Introduction

Data sufficiency questions test your knowledge of basic math facts and skills along with reasoning, analytical, and problem-solving abilities. Each data sufficiency item presents you with a question. You do not actually have to find the answer to the problem; instead, your challenge is to decide whether or not the information presented along with the question would be sufficient to allow you to answer the question. Five answer choices are provided, each of which categorizes the relationship between question and the information provided in a different way. You must select the answer choice that accurately describes this relationship.

Understanding Answer options

In Data sufficiency problems, a question consists of two statements labeled I and II, in which a certain information is given. You have to decide whether the information given in the statements is sufficient to answer the question or not. Using the information given in the statements plus your knowledge of mathematics and wellknown facts (such as Earth revolves around Sun or the meaning of counterclockwise), you must indicate whether.

•  The answer can be obtained from Statement I alone but statement II alone is not sufficient to answer the question asked;
•  The answer can be obtained from statement II alone but statement I alone is not sufficient to answer the question asked;
• The answer can be obtained from both statements I and II together; but neither statement I nor statement II alone  is sufficient to answer the question asked ;
• We can answer  the asked question from either statement I or statement  II;
• We can not answer the question asked  from Statement I and II together, and additional information is required to answer the question

Note: In data sufficiency problems, the information given in the statements is sufficient only when it is possible to determine exactly one numerical value as answer for the problem.

Data sufficiency tricks

Step 1 –  Examine the Question:
What is asked? Do we have to find a value or do we have to check a relationship?
Before looking at the two numbered statements, take twenty to thirty seconds to consider the question by itself. Figure out what is being asked. There are usually 2 possibilities a specific number may be sought (“What is the value of y?” "How many gallons of milk is in the tank?”), or a true/false answer may be needed (“Is it true that a >7?” “Is n a prime number?”) Make sure you understand what the question is asking.
Then consider what information would be needed to answer the question. This will depend on the type of question, of course. If it is a geometry question, the information needed will be based on rules you’ve learned about how one geometric fact can be deduced from another. For example, to determine the area of a circle, you need to know its radius, its diameter, or its circumference. To determine the length of the hypotenuse of a right triangle, you need to know the length of the other two sides.
On the other hand, if it is a percentage question, different rules will come into play. To determine what percentage X is of Y, for example, you need to know the value of X and the value of Y. When a change from one value to another is involved – the increase in value of an investment, for example – you need to know both the old value and the percentage by which it has increased if you want to calculate the new value.
As these examples suggest, the data sufficiency question format allows the test makers to measure your knowledge of a wide array of mathematical topics.

Step 2 – Consider each statement individually
Having figured out the nature of the question and decided, in a general way, what information is needed to answer it, look at each of the two numbered statements provided. Consider them one at a time, without reference to each other.
First look at statement A. Does it provide, all by itself, enough information to answer the question? If so, you’ve already narrowed the possible answer choices to just two: 1 and 4. If not, three answer choices are possible: 2, 3 and 5.
Then look at statement B. Does it provide, all by itself, enough information to answer the question? If so, only answers 2 and 4 are possible. If not, only answers 1, 3 and 5 are possible.
Having gotten this far, you may already be able to pick the right answer. If either statement by itself provides enough information to answer the question, you can pick from answers 1, 2 and 4, depending on which statement is sufficient or whether either statement will do.
If neither statement by itself is sufficient to answer the question, go on to the third stage:

Step 3 – Combine the two statements
Third, if necessary, combine the two statements. If neither of the statements by itself is sufficient to answer the question, consider whether you can answer the question by combining the information given in both statements. If so, the answer is 3; if not, the answer is 5.

Some example and solution

Directions for data sufficiency questions (1-5):
A. If data in the  statement I alone is sufficient to answer the question.
B. If data in the statement II alone is sufficient to answer the question.
C. If data either in the statement I alone or statement II alone are sufficient to answer the question.
D. If data given in both I & II together are not sufficient to answer the question.
E. If data in both statements I & II together are necessary to answer  the question.

Question 1. Who is taller among P, Q, R, S & T ?
I) S is shorter than Q. P is shorter than only T.
II) Q is taller than only S. T is taller than P and R.
Answer : (C)
Explanation:
From I : P is shorter than only T, this means that P is taller than all Q, R & S, so T is tallest.
From II : Q only taller than S, so S is shortest, and Q is second shortest, Now T taller than P and R both, So tallest of all.
 
Question 2. What is the distance between point P and point Q?
I) Point R is 10 m west of point P and point S is 10 m north of point P.
II) Point Q is 10 m south-east of point R. Point S is 20 m north-west of point Q.
Answer : (D)
Explanation:
From I : No relation between points P and Q
From II : In this since we don’t know the angles between sides of triangle forming with points PQS and PQR, PQ cannot be determined.

Question 3. How is Shubham related to Shivani?
I) Shubham is brother of Meenal. Shivani is niece of Pooja.
II) Neeraj is Meenal’s uncle and Preeti’s brother
Answer : (D)
Explanation:
Either statement cant give the answer.
From both statements we can get the relationship as Pooja is Neeraj’s sister but it cannot be clearly said that Shubham & Meenal are Pooja’s children or not & Shivani is Neeraj’s daughter, because there can be other siblings of Neeraj and Pooja also.

Question 4. How is PRODUCT written in that code language ?
I) In a certain code language, AIEEE is written as BJFFF.
II) In a certain code language, GYPSY is written as FXORX
Answer : (E)
Explanation:
From I: All vowels are coded as next alphabets
From II: All consonants are coded as previous alphabets
So from both the statements.

Question 5. How is ‘face’ written in that code language?
I) In a certain code language, ‘no one with face’ is coded as ‘fo to om sop’ and ‘no one has face’ is coded as ‘om sit fo sop’
II) In a certain code language, ‘face of no light’ is coded as ‘om mot fo kiz’ and ‘no one is smart’ is coded as ‘sop fo sip lik’.
Answer : (E)
Explanation:
From I : ‘no one face’ is coded as ‘om fo sop’
From II : ‘no’ is ‘fo’
Now from both – ‘one face’ is ‘om sop’ and now from II: ‘face of no light’ is written as ‘om mot fo kiz’, ‘face’ is ‘om’