CAT DILR Questions | CAT Analytical Reasoning questions
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Comprehension
An ATM dispenses exactly Rs. 5000 per withdrawal using 100, 200 and 500 rupee notes. The ATM requires every customer to give her preference for one of the three denominations of notes. It then dispenses notes such that the number of notes of the customer’s preferred denomination exceeds the total number of notes of other denominations dispensed to her.
CAT/2018.1
Question . 76
If the ATM could serve only 10 customers with a stock of fifty 500 rupee notes and a sufficient number of notes of other denominations, what is the maximum number of customers among these 10 who could have given 500 rupee notes as their preferences?
Explanatory Answer
Method of solving this CAT DILR Question from Analytical Reasoning question
Correct Answer: 6
Solution:
Wonderful question. Let us first outline the overall variables.
500x + 200y + 100z = 5000. Or, 5x + 2y + z = 50.
If the preferred denomination is 500, we know that x > (y + z).
If the preferred denomination is 200, we know that y > (x + z).
If the preferred denomination is 100, we know that z > (y + x).
After this, we are off to the questions.
From previous question, we have got the following table.
We want to have the maximum number of customers, so each customer would need to take the minimum possible number of RS. 500 notes.
We already know that the minimum number of Rs. 500 notes that a customer (with a preference for Rs. 500 notes) can take is 8.
So, we can have deliver to a maximum of 6 customers. We do not have enough Rs. 500 notes for the 7th customer.
Answer = 6.
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