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ATM Cash Withdrawal Preferences

CAT 2018 Slot 1 · Data Interpretation & Logical Reasoning · Hard · Optimization

This is a hard Data Interpretation & Logical Reasoning question set from the CAT 2018 Slot 1 paper. It tests Optimization. The full answer key and a step-by-step explanation are below — try it yourself first, then reveal the solution.

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Passage / data set

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.

Question 1 of 4

In how many different ways can the ATM serve a customer who gives 500 rupee notes as her preference?

Answer

7

Explanation

Solving 500x+200y+100z=5000500x + 200y + 100z = 5000 with x>y+zx > y + z yields 7 valid non-negative integer solutions.

Question 2 of 4

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?

Answer

6

Explanation

Minimizing 500-rupee notes used by preferred customers and non-preferred customers allows at most 6 preferred customers to be served.

Question 3 of 4

What is the maximum number of customers that the ATM can serve with a stock of fifty 500 rupee notes and a sufficient number of notes of other denominations, if all the customers are to be served with at most 20 notes per withdrawal?

  1. A.

    13

  2. B.

    10

  3. C.

    12

  4. D.

    16

Answer

C

Explanation

Optimizing the stock usage per customer under the max 20 notes constraint yields a maximum of 12 customers.

Question 4 of 4

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?

  1. A.

    750

  2. B.

    800

  3. C.

    1400

  4. D.

    900

Answer

D

Explanation

To minimize total notes, preferred 500 customers take 9 notes of 500 + 2 notes of 200/100, and preferred 100 customers take 9 notes of 500 + 5 notes of 100. Summing gives 900 notes of 500.

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