In a convenience store in a certain year, the average (arithmetic mean

Forget the conventional way to solve DS questions.

We will solve this DS question using the variable approach.

Remember the relation between the Variable Approach, and Common Mistake Types 3 and 4 (A and B)[Watch lessons on our website to master these approaches and tips]

Step 1: Apply Variable Approach(VA)

Step II: After applying VA, if C is the answer, check whether the question is key questions.

Step III: If the question is not a key question, choose C as the probable answer, but if the question is a key question, apply CMT 3 and 4 (A or B).

Step IV: If CMT3 or 4 (A or B) is applied, choose either A, B, or D.

Let's apply CMT (2), which says there should be only one answer for the condition to be sufficient. Also, this is an integer question and, therefore, we will have to apply CMT 3 and 4 (A or B).

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

Let’s apply the 3 steps suggested previously. [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 Average monthly sales (Soda X) (=, <, >) Average monthly sales (Soda Y).

=> Average (arithmetic mean) monthly sales of soda X was 'n' dollars

Second and the third step of Variable Approach: From the original condition, we have 2 variables (X and Y). To match the number of variables with the number of equations, we need 2 equations. Since conditions (1) and (2) will provide 2 equations, C would most likely be the answer.

But we know that this is a key question [Statistics question] and if we get an easy C as an answer, we will choose A or B.

Let’s take a look at each condition.

Condition(1) tells us that the average (arithmetic mean) monthly sales of soda Y from January to August were n dollars.

=> We have average sales for first '8' months but we don't have an average for last '4' months. Hence, the overall average for 12 months could be higher or lesser or equal to n.

Since the answer is not a unique YES or NO, the condition(1) alone is not sufficient by CMT 1.


Condition(2) tells us that the average (arithmetic mean) monthly sales of soda Y from May to December were 2n dollars.

=> We have average sales for the last '8' months that is total sales for the last 8 months = 8 * 2n = 16n. Hence, the overall average for 12 months would be \(\frac{(16n + [positive or zero of the first 4 months])}{ 12}\) and this will be higher than n.

Since the answer is a unique YES, the condition(2) alone is sufficient by CMT 1.

Condition(2) alone is sufficient.

So, B is the correct answer.

Answer: B

SAVE TIME: By Variable Approach, when you know that it is a key question and 'C' seems to be an answer, mark A, B or D as the correct answer.