*Monday, May 6th, 2013*

**Introduction to Data Sufficiency**

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Data Sufficiency questions often involve very simple calculations. This does not mean that the questions are simple. It just means that the chances to make conceptual mistakes and / or silly mistakes are a little higher than usual. You will need to pay attention to detail in such questions.

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. Once again – 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 / 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)

A typical set of Instructions (4 options):

- If one of the statements alone is sufficient
- If both the statements alone are sufficient
- If both statements together are sufficient but neither is sufficient alone
- If both statements together are not sufficient

Let us look at a few simple questions to understand the concept in a better way. Please note that these questions are way too simple to be asked in an exam like CAT, but they are necessary for understanding the idea.

Q1: 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**

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Q2 What is the value of ‘x + y’?

Statement A: 3x + 7y = 10

Statement B: 2x + 9y = 8

Two equations, two variables. I can solve the equations to find out the values of x & y and hence, I can find out the value of ‘x+y’ **Option 3**

** **

Q3 What is the value of ‘x + y’?

Statement A: 3x – 7y = 10

Statement B: 14y = 6x + 19

By combining the two statements I get – Two equations, two variables. I can solve the equations to find out the values of x & y. Hence, I can find out the value of ‘x+y’ **Option 3**

** ****WRONG!**

These two equations represent a set of parallel lines. They are inconsistent with each other. I will not be able to determine the values of x & y. Hence, I cannot find out the value of ‘x+y’ **Option 4**

** **Q4 What is the value of x?

Statement A: x^2 – 5x + 6 = 0

Statement B: x^2 – 6x + 8 = 0

From the first statement, I get the values of x as 2 & 3. I do not have a unique answer.

From the second statement, I get the values of x as 2 & 4. I do not have a unique answer.

After combining the two statements, I get the unique value of x as 2. **Option 3**

** **

Q5 What is the value of x?

Statement A: x^2 – 5x + 6 = 0

Statement B: x^2 – 4x + 4 = 0

From the first statement, I get the values of x as 2 & 3. I do not have a unique answer.

From the second statement, I get the value of x as 4. I have a unique answer so there is no need to combine the two statements. **Option 1**

** **Q6 What is the value of x?

Statement A: x^2 – 9x + 9 = 0

Statement B: x^2 – 4x + 4 = 0

From the first statement, I get the value of x as 3. I have a unique answer.

From the second statement, I get the value of x as 4. I have a unique answer.

I am getting a unique answer from both the statements individually. **Option 2**

Now some of you might be thinking that we have got a different answer from both the statements and so the answer is not unique. Well, that thinking is incorrect. We have to figure out whether or not the given data was sufficient. When I am looking at Statement A, I am just looking at Statement A. If I can get a unique answer from Statement A, I will not even bother with what is going on in Statement B.

Q7 Is ‘x’ a prime number?

Statement A: x^2 – 5x + 6 = 0

Statement B: x^2 – 10x + 24 = 0

From the first statement, I get the values of x as 2 & 3.

From the second statement, I get the values of x as 4 & 6.

But that is not what the question is. The question is whether or not x is a prime number. My answers should not be values of ‘x’, they should be ‘Yes’ or ‘No’ or ‘Can’t Say’.

So, let us calculate again.

From the first statement, I get the values of x as 2 & 3. So, x is a prime number. I can answer the question and my answer is **YES**.

From the second statement, I get the values of x as 4 & 6. So, x is not a prime number. I can answer the question and my answer is **NO**.

I am getting a unique answer from both the statements individually. **Option 2**

I hope you would be comfortable with Data Sufficiency questions now. I would like to repeat that the questions mentioned above are on the simpler side and probably you should practice some real Data Sufficiency question to get a hang of the topic.