Que: Is 20% of n greater than 30% of the sum of n and \(\frac{1}{4}\)?

[Max@Math Revolution]

Que: Is 20% of n greater than 30% of the sum of n and \(\frac{1}{4}\)?

(1) 0 < n < 2.
(2) n > 0.25.

[Max@Math Revolution]

Solution: Forget the conventional way to solve DS questions.We will solve this DS question using the variable approach.


The first step of the Variable Approach: The first step and the priority is to modify and recheck the original condition and the question to suit the type of information given in the condition.

To master the Variable Approach, visit https://www.mathrevolution.com and check our lessons and proven techniques to score high in DS questions.

Learn the 3 steps. [Watch lessons on our website to master these 3 steps]

Step 1 of the Variable Approach: Modifying and rechecking the original condition and the question.

We have to find ‘Is 20% of n greater than 30% of the sum of n and \(\frac{1}{4}\)’?

=> 20% of n > 30% of (n + \(\frac{1}{4}\))

=> \(\frac{20}{100}\cdot n>\frac{30}{100}\cdot\left(n+\frac{1}{4}\right)\)

=> \(\frac{20n}{100}>\frac{30n}{100}+\frac{30}{100}\cdot4\)

=> \(\frac{n}{5}>\frac{3n}{10}+\frac{6}{5}\)

=> \(-\frac{6}{5}>\frac{3n}{10}-\frac{n}{5}\)

=> \(-\frac{6}{5}>\frac{3n-2n}{10}\)

=> \(-\frac{6}{5}>\frac{n}{10}\)

=> -12 > n

=> n < -12

We have to know ‘Is n < -12’?


Condition (1) tells us that 0 < n < 2.

=> n < -12

Since the answer is a unique NO, condition (1) alone is sufficient by CMT 1 which states that there should be a unique Yes or a NO.

Condition (2) tells us that n > 0.25.

=> n < -12

Since the answer is a unique NO, condition (1) alone is sufficient by CMT 1 which states that there should be a unique Yes or a NO.

Each condition alone is sufficient.

So, D is the correct answer.

Answer: D