quantitative aptitude, maths applicable to Common Aptitude Test (CAT) Bank Competitive Exam UPSC Competitive Exams SSC Competitive Exams Defence Competitive Exams L.I.C/ G. I.C Competitive Exams Railway Competitive Exam University Grants Commission (UGC) Career Aptitude Test (IT Companies) and etc.

1. DATA SUFFICIENCY

2. • You should note that data sufficiency questions are
not new topics in themselves . All you have to do is to
analyze the given data and see if you can get the
answer to the question using the given data .
• While attempting the questions you must follow a
systematic approach as laid down below. This will
save your time .

3. INTRODICTION
 But there is no guarantee that the directions should
be given like that only. Some times, the directions
can be given to choose the answer among four
options.
 Now let us understand such set of directions.

4. DIRECTIONS
Choose (1) OR (a):
If the question can be
answered by one of
the statements alone
but not by the other.

5. For example :
Ques : Is X the brother of Y ?
1. X is the daughter of Z
2. Y is the daughter of Z
From the first statement we can see that X cannot be
the brother ( male ) because she is infact the daughter
( female )

6. Choose(2)or (b) :
If the question can be
answered by using
either of the
statements alone.

7. For example :
Ques : On what date is Anju’s Birthday ?
1. Anju’s birthday comes on in a leap year .
2. Anju’s Birthday is the same as that of Morarji Desai ?
We can get the answer from 1st statement as (29 February )
comes in a leap year. And from 2nd statement alone we can
get the answer .

8. Choose (3)or (c):
If the question can be
answered by using
both the statements
together, but cannot
be answered by using
either statement alone.

9. For example :
Ques :Is Shyam the brother of Mohan ?
1. Mohan is the son of Ram.
2. Shyam is the son of Ram.
Both the statement together gives the answer . One
alone cannot give the answer.

10. Choose (4) or (d):
If the question cannot
be answered even by
using both the
statements together.

11. For example :
Ques : Among Three friends A,B , & C who is the shortest ?
1. A is taller than B
2. A is taller than C
From both the statement we cannot find out who is the
shortest . This could be either B or C and we will need a
comparison between the heights of B & C which is not
given .

12. Formula for Solving
Number of variable = Number of equations

13. SOME TYPICAL CASES

14. RELATIONSHIPS
The wording goes like this
“HOW IS X RELATED TO Y”
In these questions one very prominent source of
confusion is the fact that students tend to conclude
about the relationship without knowing about the sex of
the person involved .

15. For example :
Ques : How is P related to Q ?
1. Q is the father of P
2. S is the brother of P
We see that statement 1 says that Q is the father of P.Is it
not enough to conclude how P is related to Q?
No P may be son or the daughter of Q.Hence , to establish
exactly how P is related to Q, we must know the sex of
P.

16. DATES
Another very typical questions is asked on DATES .
The wording of the question goes like this :
“ON WHICH DAY OF THE WEEK X REACHED
AGRA” OR “WHAT IS THE DATE OF BIRTH OF X”
In such questions you have to determine “a day” or
“a date “

17. A day or a date can exactly be established if and only if:
A – The ‘day’ or the ‘date’ of some earlier incident is
mentioned and
B – The number of days between that incident and the
required day is given.
If any of the above information is not given ,data will
be insufficient .If both are given data will be sufficient

18. For example :
Ques : On which day of the week did Atul reach
Bombay ?
1. Atul’s brother reached Bombay one day earlier
than Atul.
2. Atul’s mother reached Bombay on Thursday which
was two days later than the arrival of his brother

19. Ques : What is the Date of birth of Ratna ?
1. Vani remembers that Ratna’s date of birth is
between 17th June and 21ST June .
2. Sapna says that Ratna’s date of birth is after 19th
June but before 23rd June .

20. COMPARISONS
The wordings on the question is :
“Who is the tallest amongst X,Y and Z or “Who is the
heaviest among A,B,C and D” or “Who is sitting to
the left of A when A , B and C are sitting together”

21. In all these questions you have to write the names of
various persons in ascending and descending order
order of heights or write their setting arrangement
(from left to right or viceversa ) In other words you
have to make ‘comparisons 'of the respective places of
some persons in a fixed pattern .

22. For example :
Among four friends A,B ,C and D who is the heaviest ?
1. B is heavier than A , but lighter than D
2. C is lighter than B

23. CRITICAL ANALYSIS
 Sometimes the questions are asked are qualitative in
nature where you have to apply your value – judgment in
order to reach a conclusion .
 To tackle these type of problems you should revise
your general background of argumentation techniques,
assumptions of arguments and inference making .
 No general method can be delineated to tackle these
problems but this does not mean that these are very
difficult questions

24. For example :
Ques : Many Indian experts think that India has very
meagre oil reserve . Is that correct ?
1. India Imports about 1.5 crore tonnes of crude every
year.
2. When foreign companies were recently invited to
participate in oil exploration and production activity in
india , nearly 67 companies took up the offer.

25. Ques : Is running good for Health ?
1. Running with proper limits in an open area is good
for heart and lungs.
2. Knee , ankle , and foot-bone problems are not
uncommon as a result of protracted running .

26. Ques : Should I invite him to my wedding anniversary?
1. This is my first wedding anniversary
2. He is the only person who has helped me in bad
days.

27. AGE
Problems are concerned with age .Some data are given
and the questions generally asks you to find a
particular person’s age.
Emphasize that the questions does not ask you to
actually calculate the age of the person/

28. Formula for this :
Number of unknowns = Number of equation

29. For example
Ques : Is my son 12 year old ?
1. Four year later he will be twenty years younger
than me .
2. Now I am twenty years older than him .
Number of Unknowns = 2 ( He & me or I & him)
Number of equations = 1

30. Ques : What is the age of Shubham ?
1. Shubham is 12 years older than Shyam .
2. Four years later , Shyam will be twelve years
younger than Shubham .
Number of unknowns = 2
Number of information = 1 .

31. Ques : What is the Age of Shubham.
1. Richa is 10 years younger than Shubham.
2. 9 years later Richa’s age will be more than half of
Shubham’s
Number of Unknowns = 2
Mo of Information = 1
The word ‘MORE THAN’ is not definite .
If we replace ‘MORE THAN’ with ‘EQUAL TO’. In that case
The answer will be B. The data will be sufficient.

32. Question 1
:In which year was Rahul born ?
Statements:
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.
Answer: Option C
Explanation:
From both I and II, we find that Rahul is (35 - 25) = 10 years older
than his brother, who was born in 1964. So, Rahul was born in 1954.

33. Question:2
What will be the total weight of 10 poles, each of the same weight ?
Statements:
I.One-fourth of the weight of each pole is 5 kg.
II.The total weight of three poles is 20 kilograms more than the total
weight of two poles
Answer: Option b
Explanation:
From I, we conclude that weight of each pole = (4x5) kg = 20 kg.
So, total weight of 10 poles = (20 x 10) kg = 200 kg.
From II, we conclude that:
Weight of each pole = (weight of 3 poles) - (weight of 2 poles) = 20 kg.
So, total weight of 10 pojes = (20 x 10) kg = 200 kg

34. Question:3
How many children does M have ?
Statements:
I.H is the only daughter of X who is wife of M.
II.K and J are brothers of M.
Answer: Option D
Explanation:
From I, we conclude that H is the only daughter of M.
But this does not indicate that M has no son. The
information given in II is immaterial

35. Question:4
How much was the total sale of the company ?
Statements:
I.The company sold 8000 units of product A each costing Rs. 25.
II.This company has no other product line.
Answer: Option C
Explanation:
From I, total sale of product A = Rs. (8000 x 25) = Rs. 200000.
From II, we know that the company deals only in product A.
This implies that sale of product A is the total sale of the company, which is Rs.
200000.

36. Question:5
The last Sunday of March, 2006 fell on which date ?
Statements:
I.The first Sunday of that month fell on 5th.
II.The last day of that month was Friday.
Answer: Option C
Explanation:
From I, we conclude that 5th, 12th, 19th and 26th of March,
2006 were Sundays.
So, the last Sunday fell on 26th.
From II, we conclude that 31st March, 2006 was Friday. Thus, 26th March,
2006 was the last Sunday of the month

37. Question: 6
What is the code for 'sky' in the code language ?
Statements:
I.In the code language, 'sky is clear' is written as 'de ra fa'.
II.In the same code language, 'make it clear' is written as
'de ga jo
Answer: Option D
Explanation:
The only word common to I and II is 'clear' and as such,
only the code for 'clear' can be ascertained from the given
information

38. Question:7.
How many children are there between P and Q in a row of
children ?
Statements:
P is fifteenth from the left in the row.
Q is exactly in the middle and there are ten children towards
his right.
Answer: Option C
Explanation:
From II, Q being in the middle, there are 10 children to his right as well as
to his left. So, Q is 11th from the left. From I, P is 15th from the left.
Thus, from both I and II, we conclude that there are 3 children between P
and Q.

39. Question:8
How is T related to K?
Statements:
R's sister J has married Ts brother L, who is the only son of
hisparents.
K is the only daughter of L and J.
Answer: Option C
Explanation:
From I, we know that L is T's brother and J's husband. Since L is
the only son of his parents, T is L's sister.
From II, we know that K is L's daughter.
Thus, from I and II, we conclude that T is the sister of K's father i.e.
T is K's aunt.

40. Question:9
How is J related to P ?
Statements:
M is brother of P and T is sister of P.
P's mother is married to J's husband who has one son
and two daughters.
Answer: Option A
Explanation:
From II, we know that P's mother is married to J's
husband, which means that J is P's mother

41. Question: 10
How is X related to Y ?
Statements:
Y and Z are children of D who is wife of X.
R's sister X is married to Ys father.
Answer: Option B
Explanation:
From I, we conclude that Y is the child of D who is wife of X
i.e. X is Y's father.
From II, X is married to Y's father. This implies that X is
Y's mother.

42. Questions.11
How many ewes (female sheep) in a flock of 50 sheep
are black?
Statements:
I. There are 10 rams (male sheep) in the flock.
II.Forty percent of the animals are black
Answer :D

43. Question: 12
On which date of the month was Anjali born in February
2004 ?
Statements:
I.Anjali was born on an even date of the month.
II.Anjali's birth date was a prime number
Answer: Option C
Explanation:
From I and II, we conclude that Anjali was born in February 2004 on
a date which is an even prime number. Since the only even prime
number is 2, so Anjali was born on 2nd February, 2004.

44. Question:13
How is X related to Y?
Statements:
I.Y says, "I have only one brother".
II.X says, "I have only one sister“
Answer: Option D
Explanation:
The statements in I and II do not provide any clue
regarding relation between X and Y.

45. Question:14
How is F related to P?
Statements:
P has two sisters M and N.
F's mother is sister of M's father.
Answer: Option C
Explanation:
From I and II, we conclude that P is M's brother and so
M's father is P's father. So, F is the child of the sister of
P's father i.e. F's mother is P's aunt or F is P's cousin.

46. Question: 15
B is the brother of A. How is A related to B ?
Statements:
I.A is the sister of C.
II.E is the husband of A.
Answer: Option A
Explanation:
B is A's brother means A is either brother or sister of B.
Now, each one of I and II individually indicates that A
is a female, which means that A is B's sister.

47. Question 16 :
Will Tendulkar hit a century ?
Statement:
I.Tenduldar is the best bastman in the world.
II. The pitch is suitable for stokeplay
Answer : D
The statement does not provide solid resons why it should
be believed that Tendulkar Will hit a century today. Even
a best batsman can fail on even most suitable pitches.

48. Question :17
Has Democracy suffered after the recent poll ?
Statement :
I. Poll Violence are not good things.
II. India’s image as a vibrant democracy has taken a
beating.
Answer : D

49. Question :18
Does smoking lead to ill health ?
Statement:
I. According to the survey ,out of 1000 people are
suffering from lung cancer,876 are smokers.
II. Cancer is a sign of ill health
Answer : D

50. Question : 19
What is the colour of your eyes ?
Statement :
I. The colour of his eyes is the same as the colour of
my shirt.
II. I am not wearing a blue shirt.
Answer : D

51. Question :20
Did the murder accur on the 14th ?
Statement :
I. The murderer was caught on 18th
II. The police took four days to detech who the
murder was ?
Answer : D

52. Question :21
Is India a developing country ?
Statement :
I. The percapita income of india has been increasing
II. Inspite of large population , very few Indians die of
hunger.
Answer : D

53. Question: 22
How is 'No' coded in the code language ?
Statements:
I.'Ne Pa Sic Lo' means 'But No None And' and 'Pa Lo Le Ne' means 'If None And
But'.
II.'Le Se Ne Sic' means 'If No None Will' and 'Le Pi Se Be' means 'Not None If All'.
Answer: Option A
Explanation:
In the two statements given in I, the common words are 'But', 'None',
'And' and thecommon code words are 'Ne', 'Pa', ,'Lo'. So, 'Ne', 'Pa' and 'Lo' are
codes for 'But', 'None' and 'And'. Thus, in the first statement, 'Sic' is the code for
'No'.

54. Question: 23
Who among P, Q, T, V and M is exactly in the middle when they are
arranged in ascending order of their heights ?
Statements:
I.V is taller than Q but shorter than M.
II.T is taller than Q and M but shorter than P.
Answer: Option d
Explanation:
From I, we have: M > V > Q.
From II, we have: T > Q, T > M, P > T.
Combining the above two, we have: P>T>M>V>Q i.e. Q<v<m<t<p.<
p=""></v<m<t<p.<>
Clearly, M is in the middle.

55. Question: 24Which code word stands for 'good' in the coded
sentence 'sin co bye' which means 'He is good' ?
Statements:
I.In the same code language, 'co mot det' means 'They are good'.
II.In the same code language, 'sin mic bye' means 'He is honest'.
Answer: Option b
Explanation:
In the given statement and I, the common word is 'good' and the
common code word is 'co'. So, 'co' is the code for 'good'.
In the given statement and II, the common words are 'He' and
'is' and the common code words are 'sin' and 'bye'. So 'sin' and
'bye' are the codes for 'He' and 'is'. Thus, in the given
statement, 'co' is the code for 'good'.

56. Question:25
What is the numerical code for 'water' in a certain code ?
Statements:
The code for 'give me water' is '719'.
The code for 'you can bring water for me' is written as
'574186'.
Answer: Option D
Explanation:
In I and II, the common words are 'me' and 'water' and the
common code numbers are '7' and '1'. So, the code for
'water' is either '7' or '1'.

57. Question: 26
How many visitors saw the exhibition yesterday ?
Statements:
I.Each entry pass holder can take up to three persons with
him/her.
II.In all, 243 passes were sold yesterday.
Answer: Option D
Explanation:
From I and II, we find that maximum (243 x 3) i.e. 729
visitors saw the exhibition.
But the exact number cannot be determined.

58. Questions: 27 What is the area of rectangle PQRS?
Statement :
1.Its diagonal is 13 feet
2. PS = 5 feet

59. Questions: 28. If a car salesman earns a commission
of 5% on each vehicle he sells, how much did he earn
in total during the month of May?
Statement
1.The car salesman sold 15 cars during the month of
May.
2. The average sale price on vehicles sold in May was
$10,000

60. Questions:29 One hundred grade 12 chemistry
students took a final exam. Was the average score
higher than 60%?
Statement:
1) Over 50% of the people who wrote the test scored at
least 65%.
2)22% of the class scored 80%, while 25% scored
below 50%.

61. Questions :30If x is squared, is the resultant value
greater than 60?
Statement
1) x is a negative integer.
2) x + 60 is less than 60

62. Questions :31 A shopkeeper sells some articles at the
profit of 25% on the original price. What is the exact
amount of profit? To find the answer, which of the
following information given in Statements I and II
is/are necessary?
Statement:
I. Sale price of the article
II. Number of articles sold

63. Questions: 32 What is the percent profit earned by
the shopkeeper on selling the articles in his shop?
Statement:
I.Labeled price of the articles sold was 130% of the cost
price.
II.Cost price of each article was Rs. 550.

64. Questions :33Two towns are connected by railway.
Can you find the distance between them?
Statement :
I. The speed of the mail train is 12 km/hr more than
that of an express train.
II. A mail train takes 40 minutes less than an express
train to cover the distance.

65. Questions :How much time did X take to reach the
destination?
Statement:
I. The ratio between the speed of X and Y is 3 : 4.
II. Y takes 36 minutes to reach the same destination