Masters' Union MUSAT · Paper 3

A campus analytics team recorded the number of app downloads on 7 launch days as: 16, 29, $x$, 21, 24, 21, 30. If the mean number of downloads is 24, what is the median of the data set?

The weekly sales numbers of seven student vendors are 32, 18, 26, 40, 22, 28, and $x$. If the mean sales number is 28, what is the median of the seven sales numbers?

The average score of 28 students in a MUSAT mock test was 72. Later, one student's score was corrected, and the average increased to 74.5. If the corrected score was 91, what was the original score recorded for that student?

A box contains cards numbered from 1 to 30. What is the minimum number of cards that must be drawn to guarantee that at least two drawn cards have a sum of 31?

A grouped bar graph shows quarterly sales, in ₹ lakh, of a campus apparel brand through Online and Offline channels. Q1: Online 80, Offline 50; Q2: Online 95, Offline 65; Q3: Online 110, Offline 70; Q4: Online 115, Offline 95. The total Offline sales for the year were what percentage of the total Online sales?

A grouped bar graph shows quarterly sales, in ₹ thousand, for a campus merchandise store through Online and Pop-up Stall channels. Q1: Online 120, Stall 150; Q2: Online 160, Stall 140; Q3: Online 180, Stall 210; Q4: Online 220, Stall 200. What was the total Online sales in the quarters where Stall sales were higher than Online sales?

A founder-talk event has 200 seats in total. However, 40 seats are reserved for speakers, judges, and the organising team, so only the remaining seats are sold. Among the sold seats, student tickets and outsider tickets are in the ratio $5:3$. Student tickets cost ₹300 each, while outsider tickets cost ₹500 each. What is the total ticket revenue from the event?

At a demo day, 120 visitors could sign up for one or more of three founder labs: AI, Consumer, and Climate. 6 visitors did not sign up for any lab and only visited the investor desk. Among the lab sign-ups, 64 chose AI, 58 chose Consumer, and 46 chose Climate. Also, 24 chose both AI and Consumer, 20 chose both AI and Climate, 18 chose both Consumer and Climate, and 8 chose all three labs. How many visitors chose exactly one founder lab?

At a business bootcamp, 180 students applied and 60% were shortlisted. Among the shortlisted students, the ratio of boys to girls was $5:4$. The organisers formed teams of exactly 3 shortlisted students each. Every shortlisted student was assigned to a team, every team had at least one girl, and no team had three girls. How many teams had exactly two girls?

A business bootcamp shared two linked data sets. The total registrations were: Delhi campus 180, Mumbai campus 150, and Bengaluru campus 120. The ratio of paid registrations to scholarship registrations was $2:1$ for Delhi, $3:2$ for Mumbai, and $5:1$ for Bengaluru. If each paid registration brings ₹2,000 in revenue and scholarship registrations bring no revenue, what was the total revenue from paid registrations?

A B-school prep company ran three weekend bootcamps. The table gives total participants: North Zone 180, West Zone 240, South Zone 150. A second data note says the ratio of Paid participants to Scholarship participants was: North Zone $2:1$, West Zone $3:1$, South Zone $4:1$. Only paid participants paid a fee of ₹700 each. What was the total fee collected from paid participants across all three zones?

A signpost at a crossroads has four arms labelled North, East, South and West. A lorry knocks into it, and the whole post swings round so that the arm labelled North now points South-East. A cyclist who does not notice the damage follows the arm labelled West. In which direction is the cyclist actually riding?

In the coded inequalities below, $A * B$ means $A \ge B$, $A @ B$ means $A = B$, $A \# B$ means $A > B$, and $A \$ B$ means $A < B$. If the statement is $L * M @ N \# O$, which conclusions follow? Conclusions: I. $L > O$ II. $L > M$ III. $L = M$

Using the symbols below, $P + Q$ stands for 'P is Q's mother', $P \times Q$ for 'P is Q's brother', $P \div Q$ for 'P is Q's wife' and $P - Q$ for 'P is Q's son'. Given $R \div S - T + U \times V$, where V is female, what is R to V?