CAT 2018 Slot 1 — DILR Question 21
Answer the following question based on the information given below.
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.
In how many different ways can the ATM serve a customer who gives 500 rupee notes as her preference?
Answer & solution
Answer: 7
Preference was given to Rs. 500 notes.
The ATM machine can dispense 10 notes of Rs. 500.
(i) 500 × 10 = Rs. 5,000
If the ATM machine dispenses 9 notes of Rs. 500;
(ii) 500 × 9 = 4500, 200 × 2 = 400 and 100 × 1= 100
(Notes of Rs. 500 denomination = 9 and notes of Rs. 200 and Rs. 100 denominations = 2 + 1 = 3, 9 > 3)
(iii) 500 × 9 = 4500, 200 × 1 = 200 and 100 × 3 = 300
(Notes of Rs. 500 denomination = 9 and notes of Rs. 200 and Rs. 100 denominations = 1 + 3 = 4, 9 > 4)
(iv) 500 × 9 = 4500, 100 × 5 = 500
(Notes of Rs. 500 denomination = 9 and notes of Rs. 200 and Rs. 100 denominations = 0 + 5 = 5, 9 > 5) If the ATM machine dispenses 8 notes of Rs. 500;
(v) 500 × 8 = 4000 and 200 × 5 = 1000
(Notes of Rs. 500 denomination = 8 and notes of Rs. 200 and Rs. 100 denominations = 5 + 0 = 5, 8 > 5)
(vi) 500 × 8 = 4000, 200 × 4 = 800 and 100 × 2 = 200
(Notes of Rs. 500 denomination = 8 and notes of Rs. 200 and Rs. 100 denominations = 4 + 2 = 6, 8 > 6)
(vii) 500 × 8 = 4000, 200 × 3 = 600 and 100 × 4 = 400
(Notes of Rs. 500 denomination = 8 and notes of Rs. 200 and Rs. 100 denominations = 3 + 4 = 7, 8 > 7)
If numbers of notes of denomination Rs. 200 are reduced further, number of notes of the customer’s preferred denomination will not exceed the total number of notes of other denominations.
The ATM machine can dispense 7 notes of Rs. 500, for the minimum number of total notes of the remaining two denominations; one can have 7 notes of Rs. 200 and one note of Rs. 100. But even then, number of notes of the customer’s preferred denomination will be less than the total number of notes of other denominations. As number of notes of denominations reduces, number of notes of the denomination Rs. 500 will be less than the total number of notes of other denominations.
Thus, there are 7 different ways in which the ATM can serve a customer who gives 500 rupee notes as her preference.
Therefore, the required answer is 7.
Answer: 7