Q1. If abc ≠ 0, does b – c = 0?

Statement (1) a^b = a^c

Statement (2) a ≠ 1

Understand the QuestionStem: Review the information given in the question stem. This may include equations, statements, or any other data. 

Example: It is given that abc ≠ 0, which means that none of the a, b, c is equal to 0. The rephrased question is: does b = c?

Analyse Statement (1): Begin with statement (1). Determine whether it provides enough information to answer the question. You should not perform any calculations at this point, unless it’s required to assess sufficiency.

Example: 

(1) a^b = a^c

Using values, if a = 1, then b could be equal to or could not be equal to c. 

Therefore, statement (1) alone is not sufficient. Eliminate option A and D.

Analyse Statement (2): Repeat the same process for statement (2), assessing whether it alone is sufficient to answer the question.

Example: It is known that a ≠ 1, but the values of b and c are unknown. Therefore statement (2) alone is not sufficient to answer the question. Eliminate option B.

Combine Both Statements: In this step, consider both statements together. Determine if, when combined, they provide sufficient information to answer the question. This involves evaluating whether the two statements complement each other to give a definitive answer.

Example: It is known that a ≠ 0 and a ≠ 1, but a could be -1

If a = -1, b and c could be different such as 1 and 3 respectively.

Or b and c could be equal such as 3 and 3 respectively.

Hence, after combining the statements, there is no definite answer to the question. Eliminate option C.

Therefore, E is the correct choice. 

Here’s a step-by-step approach to solve value based type of data sufficiency question:

Q2. What is the value of x? 

Statement (1): x^2 = 4 

Statement (2): x^3 < x^2

Understand the Question Stem: 

There is no information about x is given in the question. 

Analyse Statement (1):

x^2 = 4

Taking square root on both the sides

|x| = 2. Hence, x = -2 or 2

As there is no definite value of x, the statement alone is not sufficient to answer the question. Eliminate option A and D. 

Analyse Statement (2): 

x^3 < x^2

x^3 – x^2 < 0

x^2 (x – 1) < 0

Therefore, x < 1, x and x is not equal to zero.

As there is no definite value of x, the statement alone is not sufficient to answer the question. Eliminate option B. 

Combine Both Statements: 

After clubbing, as x < 0; therefore x = -2 

As there is a definite value of x after clubbing the statements, option C is correct.