# Ch.12 :- Data – Sufficiency : Exercise 1

✦ Directions for Q. No. 1 to 5 : Each of the problem below consists of a question and three statements I, II and III given below it. Read all the statements carefully and seek all possible combinations which could be sufficient for answering the question. A single statement or statements with least combinations which could be sufficient for answering the question would be your answer.

1. How many sons D has ?
I. B and F are brothers of A.
II. C is the sister of A and F.
III. C and E are daughter of D.
(a) All I, II and III
(b) II and III only
(c) I and II only
(d) All I, II & III not sufficient to answer
(e) None of these

Ans.(d)

On the basis of statements I, II and III we can’t find the sex of A. Hence, it can’t be determined whether A is the . son or daughter of D

2. What does ‘come’ represent in a code language ?
I. ‘pit na tac’ means ‘come and go’.
II. ‘Ja ta da’ means ‘you are good’.
III. ‘na da rac’ means ‘you can come’ I
(a) II and III only
(b) I and III only
(c) either II or III
(d) All r, II and III
(e) None of these

Ans.(b)
Since ‘na’ and ‘come’ are common-in statements I and III, hence ‘na’ stands for ‘come’.

3. In which year was Tarun born ?
I. Tarun is six years older than Rabin.
II. Rabin’s brother was born in 1982.
III. Tarun’s brother is two years younger than Rabin’s brother who was eight years younger than him.
(a) I and III only
(b) II and III only
(c) All I, II and III
(d) I and II only
(e) None of these

Ans.(c)
From statements II and III, it is clear that Rabin’s brother was born in 1982, Tarun’s brother was born in 1984 and Rabin was born in 1974. Now from statement I, it is given that Tarun is six years older than Rabin, hence we know that Tarun was born in 1968.

4. Who among Girish, Prashant, Kamlesh and Jayesh is the youngest?
I. Kamlesh is younger than Jayesh but older than Girishand Prashant.
II. Jayesh is the oldest.
III. Girish is older than Prashant.
(a) I and II only
(b) I an III only
(c) II and III only
(d) I only
(e) None of these

Ans.(b)
Statement II is not required to know the youngest among Girish, Prashant, Kamlesh and Jayesh.

5. Who among P, Q, R, S and T is in the middle while standing in a line?
I. Q is to the right of T.
II. S is between P and T.
III. Q is between T and R.
(a) I and II only
(b) II and III only
(c) I and III only
(d) All I, II, III
(e) None of these

Ans.(d)
From all the statements I, II and III, the order of ranking
of P, Q, R, S, T in a line is as

Hence, T is in between the line.

✦ Directions for Q. No.6 to 17 : Each of the following questions contains a question and ,two statements giving certain informations. Decide whether the, information given in the statements are sufficient for answering the question. Indicate your answer as :

6. How many rooms does your house have?
I. The number of rooms is the same as in our house.
II. The number is sufficient to accommodate our family members.

(a) if the statement I alone is sufficient to answer,
(b) if statement II alone is needed,
(c) if both statements I and II are needed,
(d) if both statements I and II are not sufficient to answer the question.

Ans.(a)
From the statement I alone, the question can be answered.

7. Who is the best salesman in the company?
I. Rohit sold maximum number of air conditioners this summer.
II. The company made the highest profit this year.

(a) if the statement I alone is sufficient to answer,
(b) if statement II alone is needed,
(c) if both statements I and II are needed,
(d) if both statements I and II are not sufficient to answer the question.

Ans.(a)
Since Rohit has sold the maximum number of items, hence, he is the best salesman.

8. What is the colour of the curtains on the stage?
I. The curtains have the same colour as the walls of the hall.
II. The colour of the curtains is quite appealing.

(a) if the statement I alone is sufficient to answer,
(b) if statement II alone is needed,
(c) if both statements I and II are needed,
(d) if both statements I and II are not sufficient to answer the question.

Ans.(a)
From the statement I alone, question can be answered.

9. Who is a better artist – Abid or Hussain?
I. Abid had more art exhibitions.
II. The number of paintings sold by Hussain is more.

(a) if the statement I alone is sufficient to answer,
(b) if statement II alone is needed,
(c) if both statements I and II are needed,
(d) if both statements I and II are not sufficient to answer the question.

Ans.(b)
Since as given statement II, the number of paintings sold by Hussain is more, hence, he is the better artist.

10. Does TV viewing affect the performance of students?
I. The number of failures in class XII is more this year.
II. TV watching is harmful to the eyes.

(a) if the statement I alone is sufficient to answer,
(b) if statement II alone is needed,
(c) if both statements I and II are needed,
(d) if both statements I and II are not sufficient to answer the question.

Ans.(d)
Neither of the statements I and II contains sufficient data to answer the question.

11. Is cigarette smoking is injurious to health ?
I. Non-smokers have a longer life-span.
II. The incidence of heart attack is more in smokers.

(a) if the statement I alone is sufficient to answer,
(b) if statement II alone is needed,
(c) if both statements I and II are needed,
(d) if both statements I and II are not sufficient to answer the question.

Ans.(c)
Both the statements strengthen the fact that cigarette smoking is injurious to health

12. Is the number of girl students more in the B.Ed. course?
I. The girls’ performance in the annual examinations is better than boys.
II. The number of female teachers has been increasing over the last two years.

(a) if the statement I alone is sufficient to answer,
(b) if statement II alone is needed,
(c) if both statements I and II are needed,
(d) if both statements I and II are not sufficient to answer the question.

Ans.(d)
Statement I is not at all relevant for answering the question. Statement II contains some information related with teaching profession. But even this statement is inadequate to answer the question.

13. Are women more emotional?
I. Women believe that men’s way of thinking can’t help them solve the problem.
II. The reality confronted by women is entirely different from the reality men have to struggle with.

(a) if the statement I alone is sufficient to answer,
(b) if statement II alone is needed,
(c) if both statements I and II are needed,
(d) if both statements I and II are not sufficient to answer the question.

Ans.(d)
None of the statements I and II contains adequate information for answering the question.

14. Do habits make men’s life rigid?
I. It is out of habit that people envy others.
II. Men become slave of habits.

(a) if the statement I alone is sufficient to answer,
(b) if statement II alone is needed,
(c) if both statements I and II are needed,
(d) if both statements I and II are not sufficient to answer the question.

Ans.(b)
From statement II, we conclude that men are dominated by their habits. This means that habits make man’s life rigid.

15. Does intelligence predict the child’s ability to learn ?
I. Intelligence is unaffected by bad teaching or dull home environment.
II. Children from poor home backgrounds do not do well in their school-work.

(a) if the statement I alone is sufficient to answer,
(b) if statement II alone is needed,
(c) if both statements I and II are needed,
(d) if both statements I and II are not sufficient to answer the question.

Ans.(d)
From statement I, it is known that bad teaching or dull home environment has got nothing to do with child’s intelligence. Therefore, statement I is not sufficient to answer the question. Statement II is not related with
the question. Hence, none of the statements is sufficient to answer the question .

16. Can a democratic system operate without effective opposition ?
I. The opposition is indispensable.
II. A good politician always learns more from his opponents than from his fervent supporters.

(a) if the statement I alone is sufficient to answer,
(b) if statement II alone is needed,
(c) if both statements I and II are needed,
(d) if both statements I and II are not sufficient to answer the question.

Ans.(c)
It is clear from both the statements that the opposition is very much required irrespective of system of government.

17. Has decline in infant mortality rate increased the life-span of human beings?
I. The average life-span of tribals is 85 years.
II. Women outlive men in younger age-groups.

(a) if the statement I alone is sufficient to answer,
(b) if statement II alone is needed,
(c) if both statements I and II are needed,
(d) if both statements I and II are not sufficient to answer the question.

Ans.(d)

✦ Directions for Q. No. 18 to 22: Each of the following questions consists of a question followed three statements labelled I, II and III. You have to decide whether the data given in the statement (s) is/are sufficient for answering the question. Read all the statements carefully and seek all the possible combinations which could be sufficient for answering the question. A single combination of statements with least number of statements which could be sufficient for answering the question would be your answer.

18. How old was Deepak on 30th July 1996 ?
I. Deepak is six years older than his brother Prabir.
II. Prabir is twenty nine years younger than his mother.
III. Deepak’s mother celebrated her fiftieth birthday on 15th June 1996.
(a) Only I and II
(b) All I, II and III are required
(c) Only II and III
(d) None of I, II, and III is sufficient to answer the question
(e) None of the above

Ans.(b)
All statements II and III are required to answer the question.

19. On which day of the last week did Mohan definitely meet Pramod in his office?
I. Pramod went to Mohan’s office on Tuesday and Thursday.
II. Mohan was absent for three days in the week excluding Sunday.
III. Mohan was not absent on any two consecutive days of the week.
(a) I and II only
(b) I and III only
(c) II and III only
(d) All I, II and III are required
(e) Even with all I, II and III, the answer cannot be arrived at.

Ans.(e)
Even with the combination of information given in statements I, II and III, we can’t definitely say that on which day Mohan met Pramod.

20· Which of the following represents ‘come’ in a code language?
I. ‘pit na ja od’ means ‘you may come here’ in that language.
II. ‘ja ta ter’ means ‘come and go’ in that code language.
III. ‘od na pit ter’ means ‘you may go home’ in that code language.
(a) I and II or I and III only
(b) I and II only
(c) All I, II and III are required
(d) II and III only
(e) None of the above

Ans.(b)
‘ja’ and ‘come’ are common in statements I and II. Hence, ‘ja’ stands for ‘come’.

21· Who among P, Q, R, Sand T is the lightest?
I. Q is lighter than P and S and heavier than T.
II. P is heavier than Q and lighter than S.
III. R is heavier than Q.
(a) I and II only
(b) I and III only
(c) I, II and III
(d) II and III only
(e) None of these

Ans.(b)
On combining all the informations we know that T is the lightest among all the five persons. But on the other
hand from statements I and III also, we get the same answer. Since, we require least combinations of statements to get the answer, hence option (b) is the correct choice.

22· How is Q related to T ?
I. M and R are brothers.
II. S has two sons and one daughter, R being one of the sons.
III. S is the mother of T and married to Q.
(a) I and III only
(b) III only
(c) I and II only
(d) II and III only
(e) All I, II and III are required

Ans.(b)
From statement III alone, it is clear that Q is the father of T.

✦ Directions for Q. No. 23 to 39 : Each of the wing questions has a question and the statements labelled d II. You have to decide whether the data provided in the ements are sufficient to answer the question. Read both the ements and give your answer as :

23. In a library 10 % of the books are added every year. What was the number of books that the library had in 1994 ?
I. During 1996, 10,000 books were added.
II. During 1995, the library had 1,00,000 books.

(a) if 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) 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.

(c) if the data either in statement’! alone or in the statement II alone are sufficient to answer the question.

(d) if the data even in both the statements together are not sufficient to answer the question.

(e) if the data in both the statements I and II together are needed to answer the question.

Ans.(c)
From statement I, the number of books in 1994 = 10,000/1.1 x 1.1.
And from statement II, the number of books in 1995 = 1,00,000/1.1. Hence, both the statements are alone sufficient to answer the question.

24. Balwant scored an average of 60 marks in English, Mathematics and Computer. How much did he get in Mathematics?
I. His average score in English and Computer is 45.
II. He got 40 marks in Computers.

(a) if 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) 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.

(c) if the data either in statement’! alone or in the statement II alone are sufficient to answer the question.

(d) if the data even in both the statements together are not sufficient to answer the question.

(e) if the data in both the statements I and II together are needed to answer the question.

Ans.(a)
As given in the question, his total marks E + M + C = 120. From statement I, we get E + C = 90. From here his marks of Mathematics are known. Therefore, statement I alone is sufficient to answer the question. Statement II alone is not sufficient because from this C = 40 which can’t help us to know the marks of Mathematics.

25. The sum of ages of M, N, and O is 50 years. What is N’s age?
I. N is 10 years older than M.
II. O is 30 years old.

(a) if 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) 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.

(c) if the data either in statement’! alone or in the statement II alone are sufficient to answer the question.

(d) if the data even in both the statements together are not sufficient to answer the question.

(e) if the data in both the statements I and II together are needed to answer the question.

Ans.(e)
As given in the question, M + N + a = 50 years. Combining statements I and II, we get
N = 15 years.

26. Satish, Anoop and Sandeep’s salary is in the ratio 4 : 5 : 7, respectively. How much is Anoop’s salary ?
I. The difference between Anoop and Sandeep’s salary is double that of Satish and Anoop.
II. Anoop gets Rs 4000 less than Sandeep.

(a) if 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) 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.

(c) if the data either in statement’! alone or in the statement II alone are sufficient to answer the question.

(d) if the data even in both the statements together are not sufficient to answer the question.

(e) if the data in both the statements I and II together are needed to answer the question.

Ans.(b)
As given in the question, the salaries of Satish, Anoop and Sandeep are 4x, 5x and 7x, respectively. From statement II, we get 7x – 5x = 4000 and x = 2000. Hence, Anoop’s salary = 5 x 2000 = 10,000.

27. What is the difference in the ages of P and K ?
I. P is 20 years older than M.
II. M is 2 years younger than Z.

(a) if 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) 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.

(c) if the data either in statement’! alone or in the statement II alone are sufficient to answer the question.

(d) if the data even in both the statements together are not sufficient to answer the question.

(e) if the data in both the statements I and II together are needed to answer the question.

Ans.(d)
Because relation between P and K cannot be established with the help of statements I and II. Hence, even both the statements cannot answer the question.

28. D is the sister of C. How is D related to A ?
I. A is the sister of B.
II. Bis the brother of C.

(a) if 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) 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.

(c) if the data either in statement’! alone or in the statement II alone are sufficient to answer the question.

(d) if the data even in both the statements together are not sufficient to answer the question.

(e) if the data in both the statements I and II together are needed to answer the question.

Ans.(e)
With the help of statements I and II, it is clear that all the persons A, B, C, D are are brothers and sister of one another and D is the sister of A

29. In a certain code language, ‘146’ means ‘adopt good habits’. What is the code of ‘habit’ in that language?
I. ‘473’ means ‘like good pictures’.
II. ‘826’ means ‘passion becomes habit’.

(a) if 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) 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.

(c) if the data either in statement’! alone or in the statement II alone are sufficient to answer the question.

(d) if the data even in both the statements together are not sufficient to answer the question.

(e) if the data in both the statements I and II together are needed to answer the question.

Ans.(b)
146 = adopt good habits. From statement II, it is clear that 6 and habits are in common in question and statement II. Hence, 6 stands for habits.

30. A, B, C, D and E are sitting in a row. What is the position of B from the left end?
I. A is sitting at one end second right of D who is the immediate neighbour of C and B.
II. E is to the left of B.

(a) if 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) 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.

(c) if the data either in statement’! alone or in the statement II alone are sufficient to answer the question.

(d) if the data even in both the statements together are not sufficient to answer the question.

(e) if the data in both the statements I and II together are needed to answer the question.

Ans.(e)
Combining both the statements, position of B from the left end can be ascertained .

31. How INDIA will be coded?
I. If ALIVE is coded as lAIEV.
II. If JAPAN is coded as AJPNA.

(a) if 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) 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.

(c) if the data either in statement’! alone or in the statement II alone are sufficient to answer the question.

(d) if the data even in both the statements together are not sufficient to answer the question.

(e) if the data in both the statements I and II together are needed to answer the question.

Ans.(c)
Statements I and II are individually sufficient to answer the question. Word has been coded by interchanging 1st
letter with 2nd and 3rd with 4th keeping the middle letter as it is.

32. What will come in place of c in the series a, b, c, d, e ?
I. a, b, c, d, e, are five consecutive even numbers.
II. Common difference between two consecutive
numbers is 2 and a is the second smallest natural number.

(a) if 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) 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.

(c) if the data either in statement’! alone or in the statement II alone are sufficient to answer the question.

(d) if the data even in both the statements together are not sufficient to answer the question.

(e) if the data in both the statements I and II together are needed to answer the question.

Ans.(e)
With the combinations of two statements, it is clear that number 6 will come in place of c.

33. How many students are there in the class?
I. Dilip is 10th from right and Jagdish is 14th from left
II. After interchanging their positions, Dilip becomes 27th from right.

(a) if 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) 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.

(c) if the data either in statement’! alone or in the statement II alone are sufficient to answer the question.

(d) if the data even in both the statements together are not sufficient to answer the question.

(e) if the data in both the statements I and II together are needed to answer the question.

Ans.(e)
On combining both the statements, total number of students in the class is calculated. as 40.

34. Who among A, B, C, D and E is the smallest?
I. B is taller than E and D is taller than A but smaller than E.
II. D is not the tallest and C is not the smallest.

(a) if 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) 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.

(c) if the data either in statement’! alone or in the statement II alone are sufficient to answer the question.

(d) if the data even in both the statements together are not sufficient to answer the question.

(e) if the data in both the statements I and II together are needed to answer the question.

Ans.(e)
Statements I and II individually are not sufficient to answer the question. However,’ on combining both the statements, we know that A is’the smallest and C is the tallest.

35. X borrowed Rs 1,000 from x’1? imple interest. What is the rate.of.interest.per annum.?
I. After-four years; X paid Rs. 100 as interest.
II. After four years, X paid Rs. 1,100 to settle the loan.

(a) if 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) 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.

(c) if the data either in statement’! alone or in the statement II alone are sufficient to answer the question.

(d) if the data even in both the statements together are not sufficient to answer the question.

(e) if the data in both the statements I and II together are needed to answer the question.

Ans.(c)
From both,he statements using individually, it is clear that interest.for four years is 100 i.e., interest for one
year will he 25. Hence, rate of interest is 25/1000 x 100 = 2.5%.

36. What is total salary of Mr. X and his wife at present?
I. Salary of X and his wife together is 20% more than what they earned last month.
II. Last year salary of X was Rs 600 more than that of his wife.

(a) if 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) 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.

(c) if the data either in statement’! alone or in the statement II alone are sufficient to answer the question.

(d) if the data even in both the statements together are not sufficient to answer the question.

(e) if the data in both the statements I and II together are needed to answer the question.

Ans.(d)
Since Salary of X’s wife is not known for the last year. Hence, even a combination of both the statements will not be adequate for answering the question.

37. How old is Sunita now?
I. Sunita was twice as old as his brother 2 years back and his brother’s age now is 20 years.
II. Sunita was 10 years old when his brother was born.

(a) if 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) 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.

(c) if the data either in statement’! alone or in the statement II alone are sufficient to answer the question.

(d) if the data even in both the statements together are not sufficient to answer the question.

(e) if the data in both the statements I and II together are needed to answer the question.

Ans.(a)
From statement I alone, we find that Sunita is 38 years old. Statement II alone is not sufficient to answer the question.

38. How many tourists went to Shimla this year?
I. Last year 1450 tourists went to Shimla.
II. This year, there was 10% decrease over the number that went last year.

(a) if 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) 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.

(c) if the data either in statement’! alone or in the statement II alone are sufficient to answer the question.

(d) if the data even in both the statements together are not sufficient to answer the question.

(e) if the data in both the statements I and II together are needed to answer the question.

Ans.(e)
Individually, both the statements alone are not sufficient to answer the question. However, combining statements I and II, we get the number of tourists this year, i.e., 1450 x 90 %.

39. Which one of the integers a, b, c, d and e are odd numbers?
I. a, b, c, d and e are consecutive numbers.
II. c is an even number.

(a) if 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) 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.

(c) if the data either in statement’! alone or in the statement II alone are sufficient to answer the question.

(d) if the data even in both the statements together are not sufficient to answer the question.

(e) if the data in both the statements I and II together are needed to answer the question.