If x and y satisfy the equations |x| + x + y = 15 and x + |y| − y = 20, then (x – y) equals

P, Q, R and S are four towns. One can travel between P and Q along 3 direct paths, between Q and S along 4 direct paths, and between P and R along 4 direct paths. There is no direct path between P and S, while there are few direct paths between Q and R, and between R and S. One c…

A vessel contained a certain amount of a solution of acid and water. When 2 litres of water was added to it, the new solution had 50% acid concentration. When 15 litres of acid was further added to this new solution, the final solution had 80% acid concentration. The ratio of wat…

If (x + 6√2)^(1/2) − (x − 6√2)^(1/2) = 2√2, then x equals

The sum of the infinite series (1/5)((1/5) − (1/7)) + (1/5)²((1/5)² − (1/7)²) + (1/5)³((1/5)³ − (1/7)³) + …… is equal to

If x and y are real numbers such that 4x² + 4y² – 4xy – 6y + 3 = 0, then the value of (4x + 5y) is

When 3³³³ is divided by 11, the remainder is

If m and n are natural numbers such that n > 1, and mⁿ = 2²⁵ × 3⁴⁰, then m − n equals

A bus starts at 9 am and follows a fixed route every day. One day, it traveled at a constant speed of 60 km per hour and reached its destination 3.5 hours later than its scheduled arrival time. Next day, it traveled two-thirds of its route in one-third of its total scheduled trav…