5 Sundays in that March. In a normal year, 4th, 11th, 18th, 25th March only would have been Sundays. Hence, the answer for a normal year would be 4. Hence, we require both statements to answer the question.

9. Does Mr X belong to Gujarat?

I. Gujarat is a state in India.
II. Mr X is not an Indian.

Explanation –

Since Mr X is not an Indian, it follows that Mr X does not belong to any state in India. As Gujarat is a state in India, we infer that Mr X does not belong to Gujarat.

10. All who had got medals sat in the first row for the group photo. But none who was less than
five feet in height sat in the 2nd row. (There were only two rows.) Did Amar sit in the first row?

I. He had not got any medal.
II. His height was 4 feet 10 inches.

Explanation –

From statement II, we note that Amar’s height was less than five feet. Hence, we get from the introductory part that he did not sit in the 2nd row. As there were only two rows, this means that he sat in he first row.

(Note: All those who had got medals sat in the first row. But this does not mean that only those who had got medals sat in the first row.)

11. A, B, C and D stay in a four-stores building. Who stays on 3rd floor from top?

I. A and C stay on odd-numbered floor.
II. D stays above B.

Explanation –

Combining both statements I and II, B and D stay on 2nd and 4th floors respectively. Since D is above B, B is on 2nd floor, i.e. 3rd floor from top.

12. Find code for ‘Jamaica’.

I. ‘Jamaica is wonderful place’ stands for ‘Raj is sheetal’s friend’.
II. ‘Tok yo pl ace wonder ful i s’ st ands for ‘Ramesh’s friend is sheetal’s’.

Explanation –

Combining both statements I and II, when we compare between statements given, in first half other than Jamaica, remaining three words are repeated. Also in the other half of the statements, three words are repeated. Hence Jamaica stands for Raj.

13. How many wives does Sheikh have?

I. In his family there are five people of his generation.
II. Sheikh has two brothers.

Explanation –

This is because we don’t have any information about his sisters. Hence, using both statements together we cannot answer the question.

14. A was born in which year of 19th century?

I. His brother was born in the year 1972.
II. Three digits of the year are same.

Explanation –

Statement I gives no clue. And statement II gives indication to 1811 and 1888. If brother was
younger or elder, than it would have been (e) as the answer.

15. What is the code for ‘economy’?

I. ‘Opening of the economy’ stands for ‘economy is in doldrums’.
II. In the above statement one word has not been coded.

Explanation –

Statement I in itself is not sufficient, but when we consider second statement, it is clear that economy stands for economy only.

Directions: (1 – 5)

In each of the following questions, a question is followed by information given in three statements. You have to study the question along with the statements and decide the information given in which statement (s) is necessary and sufficient to answer the question.

1. How many brothers does Akash have? (Akash is a boy)

I. Neelima is Akash’s mother Sudhir is Neelima’s husband and has only one daughter Riya.
II. Riya has two younger and one elder brother.
III.Akash is not the youngest child.

A. Only II and III
B. Only I and II
C. Only I and III
D. All I, II, and III
E. Any two of the three

Explanation –

From I: Neelima and Sudhir have only one daughter Riya. Also, Akash is their son.

No information regarding other children is given, so I is not sufficient to answer the question.

From II: Riya has two younger brothers and one elder brother.

No information regarding sisters is given, so II alone is not sufficient to answer the question.

From III: no information on Akash’s brothers

Combining I and II ⇒ Akash has two brothers

i.e, Only I and II are necessary to answer the question.

2. Who among P, Q, R, S and T was the first to reach the station?

I. Q reached earlier than T; P and R were not the first to reach.
II. P reached earlier than both R and T, but could not reach earlier than S, who was at the station before Q.
III. R didn’t reach just after P.

A. Only I and II
B. Only I and II or III
C. Only II and III
D. All I, II and III
E. None of these

Explanation –

From I: Q came before T and P and R did not reach first.

No information regarding S is given, so I alone is not sufficient to answer the question.

From II: P came before R, T but not before S (who reached before Q) ⇒ S reached first.

So II alone is sufficient to answer the question.

From III: no information regarding who reached first is given.

Only statement II is required to answer the question.

i.e, None of these.

3. How is A related to C?

I. M has two daughters. One of them is Z, who is married to A.
II. C is the mother of V, the younger sister of Z.
III. M is C’s husband.

A. Only I and II
B. Only I and III
C. Only I and either II or III
D. Any two of the three
E. All are necessary

Explanation –

From I: M (parent) has two daughters, one daughter is Z whose husband is A.

We know that A is the son in law but no information on C is given, so I alone is not sufficient to answer the question.

From II: C (mother) of V and Z.

But no mention of A is made, so II alone is not sufficient to answer the question.

Combining I and II, we get A is C’s son in law.

From III: M is C’s husband .

But III alone is not sufficient to answer the question.

Combining I and III, we get A is C’s son in law.

i.e, The question can be answered using I and either II or III.

4. Yogendra is in which direction with respect to Anu?

I. Yogendra walks 1 km towards North-east from station A and then, before walking 2 km towards south, walks 2 km towards East.
II. Anu walks 2 km towards South from station A and then, before moving 8 km towards north, walks 3 km towards West.
III . Before moving 3 km towards west, Anu walks 4 km towards North from station A.

A. Only I and II
B. Only II and III
C. Either I and II or I and III
D. All are necessary
E. Any two of the three

Explanation –

From I: Yogendra is to the South East of station A.

But no information regarding Anu is given, so I alone is not sufficient to answer the question.

From II: Anu is to the North West of station A.

But no information regarding Yogendra is given, so II alone is not sufficient to answer the question.

Using the position of Yogendra from I and the position of Anu from II the question can be answered.

From III: Anu is to the North West of station A.

But no information regarding Yogendra is given, so III alone is not sufficient to answer the question.

Using the position of Yogendra from I and the position of Anu from III the question can be answered.

i.e, The question can be answered using I and either II or III

5. A, B, C, D, E and F are sitting around a circular table facing the centre. Who is sitting opposite to A?

I. B and C are sitting opposite to each other.
II. E may sit either on the immediate left of B or on the immediate right of C.
III. D cannot sit opposite E, and A cannot sit opposite E.

A. Only I and II
B. Only II and III
C. Only I and II or III
D. All I, II and III

Explanation –

From I: B and C are opposite to each other I is not sufficient to answer the question since no information regarding the others is given.

From II: E is either to the left of B or to the right of C.

II is not sufficient to answer the question since no information regarding the others is given.

From III: Both D and A are not opposite E so F is opposite E.

III is not sufficient to answer the question since no information regarding the others is given.

Combining I , II and III ⇒ D is opposite A.

i.e, All I , II and III are necessary to answer the question

Directions: (6 – 10)

In each of the following questions, a question is followed by information given in three statements. You have to decide the information given in which of the statements is necessary and sufficient to answer the given question.

6. Is the time 6 o’clock now?

I. After fifteen minutes, the minute and the hour hands of the clock will make a right angle.
II. The train which is running late by exactly two hours from its scheduled time of arrival, ie 3 pm, has reached now.
III. 6 o’clock is the time of departure of a train and it is still on the platform.

A. Only I
B. Either II or I
C. Either III or II
D. Either I or II or III
E. All I, II and III

Explanation –

From I: it is not 6 o’clock now because at 6:15 the hands are not at an exact right angle.

I is sufficient to answer the question.

From II: it is not 6 o’clock now because the 3 pm train which was 2 hours late has reached now.

II is sufficient to answer the question.

From III: it is not 6 o’clock now because the 6 o’clock train is still in the platform.

III is sufficient to answer the question.

The answer is: it is not 6 o’clock now.

i.e, Either I or II or III is sufficient to answer the question.

7. How many sisters does Neha have? (Neha is a girl.)

I. Krishna, Neha’s mother, has three children.
II. Vinod is the father-in-law of Krishna and he has only one son and one grandson.
III.Pooja, Neha’s sister, has two siblings.

A. Only I and II
B. Only II and III
C. Only II and either III or I
D. All I, II and III

Explanation –

From I and III it is clear that Neha has two other siblings.

But I and III are not sufficient to answer the question since no information regarding brother or sister is given.

From II it is clear that Neha has only one brother.

II is not sufficient to answer the question since the other siblings are not mentioned.

The answer is: the second sibling is a sister.

i.e, Only II and either III or I are sufficient to answer the question.

8. Who is the tallest among P. Q, R, S and T?

I. R is taller than Q but not as tall as T.
II. P is not the shortest.
III.P is taller than only S.

A. Only I and II
B. Only I and III
C. Only I and either II or III
D. All I, II and III

Explanation –

From I it is clear that T is taller than R and Q.

But I alone is not sufficient to answer the question.

From II no information regarding anyone other than P is given

So II is not sufficient to answer the question.

From III it is clear that P is taller than S only

⇒ P is shorter than Q, R and T.

But III alone is not sufficient to answer the question.

Combining I and III , we get T is the tallest.

i.e, Only I and III are sufficient to answer the question.

9. On which day of the week did Anu arrive?

I. Her sister, Tanu, correctly remembers that she did not arrive on Wednesday.
II. Her friend, Manu, correctly remembers that she arrived before Friday.
III. Her mother correctly mentions that she arrived before Friday but after Tuesday.

A. Only I and II
B. Only II and III
C. Only I and III
D. All I, II and III

Explanation –

From I it is clear that it is not Wednesday.

But I alone is not sufficient to answer the question.

From II it is clear that it is before Friday.

But II alone is not sufficient to answer the question.

From III it is clear that it is before Friday and after Tuesday.

But III alone is not sufficient to answer the question.

Combining I and III : Anu arrived on Thursday

(which is after Tuesday , it is not a Wednesday and it is before Friday.)

i.e, Only I and III are sufficient to answer the question.

10. A, B, C, D and E are sitting in a row facing North. Who among them is in the middle?

I. E is at the right end of the row.
II. D sits between A and C.
III. Neither A nor C sits at an extreme end.

A. Only I and II
B. Only II and III
C. Any two of the three
D. All I, II, and III

Explanation –

From I: E is at the right end.

No information regarding others is given, so I alone is not sufficient to answer the question.

From II it is clear that D sits between A and C.

No information regarding others is given, so II alone is not sufficient to answer the question.

From III it is clear that A and C, both are not sitting at the extremes.

No information regarding others is given, so III alone is not sufficient to answer the question.

Combining II and III the answer is: among 5 seats the middle 3 are occupied by A, D and C and D is in the middle.

i.e, Only II and III are sufficient to answer the question.

Directions: (11 – 15)

Each of the questions below consists of a question fallowed by the 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. Read both the statements and give answer

A. if the data in statement I alone is sufficient to answer the question while the data in statement II alone is not sufficient to answer the question.
B. if the data in statement II alone is sufficient to answer the question while the data in statement I alone is not sufficient to answer the question.
C. if the data either in statement I alone or in statement II alone is sufficient to answer the question.
D. if the data in both statements I and II together is not sufficient to answer the question.
E. if the data in both statements I and II together is necessary to answer the question.

11. What colour will be on the opposite surface of the brown surface of a cube? The surfaces of
cube have different colours, namely red, black, green, brown, white and blue.

I. The green surface is between red and black surfaces while the blue surface is adjacent to the white.
II. The brown surface is adjacent to the blue.

Explanation –

From I: More than one combinations of the given faces are possible, so I alone is not sufficient to answer the question.

From II: brown is adjacent to blue

But no information regarding other colours is given so II alone is not sufficient to answer the question.

Combining statements I and II together we get

⇒ white is opposite to brown.

i.e, Data in both statements I and II put together is necessary to answer the question

12. What characteristic is possessed by the person who is on the left of the weak person and who is sitting in a row of five persons? It is given that others possess the following qualities: fat, tall, fair and intelligent. And each individual possesses only one quality

I. The tall person is on the left of the fair person and the weak person is sitting between the intelligent person and the fat person, who is sitting on the right of the weak person.
II. One of the two persons at the extreme ends is intelligent, and is second to the left of the fat person, who is on the immediate right of the weak person.

Explanation –

From I: __, Intelligent, weak, fat,__

From II: Intelligent, weak, fat,__, __

From both the statements we can infer that the person sitting on the left of the weak person is intelligent.

i.e, Data in statement I alone or statement II alone is sufficient to answer the question

13. If tika pika mai is the code for “Renu is PO” in a code language used in territory X?

I. In the same code language “I want to be PO” is written as jai kali gai pali mai, “Renu needs money” is written as saaj tika sika; and “He needs sweets” is written as baaj koko saaj.
II. In the same code language “what he want to be” is written as jai kali aaj gai koko; “I want sweets what Renu needs” is written as baaj saaj pali kali aaj tika; and “PO are gentle” is written as bogo mai ali.

Explanation –

From I: {I, want, to, be, PO} = { jai, kali, gai, pali, mai}

{Renu ,needs, money} = {saaj, tika, sika}

{He ,needs, sweets} = {baaj, koko, saaj}

No code for ‘is’ given, so I is not sufficient to answer the question.

From II: {what, he, want, to, be} = {jai, kali, aaj, gai, koko}

{I, want, sweets, what, Renu, needs} = { baaj, saaj, pali, kali, aaj, tika}

{PO, are, gentle} = {bogo, mai, ali}

No code for ‘is’ is given, so II is not sufficient to answer the question.

Both I and II do not have a code for “is”. So data from both I and II together is not sufficient to answer the question.

14. How many cards does B have? B is playing a game of cards with A, C, D and E. It is given that the total number of cards is 158.

I. A says to B, “If you give me three cards, you will have as many as E has and if I give you three cards, you will have as many as D has.
II. A and B together have 10 cards more than what D and E together have. And B has two cards more than what C has.

Explanation –

Both statements I and II give the relation between the cards in each person’s hand but do not give the number of cards in any of the five persons’ hands.
So data in both statements I and II put together is not sufficient to answer the question.

15. The book of which subject is at the sixth position from the top in a pile of ten books, including 3 books of History, 3 of Hindi, 2 of Maths and 2 of English?

I. Starting from above there is an English book between a History and Maths book , a History book between a Maths and an English book, a Hindi book between an English and a Maths book, a Maths book between two Hindi books and two Hindi books between a Maths and a History book.
II. If we count from the bottom, the book which is at the fifth position is neither Maths nor English.

Explanation –

From I: we can clearly see that the pile of books is as follows (from top to bottom)

History

English

Mathematics

History

English

Hindi

Mathematics

Hindi

Hindi

History

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

From II: the fifth book from bottom is neither mathematics nor English.

II is not sufficient to answer the question.

i.e, Data in statement I alone is sufficient whereas data in statement II alone is not sufficient to answer the question.