Mesa MSAT · Paper 5

The profit curve of a small merchandise stall is modelled by the quadratic equation $2x^2 - 7x + 3 = 0$, where the two roots are $\alpha$ and $\beta$. What is the value of $\alpha^2 + \beta^2$?

A campus startup divides ₹96,000 between its marketing and operations teams in the ratio $7:5$. Later, ₹8,000 is transferred from marketing to operations, and an additional ₹4,000 is added only to marketing. What is the new ratio of marketing funds to operations funds?

A student-run café finds that if it sells $x$ premium snack boxes in a day, its total profit in rupees is given by $P = x(90 - x)$. What is the maximum possible profit?

Arjun can complete $25\%$ of a digital campaign in $6$ days. Bhavna can complete the remaining $75\%$ of the same campaign in $12$ days. If they work together, how many days will they take to complete $\frac{5}{6}$ of the campaign?

How many integer values of $x$ satisfy both inequalities: $-3(2x-5)<21$ and $-2(x-7)\ge4$?

The weekly pitch scores of 7 students are: 18, 22, 15, $x$, 20, 22, 17. If the mean score is 20, what are the median and mode respectively?

Arjun, Bina and Cyrus were paid ₹7,800 for setting up a pop-up store. Arjun can complete the work alone in 12 days, Bina in 18 days, and Cyrus in 24 days. They worked together for the same number of days, so the wages are shared in proportion to the work done. What is Bina’s share?

The average monthly stipend of 18 startup interns is ₹12,500. One intern leaves, and the average stipend of the remaining 17 interns becomes ₹12,400. What was the stipend of the intern who left?

A small venture fund places ₹40,000 in a 1.5-year deposit at 20% per annum, compounded half-yearly. What is the difference between the compound interest earned and the simple interest that would have been earned at the same annual rate for the same time?

A campus merchandise store invests ₹40,000 in a short-term fund that pays 12% per annum, compounded half-yearly. What is the difference between the compound interest earned and the simple interest earned on the same principal for 1 year at 12% per annum?

Pitch Deck is to Investor as Portfolio is to:

Read the statement and choose which conclusion definitely follows.

Statement: Every team shortlisted for the Mesa Venture Lab must submit a one-page business model. Some shortlisted teams are invited for a founder interview. No team invited for a founder interview skips the mentor feedback round.

Conclusions:

I. All shortlisted teams submit a one-page business model.

II. Some teams that submit a one-page business model are invited for a founder interview.

III. All teams that submit a one-page business model are invited for a founder interview.

Rhea starts from the registration desk at a business fest. She walks 8 m north, turns right and walks 15 m, turns right again and walks 3 m, then turns right and walks 3 m. How far and in which direction is she from the registration desk?

In a certain code, each letter of a word is shifted forward by its position in the word. For example, the 1st letter is shifted by 1, the 2nd by 2, the 3rd by 3, and so on. How will PITCH be written in this code?

Find the odd one out.

In the following coded inequalities, the symbols have these meanings: $A \;@\; B$ means $A \ge B$, $A \;\#\; B$ means $A = B$, $A \;\text{\textdollar}\; B$ means $A < B$, and $A \;\%\; B$ means $A > B$.

Statements: $P \;@\; Q$, $Q \;\#\; R$, $R \;@\; S$.

Conclusions: I. $P \;\%\; S$ II. $P \;\#\; S$ III. $Q \;@\; S$

Which conclusions definitely follow?

A rectangular sheet is folded once from left to right along its vertical centre line, and then folded once from bottom to top along its horizontal centre line. A single round hole is punched in the folded sheet, slightly to the right of the vertical fold line and slightly above the horizontal fold line. When the sheet is completely unfolded, what pattern of holes will be seen?

A startup’s server runs a security check that generates the code $29^{41}$. For storage, only the remainder when this code is divided by 17 is kept. What remainder will be stored?

Six founders, Aarav, Bina, Charu, Dev, Esha and Farhan, are sitting around a circular table facing outward. Aarav sits second to the left of Bina. Charu sits immediately to the right of Aarav. Dev sits opposite Charu. Esha sits immediately to the left of Dev. Who sits opposite Farhan?

A large cube is painted on the top face and all four side faces, but the bottom face is left unpainted. It is then cut into $5 \times 5 \times 5$ equal smaller cubes. How many smaller cubes will have exactly two painted faces?