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How to Solve Data Sufficiency Questions?
Data Sufficiency (DS) questions present a unique challenge within the GMAT. These questions tend to remain daunting and complex, but this is the nature of the GMAT. Solving data sufficiency questions requires a structured approach and logical reasoning.
GMAT Data Sufficiency Question Format
Question Format: Data sufficiency questions typically consist of a question followed by two statements labelled as statement (1) and statement (2).
Data sufficiency questions offer specific answer choices:
(A) Statement (1) alone is sufficient, but statement (2) alone is not sufficient.
(B) Statement (2) alone is sufficient, but statement (1) alone is not sufficient.
(C) Both statements together are sufficient, but neither statement alone is sufficient.
(D) Each statement alone is sufficient.
(E) Statements (1) and (2) together are not sufficient.
Step-by-Step approach to solve Yes/No type of data sufficiency question
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.
