# Data Sufficiency

**Data Sufficiency** is a very important chapter of Reasoning aptitude tests. Lots of reasoning questions will surely come in your examination from this chapter. Here in this page we will discuss Data Sufficiency reasoning with solution which will help you to solve Data Sufficiency questions very easily and quickly. In exam, reasoning questions can be solved very easily and quickly using reasoning shortcut tricks.

## Steps in solving Data Sufficiency questions

You must decide whether the information in each statement is sufficient to answer the question or—if neither statement provides enough information—whether the information in the two statements together is sufficient. It is also possible that the statements in combination do not give enough information to answer the question.

Begin by reading the initial information and the question carefully.Next,

**STEP-I**

Consider the first statement.

Does the information provided by the first statement enable you to answer the question?

**STEP-II**

Go on to the second statement.

Try to ignore the information given in the first statement when you consider whether the second statement provides information that, by itself, allows you to answer the question.

Now you should be able to say, for each statement, whether it is sufficient to determine the answer.

**STEP-III**

Next, consider the two statements in tandem. Do they, together, enable you to answer the question ?

Look against your answer choices. Select the one that most accurately reflects whether the statements provide the information required to answer the question.

## TIPS on cracking Reasoning Questions of Data Sufficiency type

Tip #1:Do not solve the problems

Analyze the information provided**:** Do not solve the question using the information at hand.

**Question: **Two towns are connected by railway. Can you find the distance between them?

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.

A. I alone sufficient while II alone not sufficient to answer.

B. II alone sufficient while I alone not sufficient to answer.

C. Either I or II alone sufficient to answer.

D. Both I and II are not sufficient to answer.

E. Both I and II are necessary to answer

**Solution:**

Let the distance between the two towns be D km. Let the speed of the express train be S km/hr. The speed of the mail train is S+12 km/hr.

__Creating an equation using I and II:__

D/(S+12) = (D/S) – (2/3) [because 40 minutes = 2/3 hrs]

Don’t try to solve this equation. There is one equation with two variables and cannot be solved. Hence, the correct answer is **D.**

__Note:__* Questions of this type do not require you to actually solve them- you just need to interpret the information provided to you in the statements. Also, working out the problems may mislead you into hasty assumptions. So, avoid trying to solve them.*

Tip #2:Represent the given information visually on paper to easily process it

**Question: **How many children does M have?

I. H is the only daughter of X who is wife of M.

II. K and J are brothers of M.

*Options:*

A. I alone sufficient while II alone not sufficient to answer.

B. II alone sufficient while I alone not sufficient to answer.

C. Either I or II alone sufficient to answer.

D. Both I and II are not sufficient to answer.

E. Both I and II are necessary to answer.

**Solution:**

From I, we have that H is the only daughter of M. But that does not mean that M has no son. Thus, the information is not enough to answer the question.

II does not give tell us anything about M’s children.

Thus, the correct answer is **D.**

Tip #3:Do not make assumptions that cannot be justified by the given statements

**Question: **How many ewes (female sheep) in a flock of 50 sheep are black?

I. There are 10 rams (male sheep) in the flock.

II. Forty percent of the animals are black.

*Options:*

A. I alone sufficient while II alone not sufficient to answer.

B. II alone sufficient while I alone not sufficient to answer.

C. Either I or II alone sufficient to answer.

D. Both I and II are not sufficient to answer.

E. Both I and II are necessary to answer

**Solution: **

Do not assume that the proportion of white: black sheep is uniform across rams and ewes. We know from (I) that there are 40 ewes but we do not know that 40% of ewes are black. Hence the right answer is** D.**

Tip #4:Use Venn Diagrams when possible

**Question: **Of the 70 children that visited a certain doctor last week, how many had neither caught cough nor cold?

I. 40 of 70 had cough but not cold.

II. 20 of 70 had both cough and cold.

*Options*

A. I alone sufficient while II alone not sufficient to answer.

B. II alone sufficient while I alone not sufficient to answer.

C. Either I or II alone sufficient to answer.

D. Both I and II are not sufficient to answer.

E. Both I and II are necessary to answer.

**Solution:**

As we see in the Venn diagram, neither is sufficient but together, they are enough to solve the question. Hence, the answer is **E**.

__Note:__ *Try representing Venn diagrams when possible. That way you do not have to rattle your brain on the problem unnecessarily. Also, this might be the fastest way to figuring out the answer in some questions.*

Tip #5:Typically the choices A through E tend to be the same

We have already seen from the above examples that the choices are always given as follows:

A. I alone sufficient while II alone not sufficient to answer.

B. II alone sufficient while I alone not sufficient to answer.

C. Either I or II alone sufficient to answer.

D. Both I and II are not sufficient to answer.

E. Both I and II are necessary to answer.

So you can save time by just skimming over the choices superficially...

## Test-Taking Strategies

**1. Do not waste valuable time solving a problem.**

You only need to determine whether sufficient information is given to solve it.

**2. Consider each statement separately.**

First, decide whether each statement alone gives sufficient information to solve the problem. Be sure to disregard the information given in statement (1) when you evaluate the information given in statement (2). If either, or both, of the statements give(s) sufficient information to solve the problem, select the answer corresponding to the description of which statement(s) give(s) sufficient information to solve the problem.

**3. Judge the statements in tandem if neither statement is sufficient by itself.**

It is possible that the two statements together do not provide sufficient information. Once you decide, select the answer corresponding to the description of whether the statements together give sufficient information to solve the problem.

**4. Answer the question asked.**
For example, if the question asks, “What is the value of y ?” for an answer statement to be sufficient, you must be able to find one and only one value of y. Being able to determine minimum or maximum values for an answer(e.g., y = x+ 7) is not sufficient, because such answers constitute a range of values rather than the specific value of y.

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**Data Sufficiency**Questions and Answers with explanation.