Introduction: Data Sufficiency | Logical Reasoning (LR) and Data Interpretation (DI) - CAT PDF Download

Data Sufficiency questions on the CAT exam add a unique twist to the usual problem-solving challenges. These questions not only test your knowledge but also your ability to judge whether the information provided is adequate to solve a given problem. In other words, they assess your logical reasoning and critical thinking skills.

What is Data Sufficiency

In Data Sufficiency, you need to figure out whether or not the data given in the question / statements is good enough to find out a unique answer.
Is the data enough to find out a unique answer?

Please note that in Data Sufficiency:

• You do not need to find out the answer
• You need to find out whether or not you can find out the answer
  

A Data Sufficiency question set will contain the following:
• Instructions – they may vary set per set
• Questions (with or without data)
• Two statements (with data – may or may not be sufficient)

Data Sufficiency questions always have two statements and these four options in CAT:
(A) Both statements together are sufficient to answer the question
(B) Only one of the statements alone is sufficient to answer the question but not the other.
(C) Each of the statements alone can answer the question
(D) Both the statements together are not sufficient to answer the question.

Example:
(Please note that the example is way too simple to be asked in an exam like CAT, but is necessary for understanding the idea.)

What is the value of ‘x’?
Statement A: x < 10
Statement B: x > 8
By combining both statements, I can say that x lies between 8 and 10. The only integer between 8 and 10 is 9. So my answer should be Option 3
WRONG!
Nowhere in the question it is mentioned that x is an integer / natural number. Until and unless that is specified, we cannot uniquely determine the value of ‘x’. It can take any value from 8 to 10 {eg: 8.1, 8,2, 9.999, etc.}
So, the correct answer would be Option 4

Approaching Data Sufficiency Questions

• When tackling Data Sufficiency questions, it's important to keep in mind that the objective is to decide if the information given in the statements is enough or not. The goal isn't to solve the problem entirely, but rather to pinpoint what information is lacking.
• To start, carefully read the question and statements, and identify the information needed to answer the question. Predict what details might be present in each statement. Then, assess each statement independently to determine if it furnishes sufficient information. Lastly, assess both statements together to ascertain if the combined information is enough to answer the question.
• Keep in mind that Data Sufficiency questions are crafted to be tricky, so refrain from making assumptions or hasty conclusions. Rely on logical reasoning and critical thinking to assess the provided information and figure out what additional details are required to answer the question.
  

How to Solve Data Sufficiency Questions

1. Understand the Question Statement

• Before moving on to the answer choices, it's crucial to carefully read and comprehend the question stem when dealing with Data Sufficiency questions in the CAT Exam. These questions aim to evaluate your skill in deciding whether the provided data is enough to solve the question.
• An effective strategy for tackling these questions involves planning before diving into the solution.
• Break down the question into smaller components and strive to grasp the essence of what is being inquired.

2. Use the process of elimination

• If required, you can randomly select an answer from the remaining ones after eliminating some options. Eliminating a couple of options greatly increases the probability of getting the answer right. 
• Let’s consider an example:
  Question: How old will Jagan be on Jan 1st 2015?
  Statement 1: Jagan is two years younger than Lokesh and both their ages are prime numbers on Jan 1st 2013.
  Statement 2: Jagan’s age was a prime number on Jan 1st 2011.
  A) Both statements together are sufficient to answer the question
  B) Only one of the statements alone is sufficient to answer the question but not the other.
  C) Each of the statements alone can answer the question
  D) Both the statements together are not sufficient to answer the question.
  
  The question can’t be answered by using only one of the two Statements given. We can thus eliminate (B) and (C) even before doing the rest of the calculations, we can conclude the answer is either (A) or (D).
  Using both the statements together, if Jagan is aged x in 2013, we can conclude that x-2, x and x+2 are prime.
  This is true only for the set {3, 5, 7}.
  So, x is 5 and Jagan will be aged 7 on Jan 1st 2015.

3. Don’t assume things that aren’t mentioned.

• Candidates frequently make the mistake of assuming that all numbers are positive or incorrectly assuming that a chord represents the diameter of a circle. Such assumptions can result in incorrect answers, and these errors come with a twofold consequence for the student's performance. 
• Firstly, wrong answers lead to negative marks. 
• Secondly, valuable time is squandered on erroneous calculations.

Types of Data Sufficiency

As of now we know what consists of the questions related to the Data Sufficiency reasoning section. Let us see the various types of Data Sufficiency one by one from below. 

1. Blood Relation 
In this type of data sufficiency, relation between 2 people will be asked and candidates need to find the statement(s) in which data is sufficient to find the relation or the correct answer. 

2. Order & Ranking 
In this type of data sufficiency, data on order of people or their ranking will be provided and candidates will need to find statement(s) in which data is sufficient to find the correct answer.

3. Direction & Distance 
In this type of data sufficiency, data on direction of people or points and the distance traveled by a person or distance between the points will be given and candidates will need to find the statement(s) in which data is sufficient to find the direction or distance between the points. 

4. Coding Decoding 
In this type of data sufficiency, words or letters will be coded and candidates will need to find the statement(s) in which data is sufficient to find the logic applied to decide the code. 

5. Seating Arrangement
In this type of data sufficiency, data on arrangement of people will be provided and candidates will need to find the statement(s) in which data is sufficient to find the correct answer. Seating Arrangements are of two types such as Linear Arrangement and Circular Arrangement. In Linear Arrangement, people will be arranged or seated in one or multiple rows. In Circular Arrangement, people will be arranged or seated around a circular table. 

6. Floor Puzzle 
In this type of data sufficiency, data on people living on different floors of either same or different buildings will be given and candidates will need to find the statement(s) in which data is sufficient to find the correct answer. 

7. Scheduling 
In this type of data sufficiency, data based on months, years or date will be given and candidates need to decide whether the data provided in the statements is sufficient or not.

Solved Examples

Q1: What is the value of X*Y?

Statement 1: HCF of X and Y is 3
Statement 2: LCM of X and Y is 36
(A) The question can be answered using one of the statements alone and not by using the other statement
(B) The question can be answered using either of the statements alone.
(C) The question can't be answered by either of the statements alone, but can be answered by using both
(D) The question can't be answered by using both the statements together.
Ans: (C)
Sol: 

Using either of the two statements alone, we can't calculate the value of X*Y.
Using both the statements together, we can conclude that the product of two numbers equals the product of its HCF and LCM = 108

Q2: Priya went to a candy shop to buy some caramel pops, toffee bites and mango pops. What is the total price of one caramel pop, one mango pop and one toffee bite?

Statement 1: The cost of three caramel pops, five toffee bites and seven mango pops is Rs 68
Statement 2: The cost of two caramel pops, three toffee bites and four mango pops is Rs 41
(A) The question can be answered using one of the statements alone and not by using the other statement
(B) The question can be answered using either of the statements alone.
(C) The question can't be answered by either of the statements alone, but can be answered by using both
(D) The question can't be answered by using both the statements together.

Ans: (C)
Sol:

Let the cost of caramel, toffee and mango be x, y and z.
Using Statement 1: 3x+5y+7z=68.
Using Statement 2: 2x+3y+4z=41.
We cannot determine an answer from either of the two statements alone.
Using both statements and multiplying the second equation by 2 and subtracting the first equation from it, we get
(4x+6y+8z)-(3x+5y+7z)=2*41-68=14.
or x+y+z=14
So, we can answer the question using both Statements together, but not by using any of the two statements individually.

Q3: What is Glory's age ?

I. Glory, Vijay and Katie are all of the similar age.
II. Total age of Vijay, Katie and Arica is 32 and Arica is as old as Vijay and Katie together.
(A) If the data in Statement I is alone sufficient to answer the question
(B) If the data in Statement II is alone sufficient to answer the question
(C) If the data in Statement I or Statement II alone is sufficient to answer the question
(D) If the data in both the statements together is needed
Ans: (D)
Sol: 
As given in statements I and II, we have Glory = Vijay = Katie, Vijay + Katie + Arica = 32 and Arica = Vijay + Katie.
Putting Vijay + Katie = Arica in second. we get 2Arica = 32 or Arica = 16.
Thus, Vijay + Katie = 16 and Vijay = Katie. So, Vijay = Katie = 8. Thus, Glory = 8. Hence, both the statements are needed.

Q4: In a certain code language, ‘23’ means ‘No More and ‘79’ means ‘harmful thing’. What is the meaning of ‘9’ and ‘7’ respectively in that code?

I. ‘274’ means ‘no bad thing’
II. ‘839’ means ‘more is harmful’.

(A) If the data in Statement I is alone sufficient to answer the question
(B) If the data in Statement II is alone sufficient to answer the question
(C) If the data in Statement I or Statement II alone is sufficient to answer the question
(D) If the data in both the statements together is needed
Ans: (B)
Sol: 
‘79’ means ‘harmful thing’ and ‘274’ means ‘no bad thing’. Hence common letter ‘7’ denotes ‘thing’. Hence ‘9’ is obviously ‘harmful’. So I alone can be sufficient. Also, ‘79’ is ‘harmful thing’ and ‘839’ is ‘more is harmful’ from which it can be implied that ‘9’ is ‘harmful’. Hence II alone can also be sufficient. Hence either I or II alone can be sufficient.

Q5: Zuber, Krishna and Amrish will distribute their profit in what proportion?

I. Zuber gets 2/5th of the profit.

II. 75% of the total investment is made by Krishna and Amrish.
(A) If the data in Statement I is alone sufficient to answer the question
(B) If the data in Statement II is alone sufficient to answer the question
(C) If the data in Statement I or Statement II alone is sufficient to answer the question
(D) If the data in both the statements together is needed
Ans: (D)
Sol: 
Even both the statements together are not sufficient to answer the question because we don’t have total profit or amount invested information.

Q6: In an innings of a T20 international match six batsman, Raina, Yuvraj, Kohli, Dhoni, Rahane and Dhawan have scored different number of runs. How many batsmen have scored more runs than Dhoni?
(I) Rahane has scored 7 runs less than Yuvraj and 10 runs more than Raina.
(II) Kohli has scored 56 runs, which is 8 runs less than Dhoni.
(III) Raina has scored 34, which is 1 run less than Dhawan.
Sol: If we analyze the given statements then we get,
(a) Raina has scored 34, which is 1 run less than Dhawan, which means Dhawan has scored 35.
(b) Kohli has scored 56 runs, which is 8 runs less than Dhoni, which means the score of Dhoni is 64.
(c) Rahane has scored 7 runs less than Yuvraj and 10 runs more than Raina, which means Rahane scored 10+34 = 44 and Yuvraj scored 44+7 = 51.
As we can see, no one has scored more than Dhoni and all the statements were required to get the final answer. 

Q7: If City A and City E are in a straight line and the distance between A and C is the equal in distance between F and E then find out City A is in which direction with respect to City E.
(I) A is the north of F, which is to the west of C
(II) A is to the north west of C
(III) E is to the north west of F
Sol: If we draw all the directions mentioned in the statements we can say very easily that Only the statement I and III are sufficient to get the final answer. 

Q8: In a certain code, “14” means “stop whispering” and “68” means “its irritating”. What do 8 and 6 mean respectively in that code?
(I) 167 means “stop irritating me”
(II) 4982 means “it’s sound like whispering”
Sol:
Given:
14 = stop whispering
68 = its irritating
Now in statement 1, 167 “stop irritating me”, where 1 is stop, 6 is “irritating”, so 6 means “irritating” and 8 means “it’s” we can easily find the final answer from statement I.
Now in statement 2, 4982 means “it’s sound like whispering” so 4 means “whispering”, and 8 means “it’s” so we can say that 6 means “irritating” and 8 means “it’s”. We can also very easily final the final answer from Statement II.
Therefore, both Statement I and II are sufficient. 

Q9: How is Vivaan related to Yeshna?
(I) Vivaan is the only son of Yeshna’s mother-in-law
(II) Neelam is Vivian’s only sister.
Sol: From statement I, we find that Vivaan is Yeshna’s husband, while from statement II, we don’t get any required detail. So, Statement I alone is sufficient to answer the question. 

Q10: Who is R’s partner is a game of cards involving platers P, Q, R and S?
(I) P is sitting opposite to S
(II) Q is sitting right of P and left of S
Sol: It is clear from both of the given statements that P is sitting opposite to S or P is the partner of S.