*Thursday, October 15th, 2020*

Nowadays, everything revolves around data, all major decisions are made by first collecting the mass information and then analyzing the raw data. Whether it may be a small firm, a giant MNC or governments all rely on the inferences made on this massive data. Thus, we cannot undermine the resourcefulness and significance of data. But mere collecting data is not sufficient. You have to consider that while collecting the data all the relevant information required to make inferences is covered otherwise the whole exercise of collecting and interpretation of the data proves to be a futile activity. That’s what Data Sufficiency questions are in the competitive exam. Data Sufficiency is part of reasoning section in various competitive exams such as Bank PO’s, CAT and other leading MBA entrance exams. Data sufficiency problems don’t involve difficult concepts or formulas, it just tests your reasoning and analytical skills combined with basic mathematics. In Data Sufficiency problems you have to decide whether the given data is sufficient to answer the questions or not. The format of the question in the exam is as follows:

**There would be two statements given in questions labeled (1) and (2) and you have to decide if these statements are sufficient to conclusively answer the question. The following questions are**

**If statement (1) alone is sufficient to answer the question but the statement (2) alone is not sufficient to answer the question.****If statement (2) alone is sufficient to answer the question but the statement (1) alone is not sufficient to answer the question.****If you can get the answer from (1) and (2) together although neither statement by itself****If statement (1) alone is sufficient and statement (2) alone is sufficient.****If you cannot get the answer from statements (1) and (2) together but still more data are needed.**

The questions can be categorized into following types

- Relationships
- Dates
- Comparison
- Critical Analysis
- Age
- Miscellaneous

Now I will tell you the general approach to follow in each of the above categories and then I will discuss them one by one. When you are attempting a question of data sufficiency you should follow a systematic approach as laid down below. This one is systematic approach and will save your time.

This is a general trend and method that you have to follow in solving data sufficiency problem. Now let’s discuss category-wise variation and example of each of them.

**Relationship**

The conventional questions are of the following type. Consider,

**Example 1: **How is A related to B?

- B is the father of A.
- D is the brother of A.

Now before hopping for the conclusion, I’ll point out a mistake that students tend to make in such questions is that **they conclude about the relationship without knowing the sex of the person involved.**

Now let’s check out the statement (1) says that B is the father of A. Is it enough to conclude how A is related to B? Now A can either be B’s son or daughter. So, to establish a relationship of A to B we need to learn whether A is male or female or indirect terms:

- A is the brother/sister of X.
- A is the father/mother of X.
- A is an uncle/aunt of X.

Now using the suggested method above we can notice that the statement (1) is not sufficient to answer the question. Similarly, statement (2) cannot bring us to any conclusion about the relationship of A and B. Thus, the answer is **we cannot get the answer from statements (1) and (2) together but still more data are needed.**

**Dates**

In this category, the questions asked are

- On which day of the week did X reach z city?
- What is the date of birth of X?

Note that a day or date can only be known if,

- The ‘day’ or ‘date’ of some earlier incident is mentioned,
- The number of days between that incident and the required day is given.

Consider this example now,

**Example 2: “**On which day of the week did Rahul reached Delhi?”

**Statement (1)** Rahul’s brother reached Delhi a day before than Rahul.

**Statement (2) **Rahul’s father reached Delhi on Thursday which was two days later than the arrival of his brother.

**Sol****: **As you can notice that the Statement (1) provides us the information between the no. of days between an earlier incident and the required day. Now we need to know the day when Rahul’s brother reached Delhi. And for this, we turn to statement (2), thus, we know the answer can’t be A or D as the statement (1) is not sufficient to answer the question alone. Now, statement (2) says Rahul’s mother reached Delhi on Thursday i.e. two days later after his brother thus Rahul’s brother reached Delhi on Tuesday and therefore from both the statement we can infer that Rahul reached Delhi on Wednesday. Hence, **C is the correct answer** i.e. both statements are required altogether to make a conclusion.

**Comparison**

As the name recommends, the questions require comparison and then puts up questions such as “Who’s the tallest or heaviest among X, Y, and Z?” or “Who’s sitting the left of A when A, B, and C are sitting together?” In all these questions you need to write the names of person in ascending or descending order of heights, weights or their sitting arrangement from left to right.

To solve such question the best method to employ is in the use of inequalities to write the statements and then see if the two can be combined to form into single inequality to get the answer. Let’s do an example to understand how it’s done.

**Example 3: **Among four friends K, L, M, and N, who’s the heaviest?

**Statement (1) **L is heavier than K but lighter than N.

**Statement (2) **M is lighter than L

**Sol: **To find out the answer to the above question we will form an inequality and using the information given in the statement (1) we get,

**K < L < N**

And, using the second statement we get,

**M < L**

Combining the inequalities, we get,

**K < M < L < N, or M < K < L <N**

Thus, in the either of the two N is the heaviest. Hence, the answer is C as we needed both the two statements to derive the answer to the question.

**Critical Analysis**

This category includes questions that are qualitative in nature, that involves the application of value-judgment in order to reach a conclusion. To tackle these types of problems you need to revise your general background of argumentation techniques, an assumption of arguments and inference making. There’s no general and direct method to solve such problems, but they aren’t very difficult to approach. Let’s try an example that will give you a rough idea of the thinking and approach required to cope up with them.

**Example 4:** Many Indian experts think that India has a very meager oil reserve. Is that correct?

**Statement (1): **India imports about 1.5 crore tons of crude oil every year.

**Statement (2): **When foreign countries were recently invited to participate in exploration and production activity in India, nearly 67 companies took up the offer.

**Sol: **First let’s ponder and deduce about the statement (1). Note that statement (1) does not imply that importing tons of crude oil mean India has low oil reserve. High Imports can be due to the huge consumption or small production. And when we move on to the statement (2), It also doesn’t directly suggest that 67 companies did not take up the offer because of the low reserves. They might be willing to do so because of favorable of socio, political and economic incentives. Hence, both the statements neither individually or jointly derive us to an accurate conclusion. Thus, the answer is E.

**Age**

Again, as the name suggests, this kind has two statements and then a question that demands you to find out the age of the person. Note that the real question is not to actually find the age but to tell whether the statements are sufficient to calculate the age of the desired person. Usually, one information or one statement provides one equation i.e. **one information = one equation**.

And, one person’s name implies one unknown i.e. **one person** = **One unknown**

** **The approach you need to follow in these questions is that if no. of equations is equal to the no. of unknowns then the data is sufficient otherwise not.

**Example 5: **Is my son 12 years old?

**Statement (1): **Four years later, he will be 20 years younger than me

**Statement (2)**: Now I am 20 years older than him.

**Sol: **This is a deceptive problem. Observe that there are two unknowns here Father and son and what about the no. of equations? The information is only about one i.e. the father. Both the statements tell about the father only, though the language is bit tricky and thus, there’s 1 info and two unknowns. Hence, the answer is E.

Now I have covered all the major categories of problems that might come in exam. But there are some other kinds of problems that can also be part of Data Sufficiency problems and they fall in miscellaneous. One of the examples is Syllogism another can be based on basic algebraic problems5/. They can also form Data Sufficiency problems. The language in these questions can be tricky and confusing and at times deciding whether the data is sufficient or not. You will get more understanding once you will get used to the problems and that will only happen if you practice a good number of question on Data Sufficiency.

You can also see CAT Concepts – Introduction to Data Sufficiency

How to prepare for LRDI (Logical Reasoning and Data Interpretation) for the CAT Exam?

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