A casino pays players using purple and orange chips; each

Thanks a lot for your help, Marcab & Bunuel. My apologies regarding the classification issue.

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.

StepIII: 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 the value of 2purple chips + 1 orange chip.

=> Purple($p) and Orange($n) - where 'p' and 'n' are integers

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

But we know that this is a key question [Integer 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 5p + 7n = 53.

=> 5p = 53 - 7n. The result should be divisible by 5

=> For n = 4 , 5p = 53 - 7(4) = 53 - 28 = 25. => p = 5.

Since the answer is unique, the condition is sufficient by CMT 2.


Condition(2) tells us that 6p + 3n = 42.

=> Dividing boththe sides by '3' => 2p + n = 14

Since the answer is unique, the condition is sufficient by CMT 2.


Condition (1) and Condition (2) alone are sufficient.

So, D is the correct answer.

Answer: D

S1: 5p+7o=53
I need 3 as unit digit -> 5+8=13
So, 5*5+7*4=53 YES

S2: 6p+3o=42
I have to find the value of 2p+o:
2p+o=14

Answer -> D