NinetynineCAT 2020 Slot 1 QA Q25 Equations
Question 25 of the Quantitative Ability (QA) section, CAT 2020 Slot 1, with CAT's official answer and a worked solution.
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?
TITA: type in the answer. There are no options and no negative marking.
Answer: 62 Equations TITA
Solution
- Work backwards. If n toffees remain before a child, after giving \(\frac n2+1\), \(\frac n2-1\) remain, so \(n = 2(\text{after}+1)\).
- After child 5 there are 0, so before child 5: 2; before 4: 6; before 3: 14; before 2: 30; before 1: 62.
- Initial stock = 62.
Shortcut. Before k children from the end: \(2^{k+1}-2\); for k = 5 that is 62.