Basics of Data Sufficiency

Imagine your professor gives a question during viva and ask you "Can you solve it" and you said "Yes, I can". He is happy and gives you credit without asking you to actually solve it! Happy ? Wait there is more. You said "No, I can’t". He is still happy and gives you the same credit!!! Too good to be true…??? Not sure how cool your professor will be with this proposition but this is what data sufficiency does. An aptitude test checks your ability to gauge the chances to solve a question with the given data. If you know what you have, what you need and the best way to connect both, that’s all it takes :)
Each question is followed by two statements. We need to choose the option as per below guidelines
Mark (A): If the question can be answered by using the statement 1 alone but not by using statement 2 alone.
Mark (B ): If the question can be answered by using the statement 2 alone but not by using statement 1 alone.
Mark (C) : If the question can be answered by using either of the statements alone.
Mark (D): If the question can be answered by using both statements together but not by either of statements alone.
Mark (E) : If the question cannot be answered on the basis of the two statements.The thought process while approaching DS question is as follows
Step1: Take Statement 1 and try to reach a conclusion.
Step 2: Take Statement 2 and try to reach a conclusion. Information given in statement 1 is NOT used in this step.
Step 3: If we are not able to reach a conclusion in step 1 or step 2, take both statements together and try to reach a conclusion.
We will learn with examples
Question: Is x > 3?
Statement 1: x is the smallest prime.
Statement 2: x^{2}=4Using statement 1 alone: smallest prime is 2. Hence x = 2, we can conclude that x is NOT greater than 3. Remember that getting No is also a conclusion.
Using statement 2 alone: √4 = +2 or 2. Both case x is NOT greater than 3.
As we can conclude in both step1 and step2 we don’t have to go for the step 3.We can Mark [ C ]
Question: Is A taller than B ?
Statement 1: A is tallest in his class
Statement 2: A and B are class matesUsing Statement 1 Alone: We don’t know whether A and B are classmates or not. We cannot conclude about their height.
Using Statement 2 Alone: We cannot reach any conclusion as no information regarding height is given.
Using both statements Combined: A and B are in same class and A is the tallest in that class. We can conclude that A is taller than B.We can mark [ D ]
Question: is x > 0 ?
Statement 1: x – 1245/247 = 134/1209 – 87/45
Statement 2: 1 < x < 1Using statement 1 alone: we can get a unique value of x by solving the given equation. Hence we can conclude whether x is positive or not by using statement 1 alone. Now the most important point, don’t try to find x by solving the equation. Question is Can you find x, not to Find x. finding actual values ‘Just to be sure’ is a major wastage of time when we deal with data sufficiency.
Using statement 2 alone: going by the given information, x can be anywhere between 1 and 1. We cannot conclude x to be positive or negative using this statement.We can mark [ A ]
Question: ABCD is a quadrilateral. Is ABCD a square ?
Statement 1: opposite angles are equal.
Statement 2: Diagonals are equal in length.Using Statement 1 alone: Information from this statement can make ABCD, a square, rectangle, rhombus or a parallelogram. We cannot conclude the shape of ABCD using this statement alone.
Using Statement 2 alone: from the information given, ABCD can be either a square or a rectangle. We cannot conclude the shape of ABCD using this statement.
Using both statements: By clubbing the data of both statements, ABCD fits the definition of a rectangle and a square. We cannot uniquely identify the shape of ABCD using both statements together.Given data is not sufficient. Hence mark [ E ]
Question: is x divisible by 9 ?
Statement 1 : sum of digits of x is divisible by 3
Statement 2 : sum of digits of x is divisible by 9Using Statement 1 alone: from this information we cannot conclude that x is divisible by 9. It just says x is divisible by 3.
Using Statement 2 alone: from this information we can conclude that x is divisible by 9.We can mark [ B ]
Keep your number system and geometry concepts handy. You will need them in DS.
Happy learning :)