Masters' Union MUSAT · Paper 4

The visibility score of a digital campus poster is directly proportional to its screen area and inversely proportional to the square of the viewer’s distance from it. Poster A is on a $24 \text{ cm} \times 15 \text{ cm}$ screen and viewed from $6$ m. Poster B is on a $30 \text{ cm} \times 18 \text{ cm}$ screen and viewed from $9$ m. What is the ratio of the visibility score of Poster B to Poster A?

In a cohort of 120 freshers, 58 joined the Marketing club, 52 joined the Finance club, and 45 joined the Analytics club. Exactly 28 students joined exactly two of these clubs, and 12 students joined all three clubs. How many students did not join any of the three clubs?

A campus store has startup stickers in 4 designs and 3 colours, with many stickers of each design-colour combination. Without looking, what is the minimum number of stickers a student must pick to guarantee that at least two stickers have both the same design and the same colour?

A $180$-metre-long metro train is running at $54$ km/h. It crosses a $120$-metre-long platform completely. How much time does it take to cross the platform?

A campus merchandise stall finds that if it sells $x$ hoodies in a day, the price per hoodie must be set at ₹$(120 - 2x)$. What is the maximum possible daily revenue from hoodie sales?

A campus coding club uses base-7 numbers for its event IDs. If two IDs, $(356)_7$ and $(124)_7$, are added, what is the result in base 7?

A student-run food delivery club tracked new app sign-ups from two sources across four quarters. Organic sign-ups were: Q1 = 300, Q2 = 360, Q3 = 420, Q4 = 520. Paid-ad sign-ups were: Q1 = 200, Q2 = 240, Q3 = 300, Q4 = 380. Paid-ad sign-ups for the year were what percentage of organic sign-ups for the year?

A MUSAT prep centre has three batches. Batch A has 15 students with an average score of 76, Batch B has 25 students with an average score of 84, and Batch C has 20 students. If the combined average score of all 60 students is 82, what is the average score of Batch C?

The line graph for weekly sign-ups on a startup’s app is described as follows: Week 1 = 180, Week 2 = 220, Week 3 = 210, Week 4 = 270, Week 5 = 300, Week 6 = 290. Between which two consecutive weeks was the steepest increase in sign-ups recorded?

At a campus merchandise pop-up, the units sold were: Notebooks $= 400$, Bottles $= 300$, Hoodies $= 200$. The return rates were: Notebooks $= 5\%$, Bottles $= 10\%$, Hoodies $= 15\%$. The profit per unit that was not returned was: Notebook $=$ ₹30, Bottle $=$ ₹80, Hoodie $=$ ₹150. What was the total profit from the units that were not returned?

A line graph shows monthly app installs for a finance-learning app from January to June. The values are: January 1,200; February 1,800; March 1,500; April 2,400; May 2,700; June 2,300. During which month-to-month period did the app see the steepest increase in installs?

The line graph for monthly active users of a campus finance app is described as follows: January = 12,000, February = 15,000, March = 14,000, April = 19,000, May = 21,000, and June = 18,000. Between which two consecutive months was the steepest change in users recorded?

A B-school fest team released applications and shortlist rules for three startup challenge tracks. Applications received were: Product Track = 280, Finance Track = 360, and Creator Track = 300. The shortlist percentages were: Product = 25%, Finance = 20%, and Creator = 30%. Among shortlisted candidates, the male:female ratios were: Product = $3:4$, Finance = $5:4$, and Creator = $2:3$. How many female candidates were shortlisted in Product and Finance tracks together?

In a single-file queue at a passport-photo booth, Aman is 14th from the front and Bina is 17th from the back. Exactly 5 people stand between Aman and Bina. What is the smallest number of people the queue could have?

Eight volunteers, Tanmay, Urvi, Vihaan, Wahida, Yash, Zainab, Kriti and Hemant, stand in a single row at a registration desk, all facing south. Left and right are the volunteers' own: each volunteer's right hand points west and left hand points east.

Exactly two volunteers stand to Zainab's left.

Tanmay is third to the right of Zainab, and Kriti is immediately to the right of Tanmay.

Vihaan is at one of the two ends of the row, but not next to Kriti.

Wahida and Yash are neighbours, and Yash is not next to Zainab.

Hemant is somewhere to the left of Urvi.

Who is second to the right of Yash?