List of practice Questions

In a meeting held by ACS, there were 10 attendees. If N attendees are selected to deliver speeches during the meeting, and it is given that N is a positive integer, what is the value of N?
Statement 1: N is a multiple of 3.
Statement 2: There are 210 ways to select the N attendees to deliver speeches.

Peter takes 4 hours longer than Samuel to prepare 30 sandwiches. Working together, they can make 50 sandwiches in 150 minutes. How long would it take Peter alone to make 40 sandwiches?

The sum of two numbers is 16. Thrice the smaller number is greater than twice the larger by 3. The product of the numbers is ?

What is the remainder when \(43^{380}\) is divided by 20?

If \(2x^2 + 10 = 7y - 5x\) and \(4y^2 - 5y = -(7x + 17)\), then find the value of \((x + y)\)?

Find the remainder when \(2^{88} \times 5^{41}\) is divided by 7.

Nihal took a 1,00,000 loan at 15% interest per year. If he repays in two equal yearly instalments, the amount per instalment is x. If he repays in three equal yearly instalments, the amount per instalment is y. What is the approximate difference between x and y?

Consider a function f satisfying f(x * y) = f(x) + f(y) where x, y are positive integers, then what is the value of \( \frac{f(3) + f(12){f(12) - f(4) + f(2)} \)?}

A regular dodecagon (12-sided regular polygon) is inscribed in a circle of radius \( r \) cm as shown in the figure. The side of the dodecagon is \( d \) cm. All the triangles (numbered 1 to 12 in the figure) are used to form squares of side \( r \) cm, and each numbered triangle is used only once to form a square. The number of squares that can be formed and the number of triangles required to form each square, respectively, are: