This delighftul puzzle is based on the ATM dispensary. With many combinations and permutations, you are required to input the right choice as the answer. This question is a classic example of how the DILR section of the CAT has changed. There is now little difference between data interpretation and logical reasoning. Let us see if you can solve this CAT previous year paper problem from CAT 2018 Slot 1 - DILR.
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 : In how many diﬀerent ways can the ATM serve a customer who gives 500 rupee notes as her preference? [TITA]
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.
There should be more 500 rupee notes than the sum of the other two. Since there is no condition that says that we should have at least one note of every denomination, we could have all notes to be of the Rs. 500 denomination.
After this, we go for the number of Rs. 500 notes to be 9. This gives us Rs. 4500. Now, we need to get the final Rs. 500 with Rs. 200 and Rs. 100 notes.
We can have 5 Rs. 100 notes, or 3 Rs. 100 notes and one Rs. 200 note, or 1 Rs. 100 note and 2 Rs. 200 notes.
After this, we go for the number of Rs. 500 notes to be 8. This gives us Rs. 4000. Now, we need to get the final Rs. 1000 with Rs. 200 and Rs. 100 notes.
We can have 5 Rs. 200 notes; or 4 Rs. 200 notes and two Rs. 100 notes; or 3 Rs. 200 notes and 4 Rs. 100 notes.
If we go for 2 Rs. 200 notes we would need 6 Rs. 100 notes making it a total of 8 non Rs. 500 notes. This is not possible.
So, with 8 Rs. 500 notes only 3 options are possible.
Let us see if we can get any combination with 7 Rs. 500 notes. This amounts to Rs. 3500. We need to get Rs. 1500 from other notes.
Even if we went for least number of non-Rs 500 notes – we would need 7 Rs. 200 notes and one Rs. 100 note.
This is not possible as we would have more non-Rs. 500 notes than Rs. 500 notes.
So, we have 7 different ways.
The question is "In how many diﬀerent ways can the ATM serve a customer who gives 500 rupee notes as her preference? [TITA]"
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