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CAT Previous Year Paper | CAT Quants Questions | Question 25

Do you get stumped by those questions that look vague even after multiple readings? There are some questions where rather, than the formulaic approach something intuitive or out of the box works better. This question discusses about a person who distributes toffees following a certain pattern. We need to find the total number of toffee he initially had. To practice more questions with detailed video solutions like these check out the 2IIM questions bank and give your CAT preparation the right direction.

Question 25 : A gentleman decided to treat a few children in the following manner. He gives half of his total stock of toffees and one extra to the first child, and then the half of the remaining stock along with one extra to the second and continues giving away in this fashion. His total stock exhausts after he takes care of 5 children. How many toffees were there in his stock initially?

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Explanatory Answer

Let us take 5th kid has 2 toffees
Because we know that after 5th toffee his stock exhausts.
So only if the 5th kid has 2 toffees, he can give away half of it and 1 extra = 0
Then for 4th kid, (2+1) × 2 = 6 (Since we are moving in reversing order)
3rd = 14 and 2nd = 30 and 1st kid = 62

The answer is, " 62"

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