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 . 78
What is the number of 500 rupee notes required to serve 50 customers with 500 rupee notes as their preferences and another 50 customers with 100 rupee notes as their preferences, if the total number of notes to be dispensed is the smallest possible?
Explanatory Answer
Method of solving this CAT DILR Question from Analytical Reasoning question
Correct Option: D
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.
The number of notes dispensed should be the smallest possible.
50 customers have given the preference as Rs. 500 notes. For these if we need to have the least number of notes, we should go for the option of having 10 Rs. 500 notes and nothing else.
What about when the preference is Rs. 100 note? We could have all as Rs. 100 notes, but that would demand 50 notes which is a large number.
We could have, say, 45 Rs. 100 notes and one Rs. 500 note. This is also large.
Let us take a leap and say, we get to have 7 Rs. 500 notes, we would need to get RS. 1500 from other notes.
We could have 11 Rs. 100 notes and 2 Rs. 200 notes but this would still result in 20 notes.
The best scenario would have only Rs. 500 and Rs. 100 notes.
We could have 8 Rs. 500 notes and 10 Rs. 100 notes, resulting in 18 notes totally.
For servicing 50 customers with this combination, we would require 50 × 8 = 400 Rs. 500 notes.
So, in total, we need 500 + 400 = 900 customers.
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