# Ch.12 :- Data – Sufficiency : Exercise 3

✦ Directions for Q. No. 1 to 25 : Each of the question given below contains a question and two statements numbered
I and II. You have to decide whether the data given in the statements are sufficient for answering the question. The correct answer is :

1. Which of the integers a, b, c, d, e are odd numbers ?
I. a, b, c, d, e are consecutive integers.
II. c is an even integer.

(a) if statement I alone is sufficient but statement II alone is not sufficient.

(b) if statement II alone is sufficient but statement I alone is not sufficient.

(c) if both statements I and II together are sufficient but neither of statements alone is sufficient.

(d) if each statement alone is sufficient.

(e) if statements I and II together are not sufficient.

Ans.(c)
With the help of statements I and II using together, odd numbers out of a, b, c, d and e can be found out.

2. What is 4th consecutive even number in a given series of even real numbers?
I. The sum of 1st two numbers is 18.
II. The sum of last two numbers is 26.

(a) if statement I alone is sufficient but statement II alone is not sufficient.

(b) if statement II alone is sufficient but statement I alone is not sufficient.

(c) if both statements I and II together are sufficient but neither of statements alone is sufficient.

(d) if each statement alone is sufficient.

(e) if statements I and II together are not sufficient.

Ans.(d)
From statement I, x + (x + 2) = 18 i.e., x = 8, hence, 4th consecutive even number is (x + 6) = 14. In statement II, it is given that sum of last two numbers is 26. Since it is not known which last two numbers’ sum together is 26, hence, statement II can’t answer the question.

3. How many girls passed B.Ed. entrance examination this year?
I. Last year 500 girls passed.
II. This year there was a 10% decrease over last year in the number of failures.

(a) if statement I alone is sufficient but statement II alone is not sufficient.

(b) if statement II alone is sufficient but statement I alone is not sufficient.

(c) if both statements I and II together are sufficient but neither of statements alone is sufficient.

(d) if each statement alone is sufficient.

(e) if statements I and II together are not sufficient.

Ans.(e)
Even a combination of both the statements will not be sufficient to answer the question.

4. What will be the age of Saurabh after 5 years from now?
I. Saurabh is 30 years younger than his father.
II. His father was 50 years old 5 years ago.

(a) if statement I alone is sufficient but statement II alone is not sufficient.

(b) if statement II alone is sufficient but statement I alone is not sufficient.

(c) if both statements I and II together are sufficient but neither of statements alone is sufficient.

(d) if each statement alone is sufficient.

(e) if statements I and II together are not sufficient.

Ans.(c)
From statement II, it is clear that Saurabh’s father is 55 years now. Now using statement I, it is clear that Saurabh will be 25 years old now.

5. In a class of 60 students, how many boys scored over
80 % in the Chemistry test?
I. Exactly 5 girls scored over 80% in the test.
II. 2/3rd of the class scored over 80% in the test.

(a) if statement I alone is sufficient but statement II alone is not sufficient.

(b) if statement II alone is sufficient but statement I alone is not sufficient.

(c) if both statements I and II together are sufficient but neither of statements alone is sufficient.

(d) if each statement alone is sufficient.

(e) if statements I and II together are not sufficient.

Ans.(c)
From statement II, it is clear that out of 60 students, 40 students scored over 80% in the test. Now it is given in statement I that 5 girls scored over 50 %.
Hence, number of boys who scored more than)50 % = 40 – 5 = 35

6. P, Q, R are negative integers and t is a number. Is it negative?
I. t = P – Q.
II. tR = P.

(a) if statement I alone is sufficient but statement II alone is not sufficient.

(b) if statement II alone is sufficient but statement I alone is not sufficient.

(c) if both statements I and II together are sufficient but neither of statements alone is sufficient.

(d) if each statement alone is sufficient.

(e) if statements I and II together are not sufficient.

Ans.(b)
From statement I, it can be negative as well as positive. Hence, statement I alone is not sufficient to answer the question. From statement II, it is clear that since P and R are negative hence t will be positive.

7. What is John’s age?
I. In 15 years, John will be twice as old as Dias would be.
II. Dias was Born 5 years ago.

(a) if statement I alone is sufficient but statement II alone is not sufficient.

(b) if statement II alone is sufficient but statement I alone is not sufficient.

(c) if both statements I and II together are sufficient but neither of statements alone is sufficient.

(d) if each statement alone is sufficient.

(e) if statements I and II together are not sufficient.

Ans.(c)
From statement II, it is clear that Dias is 5 years old now. Using statement I with it we get the age of John.

8. In a s-term series 4, P, Q, R, 16 what is the value of R, all numbers being real?
I. 3rd term is twice 1st term.
II. 4th term is twice the 2nd term.

(a) if statement I alone is sufficient but statement II alone is not sufficient.

(b) if statement II alone is sufficient but statement I alone is not sufficient.

(c) if both statements I and II together are sufficient but neither of statements alone is sufficient.

(d) if each statement alone is sufficient.

(e) if statements I and II together are not sufficient.

Ans.(e)
Even using both the statements Land II together, the value of R can’t be determined.

9. Is A – S even? A is a real number.
I. A – I S is an integer.
II. A – I O is an odd integer.

(a) if statement I alone is sufficient but statement II alone is not sufficient.

(b) if statement II alone is sufficient but statement I alone is not sufficient.

(c) if both statements I and II together are sufficient but neither of statements alone is sufficient.

(d) if each statement alone is sufficient.

(e) if statements I and II together are not sufficient.

Ans.(b)
From statement I, (A – 15) is an integer-A can be even as well as odd. From statement II, if (A – 10) is an odd integer, A will always be odd. Hence, (A – 5) will be even.

10. The average marks of three students A, Band C in Mathematics are 180, what are the marks of each of the student?
I. Band C together obtained 85 marks.
II. A and C together obtained 70 marks.

(a) if statement I alone is sufficient but statement II alone is not sufficient.

(b) if statement II alone is sufficient but statement I alone is not sufficient.

(c) if both statements I and II together are sufficient but neither of statements alone is sufficient.

(d) if each statement alone is sufficient.

(e) if statements I and II together are not sufficient.

Ans.(c)
Using the information given in the question A + B + C = 180 and that of given in statements I and II together we can find the marks of each of the student.

11. How old is the teacher?
I. The average age of 10 students and their teacher is 25 years.
II. The teacher’s age is 10 years more than the oldest student’s age.

(a) if statement I alone is sufficient but statement II alone is not sufficient.

(b) if statement II alone is sufficient but statement I alone is not sufficient.

(c) if both statements I and II together are sufficient but neither of statements alone is sufficient.

(d) if each statement alone is sufficient.

(e) if statements I and II together are not sufficient.

Ans.(e)
None of the statements I and II alone or even combination of, both the statements is not sufficient to answer the question.

12. What are the sides of a right-angled traingle?
I. The difference between the hypotenuse and base is 6 cm.
II. The difference between the hypotenuse and perpendicular is 3 cm.

(a) if statement I alone is sufficient but statement II alone is not sufficient.

(b) if statement II alone is sufficient but statement I alone is not sufficient.

(c) if both statements I and II together are sufficient but neither of statements alone is sufficient.

(d) if each statement alone is sufficient.

(e) if statements I and II together are not sufficient.

Ans.(c)
From statement I, H – B = 6 and from statement II, H – P = 3. Now we know that in right angle triangle H2 = P2 + B2.By solving these three equations, sides of triangle can be known. Hence, both the statements are required to answer the question.

13. How long would it take Amit to complete the work?
I. Amit and Sumit together complete the work in 10 days.
II. Amit takes 5 days more than Sumit to complete the work.

(a) if statement I alone is sufficient but statement II alone is not sufficient.

(b) if statement II alone is sufficient but statement I alone is not sufficient.

(c) if both statements I and II together are sufficient but neither of statements alone is sufficient.

(d) if each statement alone is sufficient.

(e) if statements I and II together are not sufficient.

Ans.(c)
Using statements I and II together, question can be answered easily.

14. Is B positive?
I. A + B is positive .
II. A – B is positive.

(a) if statement I alone is sufficient but statement II alone is not sufficient.

(b) if statement II alone is sufficient but statement I alone is not sufficient.

(c) if both statements I and II together are sufficient but neither of statements alone is sufficient.

(d) if each statement alone is sufficient.

(e) if statements I and II together are not sufficient.

Ans.(e)
B can be positive as well as negative using statements I and II individually. Statements I and II can’t be used together.

15. When will the Indian population exceed chinese population?
I. Population of China grows at the rate of 10% per decade and that of India at the rate of 15% per decade.
II. In 1980, chinese population was 10 crores more than the Indian population.

(a) if statement I alone is sufficient but statement II alone is not sufficient.

(b) if statement II alone is sufficient but statement I alone is not sufficient.

(c) if both statements I and II together are sufficient but neither of statements alone is sufficient.

(d) if each statement alone is sufficient.

(e) if statements I and II together are not sufficient.

Ans.(e)
Since the population of India as well as China is not given in the year 1980, hence, both the statements are not sufficient to answer the question.

16. How much more per kg does tea cost than sugar?
I. 7 kg sugar and 1 kg tea cost Rs 80.
II. 4 kg of sugar and 2 kg of tea cost Rs 200.

(a) if statement I alone is sufficient but statement II alone is not sufficient.

(b) if statement II alone is sufficient but statement I alone is not sufficient.

(c) if both statements I and II together are sufficient but neither of statements alone is sufficient.

(d) if each statement alone is sufficient.

(e) if statements I and II together are not sufficient.

Ans.(e)
If we suppose price per kg of sugar and tea be Rs x and Rs y, respectively. Then as per statement I x + Y = 80 and from statement II 4x + 2y = 200. Both the equations can’t be solved for the positive values of x and y.
Hence, even both the statements together are not sufficient to answer the question.

17. A’s salary was increased by 20%, by what % his savings is increased?
I. He used to save 10% of his income before increment.
II. He increased his expenses just by 10% after increment.

(a) if statement I alone is sufficient but statement II alone is not sufficient.

(b) if statement II alone is sufficient but statement I alone is not sufficient.

(c) if both statements I and II together are sufficient but neither of statements alone is sufficient.

(d) if each statement alone is sufficient.

(e) if statements I and II together are not sufficient.

Ans.(c)
If we suppose the income to be Rs 100, then from statement I, A spends Rs 90 and saves Rs 10. From statement II, his expenses now become 99. Therefore, savings as becomes 120 – 99 = Rs 21. Hence, A’s saving is increased by Rs 11 i.e., 110 %.

18. What is the average salary of three employees P, Q and R of an organisation?
I P and Q together earn Rs 60 more than R, and R earns Rs 100.
II Q’s salary is half of the combined salary of P and R.

(a) if statement I alone is sufficient but statement II alone is not sufficient.

(b) if statement II alone is sufficient but statement I alone is not sufficient.

(c) if both statements I and II together are sufficient but neither of statements alone is sufficient.

(d) if each statement alone is sufficient.

(e) if statements I and II together are not sufficient.

Ans.(a)
From statement I, P + Q = 160 and R = 100. Average salary now can be calculated. Statement II is not sufficient to answer the question.

19. What is the percentage increase in profit of company A in 1998 with that of 1996.
I. Company’s profit in 1996 was Rs 200 crore which was 20% more than that of 1997.
II. Profit in 1998 was Rs 250 crore and was more by Rs 50 crore with that of 1996.

(a) if statement I alone is sufficient but statement II alone is not sufficient.

(b) if statement II alone is sufficient but statement I alone is not sufficient.

(c) if both statements I and II together are sufficient but neither of statements alone is sufficient.

(d) if each statement alone is sufficient.

(e) if statements I and II together are not sufficient.

Ans.(b)
From statement II alone, it is clear that profit in 1998 was Rs 250 crore and in 1996 it wall Rs 200 crore. Therefore, percentage increase in profit can be found from this information.

20. If A > 0 (zero), what is the value of one-fourth of NB ?
I. B = 3 A.
II. A = S.

(a) if statement I alone is sufficient but statement II alone is not sufficient.

(b) if statement II alone is sufficient but statement I alone is not sufficient.

(c) if both statements I and II together are sufficient but neither of statements alone is sufficient.

(d) if each statement alone is sufficient.

(e) if statements I and II together are not sufficient.

Ans.(a)
From statement I AB = 13 hence 14 of AB = 112

21. How much did a man earn in 1960?
I. He earned Rs 6,500 in 1963 which is 12.5% more than he earned in 1960.
II. His wife (who earned half the amount he earned) and he earned Rs 8,666.62 together in 1960.

(a) if statement I alone is sufficient but statement II alone is not sufficient.

(b) if statement II alone is sufficient but statement I alone is not sufficient.

(c) if both statements I and II together are sufficient but neither of statements alone is sufficient.

(d) if each statement alone is sufficient.

(e) if statements I and II together are not sufficient.

Ans.(d)
Man’s earning in the year 1960 can be calculated with the help of either of the statements.

22. Is Akbar taller than Raees ?
I. Akbar is taller than Rahim.
II. Rahim is not as tall as Raees.

(a) if statement I alone is sufficient but statement II alone is not sufficient.

(b) if statement II alone is sufficient but statement I alone is not sufficient.

(c) if both statements I and II together are sufficient but neither of statements alone is sufficient.

(d) if each statement alone is sufficient.

(e) if statements I and II together are not sufficient.

Ans.(e)
Using both the statements together, it is clear that Akbar can be taller or smaller than Raees as the relationship between Akbar and Raees can’t be established.

23. If ‘x is an integer, is x/2 an even integer?
I. x is a multiple of 2.
II. x is a multiple of 4.

(a) if statement I alone is sufficient but statement II alone is not sufficient.

(b) if statement II alone is sufficient but statement I alone is not sufficient.

(c) if both statements I and II together are sufficient but neither of statements alone is sufficient.

(d) if each statement alone is sufficient.

(e) if statements I and II together are not sufficient.

Ans.(b)
From statement I, if x is a multiple of 2, then x/2 is even as well as odd. From statement II, if x is a multiple of 4, then x/2 is even.
Hence, statement II alone is sufficient to answer the question.

24. In a factory capacity of a solution tank A is 70% of the capacity of the another tank B. How many more gallons of solution are in tank A than in tank B ?
I. Tank A is 80% full and tank B is 40% full.
II. Full tank of A contains 14,000 gallons of solution.

(a) if statement I alone is sufficient but statement II alone is not sufficient.

(b) if statement II alone is sufficient but statement I alone is not sufficient.

(c) if both statements I and II together are sufficient but neither of statements alone is sufficient.

(d) if each statement alone is sufficient.

(e) if statements I and II together are not sufficient.

Ans.(c)
From statement II, it is clear that capacity of tank A is 14,000 gallons. Now, as per question, capacity of tank B is 20,000 gallons because capacity of tank A is 70% of capacity of tank B. From statement I, solution in tank A is 11,200 gallons and in tank B it is 8000 gallons. Therefore, both the statements are needed to answer the question.

25. What is the cost price of an article?
I. The article is sold for Rs 24 at a loss of 10%.
II. The % loss is as much as the cost price of the article.

(a) if statement I alone is sufficient but statement II alone is not sufficient.

(b) if statement II alone is sufficient but statement I alone is not sufficient.

(c) if both statements I and II together are sufficient but neither of statements alone is sufficient.

(d) if each statement alone is sufficient.

(e) if statements I and II together are not sufficient.

Ans.(a)
From statement I, cost price of the article = Rs 80/3. Statement II alone is not sufficient to answer the question.

✦ Directions for Q. No. 26 to 36: Each of the questions below consists of a question and 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 your answer as :

26. How many students in standard V of our school play chess?
I. No girl has interest in chess.
II. In standard V, there are 40 boys.

(a) if the data in the statement I alone are sufficient to answer the questions.

(b) if the data in statement II alone are sufficient to answer the question.

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

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

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

Ans.(d)
From both the statements we do not know how many boys do not play chess. Hence, the question can’t be answered.

27. How old is Tomar?
I. Tomar could not appear for the final exams because he was short by two months for the stipulated 18 years of age in Jan. this year.
II. He will become eligible for casting his vote, where minimum age limit is 18, in March this year.

(a) if the data in the statement I alone are sufficient to answer the questions.

(b) if the data in statement II alone are sufficient to answer the question.

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

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

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

Ans.(c)
Data either in statement I or statement II alone are sufficient to know the age of Tomar.

28. Jai ranks 10th in the class. How many students are there in the class?
I. His class-friend got 58th rank which is the last.
II. Jai’s rank from the last (other and) is 49th.

(a) if the data in the statement I alone are sufficient to answer the questions.

(b) if the data in statement II alone are sufficient to answer the question.

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

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

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

Ans.(c)
From statement I, it is clear that there are 58 students as 58th is the last rank. From statement II, total number of students = 10 + 49 -1 = 58.

29. How many brothers does Ramu have.
I. Ramu’s father has three children.
II. Ramu has two sisters.

(a) if the data in the statement I alone are sufficient to answer the questions.

(b) if the data in statement II alone are sufficient to answer the question.

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

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

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

Ans.(e)
Using both the statements together it is ascertained that Ramu has no brother.

30. Lal is taller than N and, Jim is taller than Harry. Who among them is the tallest?
I. Jim is taller than N and.
II. Lal is taller than Harry.

(a) if the data in the statement I alone are sufficient to answer the questions.

(b) if the data in statement II alone are sufficient to answer the question.

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

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

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

Ans.(d)
Even both the statements I and II together are not sufficient to answer the question.

31. Who is the heaviest among Arnol, Prabhu, Narayan and Navin?
I. Arnol and Prabhu are of the same weight.
II. Prabhu’s weight is more than Narayan, but less than Navin.

(a) if the data in the statement I alone are sufficient to answer the questions.

(b) if the data in statement II alone are sufficient to answer the question.

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

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

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

Ans.(e)
From both the statements using together it is ascertained that Navin is the heaviest.

32. How many daughters does ‘L’ have.
I. R’s father has three daughters.
II. T is R’s sister and the daughter of L.

(a) if the data in the statement I alone are sufficient to answer the questions.

(b) if the data in statement II alone are sufficient to answer the question.

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

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

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

Ans.(e)
From statement II, it is clear that T is R’s sister and it is given in statement I that R’s father has three daughters it means that L is the father of R and T both. Hence, L has three daughters.

33. Rajiv’s rank is 17th in his class. What is his rank from the last?
I. ‘There are 70 students in his class.
II. Abhijeet, who ranks 20th in Rajiv’s class is 51st from the last.

(a) if the data in the statement I alone are sufficient to answer the questions.

(b) if the data in statement II alone are sufficient to answer the question.

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

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

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

Ans.(c)
Statement I and statement II alone are sufficient to answer the question. From statement I, Rajiv’s rank
from the last = 70 -17 + 1 = 54th. From statement II, we can calculate the total number of students in the class = 20 + 51 – 1 = 70. Now, we can calculate Rajiv’s rank from the last.

34. A library contains only English, Hindi and Telugu novels. How many Telugu novels are there in the library ?
I. Of the one thousand novels in the library, fifty, percent novels are in English and Hindi.
II. The number of Hindi novels is double the number of English novels.

(a) if the data in the statement I alone are sufficient to answer the questions.

(b) if the data in statement II alone are sufficient to answer the question.

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

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

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

Ans.(a)
From the statement I, it is clear that number of Telugu novels is 500. From the statement II, number of Telugu no novels can’t be determined.

35. The area of a playground is 484 square metre. What is its perimeter?
I. It costs Rs 912 to put a fence around the playground.
II. The playground is a perfect square.

(a) if the data in the statement I alone are sufficient to answer the questions.

(b) if the data in statement II alone are sufficient to answer the question.

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

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

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

Ans.(b)
From statement II we know that one side of the field is 22 m. Since the field is a square, hence its perimeter is 88 m.

36. In a certain code language ‘pe nop con’ means ‘we like roses.’ Which word means ‘roses’?
I. ‘nop to cop’ means ‘we are honest’.
II. ‘pe me say’ means ‘they like flowers’.

(a) if the data in the statement I alone are sufficient to answer the questions.

(b) if the data in statement II alone are sufficient to answer the question.

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

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

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