TheCATExam
Sign in

CAT 2023 Slot 2 — QA Question 15

Change in AverageEasy

If a certain amount of money is divided equally among n persons, each one receives Rs. 352. However, if two persons receive Rs. 506 each and the remaining is divided equally among the other persons, each of them receive less than or equal to Rs. 330. Then, the maximum posssible value of n is:

Answer & solution

Answer: 16

Solution

Easy

The total pot is fixed at 352n352n (everyone got 352352). In the second scheme, two people grab 506506 each, leaving the rest to share. Write the inequality "average of the remaining ≤330\le 330", solve for nn, and take the largest integer that works.

1

Total money from the equal split:

Total=352n\begin{aligned} &\text{Total}=352n \end{aligned}
2

Remove the two large shares and spread the rest over the other (n−2)(n-2) people:

Two get=2×506=1012Each of the rest=352n−1012n−2≤330\begin{aligned} &\text{Two get}=2\times506=1012\\ &\text{Each of the rest}=\frac{352n-1012}{n-2}\le 330 \end{aligned}
3

Solve the inequality:

352n−1012≤330(n−2)352n−1012≤330n−66022n≤352n≤16\begin{aligned} &352n-1012\le 330(n-2)\\ &352n-1012\le 330n-660\\ &22n\le 352\\ &n\le 16 \end{aligned}

The maximum possible value of nn is 16\mathbf{16}.

CAT 2023 Slot 2 QA Q15: If a certain amount of money is divided equally among n persons, each one receives Rs. 352. However, if two pe — Solution | TheCATExam