# 19.Data Sufficiency

Introduction:
Problems under this category test the ability of the students to find out whether the given set of statement or data is sufficient or not to answer the question asked. The section consists of problems in which a question on any topic such as Number systems, Blood relations, Trains, Percentage, Compound Interest, Simple Interest, Number Ranking, Circle, etc.
1. No need to solve the problem
2. Only to conclude that the given question can be or cannot be answered with the given set of statement / data / information.

EXERCISE:
Directions for Q. No. 1 to 5: Each of the questions below consists of a question and two statements labeled I and II given below it. You have to decide whether the data provided in the statements are sufficient to answer the questions. Read both the statements and give your answer as:
(a) If the data in statement I alone are sufficient to answer the question, while the data in statement II alone are not sufficient to answer the question.
(b) If the both in the statement II alone are sufficient to answer the question while the data in statement I alone are not sufficient the 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 given in both the statements I and II together are not sufficient to answer the question and.
(e) If the data both in statement I and II together are necessary to answer the question.
1. On which day of the week was Varun’s birthday?
I. Varun celebrated his birthday on day after Ashish celebrated his birthday.
II. Varun was born two days after his sister, who was born on 3rd day of the week.
2. Among P, Q, T, V and Z, who is 3rd from the top when arranged in descending order of the heights?
I. V is taller than P and Q and is shorter than T who is not the tallest?
II. T is taller than only Z.
3. How is M related to P?
I. P’s mother and K are sisters.
II. M is the only child of D and K.
4. What is K’s rank from the bottom in a class of thirty students?
I. M’s position 3rd from the top and there are five students between M and K
II. P’s position is 4th from the bottom and there are 7th students between P and K.
5. What does ‘pit’ stand for in a certain a code language?
I. ‘na ja ho’ means ‘how and why’ in that code language.
II. ‘ja pit ha’ means ‘ how they went’ in that code language.

Directions for Q. No. 6 to 10: Each of the questions below consists of a question and two statements labeled I and II given below it. You have to decide whether the data provided in the statements are sufficient to answer the questions.
(a) If the data in statement I alone are sufficient to answer the question, while the data in statement II alone are not sufficient to answer the question.
(b) If the data in the statement II alone are sufficient to answer the question while the data in statement I alone are not sufficient the 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 given in both the statements I and II together are not sufficient to answer the question and.
(e) If the data in both the statements I and II together are necessary to answer the question.
6. How many sisters does P have?
I.T and V are only sisters of D.
II. D is brother of P.
7. How is ‘over’ written in a code language?
I. ‘Over and again’ is written as ‘ka ja ha’ that code language.
II. ‘Came and go’ is written as ‘ja pa na’ in that code language.
8. Who is the immediate right of Mohan when Mohan, Sail, Bhushan, Suresh and Jayesh are sitting around a circle facing at the centre?
I. Sail is 3rd to the left of Mohan.
II. Bhushan is between Sail and Jayesh.
9. How is N related to K?
I. N’s brother is married to D.
II. D’s sister is married to K.
10. Who among M, T, K, J and R is the shortest but one?
I.T is taller than J and R.
II. K is shorter than R and M.

Directions for Q. No. 11 to 17: Each of the questions below consists of a question and two statements labeled I and II given below it. You have to decide whether the data provided in the statements are sufficient to answer the questions.
(a) If the data in statement I alone are sufficient to answer the question, while the data in statement II alone are not sufficient to answer the question.
(b) If the data in the statement II alone are sufficient to answer the question while the data in statement I alone are not sufficient the 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 given in both the statements I and II together are not sufficient to answer the question and.
(e) If the data in both the statements I and II together are necessary to answer the question.
11. Among P, K, D and R, who is the son of M?
I. P and R are sisters of K.
II. D is the mother of K and wife of M.
12. How is ‘call written in code language?
I. ‘Call me back is written as ‘531’ in that code language.
II. You can call me anytime’ is written as ‘94163’ in that code language.
13. If ‘over and above’ is written as ‘ja na ta’ in a code language, how is ‘and’ written in that code language?
I. ‘Come and go’ is written as ‘ha la ja’ in that code language.
II. ‘he and you’ is written as ‘da ja ma’ in that code language.
14. Among Sanjay, Suresh, Navin, Prakash and Karan, who has secured maximum marks in mathematics?
I. Karan has secured more marks in Mathematics than Suresh and Navin.
II. Sanjay and Prakash have secured less mark in Mathematics than Navin.
15. B is the brother of D, D is the sister of K, K is the brother of M. how is M related to B?
I. P is mother of B.
II. H is husband of P.
16. On which day in June did the school reopen?
I. Manoj correctly remembers that the school reopened after 12th June but before 16th June.
II. Manoj’s classmate Ashok correctly remembers that the school reopened after 14th June but before 18th June.
17. Who among N, F, P, J and D is the youngest?
I. P and J are younger than N and D.
II. F is younger than N, D and P but older than J.

Directions for Q. No. 18 to 20: Each of the questions below consists of a question and two statements labeled I and II given below it. You have to decide whether the data provided in the statements are sufficient to answer the questions.
(a) If the data in statement I alone are sufficient to answer the question, while the data in statement II alone are not sufficient to answer the question.
(b) If the data in the statement II alone are sufficient to answer the question while the data in statement I alone are not sufficient the 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 given in both the statements I and II together are not sufficient to answer the question and.
(e) If the data in both the statements I and II together are necessary to answer the question.
18. Who among T, R and S is (are) to the East of P?
I. R, who is to the west of P, is not as near to S as P is, S is in the farthest East.
II. P is not as far away from S as T is.
19. Who amongst A, B, C, D and E was the first to reach the function?
I. B, who reached earlier than E, A and C was not the first reach.
II. A, who reached earlier than E and C could not reach earlier than D, who was at the function before B.
20. How many students did secure Ist class in a class of 48 students?
I. Double the number of Ist class students secured IInd class and all the remaining failed.
II. Number of students failed was twice the number of Ist class students in the class.

Directions (Questions 21 to 35): 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.
(a) if the data in statement I alone are sufficient to answer the question, while the data in statement II alone are not sufficient to answer the question;
(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 I alone or in statement II alone are sufficient to answer the question;
(d) if the data given in both statements I and II together are not sufficient to answer the question; and
(e) if the data in both statements I and II together are necessary to answer the question.
21. What is the color of the fresh grass?
I. Blue is called green, red is called orange, and orange is called yellow.
II. Yellow is called white, white is called black, green is called brown and brown is called purple.
22. In a certain code, ‘no paled’ means ‘They like flowers’. Which code word means ‘flowers’?
I. ‘id nim nop’ means ‘They are innocent’
II. ‘gob ots al’ means ‘We like roses’
23. What is Suman’s rank from the top in the class of 40 students?
I. Reena is 4 ranks below Suman and is thirty-first from the bottom.
II. Anuj is two ranks above Suman and is thirty-seventh from the bottom.
24. Among D, F, J, P and A who reached office last?
I. F and J reached office together.
II. Only D and P reached office ahead of J.
25. How is J related to P?
I. M is brother of P and T is sister of P.
II. P‘s mother is married to J’s husband who has one son and two daughters.
26. What is the value of 144 $16 * 7 # 9? I.$ means ÷, * means × and # means +
II. 16 $4 * 2 # 2 = 10 27. On which date in August was Kapil born? I. Kapil’s mother remembers that Kapil was born before nineteenth after fifteenth. II. Kapil’s brother remembers that Kapil was born before seventeenth but after twelfth 28. How many visitors saw the exhibition yesterday? I. Each entry pass holder can take up to three persons with him / her. II. In all, 243 passes were sold yesterday. 29. On a T.V. channel, four serials A, B, C and D were screened, one of each day, on four consecutive days but not necessarily in that order. On which day was the serial C screened? I. The first serial was screened on 23rd, Tuesday and was followed by serial D. II. Serial A was not screened on 25th and one serial was screened between serials A and B. 30. In which direction is Rahul facing? I. In the early morning Rahul was standing in front of a puppet and the shadow of puppet was falling to the right of Rahul. II. In the early morning Rahul was standing on the ground. His shadow was falling behind him when he turned to his left. 31. Five friends P, Q, R, S and T are standing in a row facing east. Who is standing at the extreme right end? I. Only P is between S and T. R is to the immediate right of T. II. R is between T and Q. 32. On which date of the month was Anjali born in February 2004? I. Anjali was born on even date of the month II. Anjali’s birth date was a prime number 33. Madan is taller than Kamal and Sharad is younger than Arvind. Who among them is the youngest? I. Sharad is younger than Madan II. Arvind is younger than Kamal 34. In a row of five buildings – P, Q, R, S and T, which building is in the middle? I. Buildings S and Q are at the two extreme ends of the row. II. Building T is to the right of building R. 35. How many employees of Bank Z opted for VRS? I. 18% of the 950 officer cadre employees and 6% of the 1100 other cadre employees opted for VRS. II. 28% of the employees in the age-group of 51 to 56 and 17% of the employees in all other age-groups opted for VRS. Directions (Questions 36 to 40): In each of the following problems, there is one question and three statements I, II and III given below the question. You have to decide whether the data given in the statements is sufficient to answer the question. Read all the statements carefully and find which of the statements is / are sufficient to answer the given question. Choose the correct alternative in each question. 36. How is ‘DATE’ written in the code language? I. DEAR is written as$#@? In that code
II. TREAT is written as %?#@% in that code
III. TEAR is written as %#@? In that code

(a) Only I and II
(b) Only II and III
(c) All I, II and III
(d) Only I and either II or III
(e) None of these
37. What is Suman’s rank from the top in a class of forty students?
I. Suman is 3 ranks below Deepak from the top
II. Deepak’s rank from the bottom is 23
III. Suman is 3 ranks above Deepak from the bottom

(a) Any two of the three
(b) Only I and II
(c) Only II and III
(d) All I, II and III
(e) Only II and either I or III
38. Village T is in which direction with respect to village R?
I. T is to the North of W which is to the West of S.
II. T is to the North-West of S
III. W is to the North-West of R.

(a) Any two of the three
(b) Only I and II
(c) Only II and III
(d) Only I and III
(e) None of these
39. How is the girl in the photograph related to Kunal?
I. Pointing to the photograph, Kunal said, “She is the mother of my father’s only grand-daughter”.
II. Kunal has no siblings.
III. Pointing to the photograph, Kunal said, “She is the only daughter-in-law of my mother”.

(a) Any two of the three
(b) Only I and II
(c) Only II and III
(d) Either only III or only I and II
(e) None of these
40. Among P, Q, R, S and T, Q is the second tallest and S is immediate taller than the shortest. Who among them is in the middle when they stand in the order of their heights?
I.T is not the shortest
II. R is taller than S but shorter than Q
III. P ranks third in height above S when all are arranged in the order of height.

(a) Only I and II
(b) Either II only or I and III only
(c) Only II
(d) Only II and III
(e) None of these
41. How’ is Raju related to Manohar?
I. Pramila is the mother-in-law of Rashmi, the wife of Raju.
II. Pramila’s brother is Raju’s maternal uncle.
III. Pramila’s husband is the only son of Manohar.

(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) Question cannot be answered even with the information in all three statements
42. Who amongst Subodh, Neeraj, Tara, Meena and Anil is the first to take the lecture ?
I. Subodh takes lecture before Meena and Neeraj but not before Anil:
II. Tara is not the first to take the lecture.
III. Meena is not the last to take the lecture.

(a) Only I
(b) Only I and II
(c) Only I and either II or III
(d) All I, II and III are necessary
(e) Question cannot be answered even with the information in all three statements
43. What is the code for ‘rope’ in a code language?
I. ‘use the rope’ is written a s ‘nik ta re’ in the code language.
II. ‘Rope is straight' is written as ‘pe da ta’.
III. ‘Always use rope’ is written a s ‘ma re ta’.

(a) Only I and II or II and III
(b) Only I and III
(c) Only II and III
(d) All I, II and III are necessary
(e) Question cannot be answered even with the information in all three statements
44. P is in which direction with respect to Q ?
I. M is to the North of R who is to the West of Q.
II. P is to the East of M.
III. P is to the North-East of R.
(a) Only I and II
(b) Only III
(c) Any two of the three
(d) All I, II and III are necessary
(e) Question cannot be answered even with the information in all three statements
45. What is Sunita’s rank from top in the class of 45 students?
I. Sunita is five ranks below Samir who is 15th from the bottom.
II. Radha is 30th from the top and Neeta is 5th from the bottom.
III. Sunita is exactly in the middle of Radha and Neeta.

(a) Only I
(b) Only II and III
(c) Either only I or only II and III
(d) Only I and either II or III
(e) None of these

Directions (46 -50): 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 answer (1) If the data in Statement I alone are sufficient to answer the question, while the data in Statement II alone are not sufficient to answer the question.
Give answer (2) If the data in Statement II alone is sufficient to answer the question, while data in Statement I alone is not sufficient to answer the question.
Give answer (3) if the data in Statement I alone or in the Statement II alone are sufficient to answer the question.
Give answer (4) if the data in both the Statements I and II are not sufficient to answer the question.
Give answer (5) if the data in the Statements I and II together are necessary to answer the question.
46. How many marbles does Sanjay have?
I. Sanjay has 3 times more marbles than Ahmed.
II: Ahmed has one third the number of marbles which Suresh has who has as many marbles as Sanjay.
47. How is Ramesh related to Lata?
I. Yogendra is Lata’s father.
II. The only sibling of Ramesh’s maternal aunt is married to Yogendra.
48. If ‘world peace is important' is written as ‘ni pe la so’ in a code language, what is the code for peace?
I. ‘an important call’ is written as ‘ka so ba’.
II. ‘this is world map’ is written as ‘de la ni ru ’
49. In which direction is Neha walking?
I. Neha walked 15 kms from the starting point and took a left turn.
II. She was walking towards north before taking a left turn.
50. What was the day of the week on fifteenth of the month?
I. The first Sunday of the month was sixth.
II. The last day of the month was thirty first.

 ANSWER KEY 1 d 11 d 21 B 31 e 41 b 2 d 12 d 22 e 32 e 42 b 3 e 13 c 23 c 33 b 43 a 4 c 14 e 24 e 34 d 44 a 5 d 15 b 25 b 35 a 45 a 6 e 16 e 26 c 36 d 46 d 7 d 17 b 27 e 37 e 47 e 8 e 18 a 28 d 38 d 48 e 9 e 19 c 29 e 39 d 49 e 10 d 20 e 30 c 40 b 50 a

EXERCISE:-II
1. Is ‘A’ is grandmother of ‘B’?
I) A’s mother’s only daughter’s grandson is ‘B’.
II) A’s wife ‘C’ is the mother of ‘D’
III) D’s son is ‘B’.

a) I alone is sufficient
(b) II alone is sufficient
c) III alone is sufficient
(d) Only III & Either I (or) II are sufficient
e) Both I & III together are sufficient
2. A, B, C, D, E, F and G each are different in height. Who is the shortest?
I) ‘D’ is taller than A but Shortest than ‘B’
II) II) ‘F’ is taller than ‘E” who is taller than ‘G’
III) ‘C’ is shortest than ‘A’ but taller than ‘G’

a) Both I & II together are sufficient
b) Both I & III together are sufficient
c) Both II & III together are sufficient
d) All I, II & III together are sufficient
e) None of these

Directions 3-6
Each problem contains a question and two statements I & II givens certain data. You have to select the correct answer from 1 to 5 depending on the sufficiency of data given in the statement to answer the question. Mark your answer as
1) If statement I alone is sufficient & Statement II alone is not sufficient to answer the question.
2) If statement II alone is sufficient & Statement I alone is not sufficient to answer the question.
3) If each statement alone is sufficient to answer the question
4) If both the statement I & II together are not sufficient to answer the question and additional data specific to the problem are needed
5) If statements I & II together are sufficient but neither statement alone is sufficient to answer the questions.
3. Five friends-A, B, C, D and E are having different ages, who among them is the oldest?
I) A is elder than ‘B’ who is elder than ‘E’
II) D is elder than ‘B” but younger than ‘C’
4. There are 25 people in a queue and ‘Vijay’ is one of them. What is the position of Vijay from the front of the queue?
I) Behind Ajay there are as many people as Vijay has ahead of him, and there is only one person in between them.
II) If two more people are added to the end of the queue, then Vijay is exactly in the middle. Each of the questions below consists of a question and 3 statements numbered I, II and III. You have to decide whether the data provided in the statement is/are sufficient to answer the questions
5. How is ‘P’ related to ‘K’?
I) K is the father of R
II) R is the only sibling of ‘S’
III) S is the daughter of P’s sister

1) Only I & II are sufficient
2) Only II & III are sufficient
3) Only I & III are sufficient
4) All I, II & III are sufficient
5) All the statement I, II & III together also are not sufficient
6. Among the 6 person P, Q, R, S, T and U, each have different heights. Who is the shortest?
Statements:

I) ‘P’ is taller than Q and R but not the tallest
II) Q is taller than S and T, T is not the shortest
III) R is taller than T

1) Only I & II are sufficient
2) Only II & III are sufficient
3) Only I & III are sufficient
4) I, II & III together are sufficient
5) All statement together are not sufficient
7. How many persons are there in a row?
I) A sits 10th from right
II) B sits 15th from the left end
III) 5 persons sits between A and B

1) Only I & II are sufficient
2) Only II & III are sufficient
3) Only I & III are sufficient
4) I, II & III together are sufficient
5) All statement together are not sufficient
8. Who is the heaviest among P, Q, R, S and T?
I) P is heavier than Q who is heavier than R
II) Q is heavier than S who is heavier than T
9. Who is mother of B?
I) B & E are daughters of D, who is the only sister of A
II) A is the brother-in-law of C whose wife is ‘D’
10. In which direction is city ‘B’ located with respect to city ‘E’?
I) City B is to the south of City C
II) City B is to the east of City D which is to the north of city ‘E’
III) City C is to the west of city A

1) Only I & II are sufficient
2) Only II & III are sufficient
3) only II is are sufficient
4) I, II & III together are sufficient
5) All three statement together are not sufficient
11. Among P, Q, R, S and T who is the 2nd shortest?
I) R is taller than S but shorter than T
II) T is shortest than P but taller than Q
III) Q is taller than S but shorter than R

1) Only I & II are sufficient
2) Only II & III are sufficient
3) Only I & III are sufficient
4) I, II & III together are sufficient
5) All statement together are not sufficient
12. B is the brother of A. how is A related to B?
I. A is the sister of C
II. E is the husband of A
13. How is D related to A?
I. B is the brother of A
II. B is D’s son
14. How is J related to P?
I. M is brother of P and T is sister of P
II. P’s mother is married to J’s husband who has one son and two daughters.
15. How is M related to N?
I. P, who has only two kids, M and N, is the mother-in-law of Q, who is sister –in-law of N.
II. R, the sister-in-law of M, is the daughter-in-law of S, who has only two kids, M and N
16. How is Tanya related to the man in the photograph?
I. Man in the Photograph is the only son of Tanya’s grandfather.
II. The man in the photograph has no brothers or sisters and his father is Tanya’s grandfather.
17. How is F related to P?
I. P has two sister M and N
II. F’s mother is sister of M’s father
18. How is X related to Y?
I. Y says, “I have only one brother”
II. X says, “I have only one sister”.
19. How is T related to K?
I) K has two sons; one of the son is A.
II. The mother of T has only two sons-A and B
20. How is X related to Y?
I. Y and Z are children of D who is wife of X.
II. R’s sister X is married to Y’s father.
21. Village R is in which direction with respect to Village D?
I. Village R is to the north of village T which is to the west of Village F.
II. Village D is to the west of village T.
22. Village K is towards which direction of the village N?
I. Village M is to the North of village N and to the east of village K
II. Village D is to the west of village N and to the south of village K.
23. In which direction is Rahul facing?
I. In the early morning Rahul was standing in front of a puppet and the shadow of puppet was falling to the right of Rahul.
II. In the early morning Rahul was standing on the ground. His shadow was falling behind him when he turned to his left.
24. What is the distance between villages X and Y by the shortest route?
I. Village X is to the north of village Z at a distance of 35 kms.
II. Village Y is to the west of village Z at a distance of 20 kms.
25. Which village is to the north-east of village A?
I. Village B is to the north of village A, village C and D are to the East and West of village B respectively
II. Village P is to the South of village A and village E is to the East of village P, village K is to the north of village P.
26. What is Sachin’s rank from the top in a class of 25 students?
I. Sachin ranks three ranks above Amit who ranks 18th from the bottom.
II. Sachin’s rank from the top is two ranks below Deepti who ranks 23rd from the bottom.
27. What is the rank of P from the bottom in a class of 30 students?
I. M is third from the top and there are five students between M and P.
II. The rank of K is fourth from the bottom and there are 17 students between K and P.
28. Gaurav ranks eighteenth from the top in a class. What is his rank from the last?
I. there are 47 students in the class.
II. Jatin who ranks 10th in the same class, ranks 38th from the last.
29. How many children are there between P and Q in a row of children?
I. P is fifteenth from the left in the row
II. Q is exactly in the middle and there are ten children towards his right.
30. What is Sumit’s position from the right end in a row of children?
I. There are 10 children between Sumit and Rajan
II. Rajan is twentieth from the left end of the row of children.
31. Total money with Naresh and Ajay is 28 percent of what with Usman. How much money is Ajay having?
I. Usman has got Rs. 75000
II. The ratio of money of Naresh to money held by Ajay is 1:3.
32. In which year was Rahul born?
I. Rahul at present is 25 years younger to his mother.
II. Rahul’s brother, who was born in 1964, is 35 years younger to his mother
33. How many students in a class play football?
I. Only boys play football
II. There are forty boys and thirty girls in the class
34. Can Ritesh retire from office X in January 2006, with full pension benefits?
I. Ritesh will complete 30 years of service in office X in April 2000 and desires to retire.
II. As per office X rules, an employee has to complete minimum 30 years of service and attain age of 60. Ritesh has 3 years to complete age of 60
35. What time did the train leave today?
I. the train normally leaves on time
II. The scheduled departure is at 14:30.

 ANSWER KEY 1 b 11 4 21 e 31 e 2 d 12 c 22 c 32 e 3 4 13 d 23 c 33 d 4 2 14 b 24 e 34 e 5 5 15 a 25 a 35 d 6 4 16 c 26 c 7 5 17 e 27 c 8 5 18 d 28 c 9 1 19 e 29 e 10 3 20 c 30 d
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