# Data Sufficiency

## Introduction

In this blog, we will discuss Data Sufficiency and how to use it in various logical problems. Let’s understand the definition of Data Sufficiency?

## Data Sufficiency

In Data Sufficiency, we are interested in analyzing the given data and figure out if the provided information is enough to solve the problem or not.

So let’s say we have given a question and 2 statements providing certain information, and there will be some answer options.

Now we have to analyze those statements and figure out if the statements are sufficient to solve the problem. We are not required to do the calculation, we just have to check whether, with the help of given data, we can find the answer or not.

**Examples**

Let’s understand it with the below example -

**Question 1 **- There are 4 friends A, B, C, and D, and we have to find who among them is the heaviest?

**Statement 1 **- B is heavier than A and D but lighter than C.

**Statement** **2** - A is lighter than B and C but heavier than D.

**Analysis** - If we analyze the above statements, we will figure out from statements 1, B > A, B > D, and B < C.

From statement 2, A < B, A < C, A > D.

If we combine above two statements, we get C > B > A > D

That means Data in statements 1 and 2 are sufficient to solve the problem.

Let’s take another example of Simple Interest and Compound Interest to understand this concept more clearly -

**Question 2 **- Find Net Worth of Alice’s Assets?

**Statement** **1** - A compound interest at 15% on his assets, followed by a tax of 4% on the interest, fetches Alice Rs. 2000 this year.

**Statement** **2** - The interest is compounded once every four months.

**Analysis** - Let’s start analyzing the above statements and try to solve them using statements alone. If we cannot find the answer, we will solve the question using both statements.

In Statement 1, we can see that the compound interest of 15% is given to us, and 4% interest on this compound interest is also given. This interest will be a total of Rs. 1500. But to calculate the net worth, we need to have a time of the compound interest and the total amount or the principal amount given to us. This data is not present in statement 1. That means statement 1 is not sufficient to find out the answer.

In statement 2, the time on which compound interest can be calculated is given to us, but there is no other information or data provided which can be helpful to find the answer. That means statement 2 is also not sufficient to determine the solution.

That means Both statements alone cannot determine the answer. But when we combine these 2 statements, we can see that all the information is given to us, and we can determine the net worth of Alice’s assets.

## Coding Data Sufficiency

Data sufficiency is tricky because we are not required to solve the question, instead, we are asked to mention whether the questions can be solved with the given data. Data sufficiency consists of the following things:

**Test of Sufficiency**- As discussed above, we need to find out which set of data together or alone is required to answer the question in these types of questions. Hence, it is just a sufficiency test, and we are not required to calculate the actual answer.**Problem Statement**- This gives us primary data and the question. It is suggested to understand the problem statement properly before jumping to any conclusion.**Additional DataSet**- There can be multiple other data along with the problem statement, which helps solve the question and support the data.

## Steps to Solve Data Sufficiency

Below are the steps that should be followed to solve data sufficiency problems -

- Read the data carefully and comprehend it. One of the most critical cautious points in data sufficiency is never to assume any extra information that is not given in the question.
- The Next Step is to combine the data that is available to us in the question and analyze whether we can arrive at any solution or not. It is not necessary to solve the question. Just get an idea of whether the question can be solved or not.
- If we cannot get the solution from Statement 1, go to Statement 2 and check the same for the 2nd Statement. Don’t use the data available in statement 1.
- If we cannot get any solution from either of the statements, combine the data available in both the statements and try to find the solution.
- Choose the correct answer.

## More Examples

**Question **- What is the value of ‘X’

Statement 1 : X ^ 2 + X – 12 = 0

Statement 2 : X ≥ 0

a) Statement 1 alone is sufficient

b) Statement 2 alone is sufficient

c) Both statement 1 and statement 2 together are sufficient.

d) Both statement 1 and statement 2 even together are not sufficient

e) Data from both statements are necessary to determine the answer.

Analysis - Let’s consider statement 1 alone,

X ^ 2 + X – 12 = 0

X ^ 2 + 4X – 3X – 12 = 0

(X + 4) (X – 3) = 0

X = -4, 3

Now, Consider statement 2 alone, we have X ≥ 0

Combining the two statements, we can safely say that X = 3

Hence, both statement 1 and statement 2 together are sufficient to solve the problem.

**Question **- Check if two triangles are congruent?

**Statement** **1**: Both triangles have equal bases and equal heights.

**Statement** **2**: Both are equal equilateral triangles.

a) Statement 1 alone is sufficient

b) Statement 2 alone is sufficient

c) Both statement 1 and statement 2 together are sufficient.

d) Both statement 1 and statement 2 even together are not sufficient

e) Data from both statements are necessary to determine the answer.

Analysis - If we look at this problem, we will notice that we need to determine whether the two triangles are congruent or not and don’t need answers to the question. We will start by solving the statements individually, and then if we cannot find the answer, we will combine the data given in both statements.

Let’s consider statement 1; It tells that both the triangles have equal heights and bases. The rule of congruence says that the two triangles with the same base and equivalent size may or may not be congruent.

That means from statement 1, we cannot determine the answer.

Let’s consider statement 2; It tells that both are equal equilateral triangles. If both triangles are equilateral, it doesn’t mean that they are congruent.

Both the sides of the triangles should be equal then we can say that two equilateral triangles are congruent. It is not mentioned in this statement. So statement 2 can not determine the answer.

If we combine both statements, we get the data that both the triangles are equilateral and have the same base. It satisfies the congruence of the triangles.

So the answer is option e).

## Frequently asked questions

**1) What is Data Sufficiency?**

Data Sufficiency is a concept in which we are interested in analyzing the given data and figuring out if the provided information is enough to solve the problem.

**2) Do we need to solve the question of Data Sufficiency?**

We are not required to solve the question. Instead, we are asked to mention whether the questions can be solved with the given data or not.

**3) Should we consider all statements while analyzing the reports****?**

We should not consider all statements initially. Firstly, If we cannot get the solution from Statement 1, move to Statement 2 and check the same for the 2nd Statement. Don’t use the data available in statement 1. If we can still not solve the question, combine both the statements and solve the question.

## Key takeaways

In this article, we discussed Data Sufficiency and approached using it in various logical problems.

If you think that this blog helped you, then share it with your friends!. Refer to the __DSA C++__ course for more information.

Until then, All the best for your future endeavors, and Keep Coding.