If c = 16x/y + 49y/x for some non-zero real numbers x and y, then c cannot take the value

Two ships are approaching a port along straight routes at constant speeds. Initially, the two ships and the port formed an equilateral triangle with sides of length 24 km. When the slower ship travelled 8 km, the triangle formed by the new positions of the two ships and the port…

The average of all 3-digit terms in the arithmetic progression 38, 55, 72, ..., is

The lengths of all four sides of a quadrilateral are integer valued. If three of its sides are of length 1 cm, 2 cm and 4 cm, then the total number of possible lengths of the fourth side is

A school has less than 5000 students and if the students are divided equally into teams of either 9 or 10 or 12 or 25 each, exactly 4 are always left out. However, if they are divided into teams of 11 each, no one is left out. The maximum number of teams of 12 each that can be fo…

Suppose k is any integer such that the equation 2x² + kx + 5 = 0 has no real roots and the equation x² + (k − 5)x + 1 = 0 has two distinct real roots for x. Then, the number of possible values of k is

Consider six distinct natural numbers such that the average of the two smallest numbers is 14, and the average of the two largest numbers is 28. Then, the maximum possible value of the average of these six numbers is

The arithmetic mean of all the distinct numbers that can be obtained by rearranging the digits in 1421, including itself, is

Let r be a real number and f(x) = 2x − r if x ≥ r, and f(x) = r if x < r. Then, the equation f(x) = f(f(x)) holds for all real values of x where