Q. A,B and C buy a box of chocolates each. Mr.A distributes the chocolates in his box equally among his 6 children, Mr.B among his 7 children and Mr.C among his 8 children. Then they pool their respective remaining number of chocolates and find that they could distribute these equally among themselves or equally among themselves when a fourth friend D joins them. Which of the following can be the total amount that the three friends spent on the chocolates if each chocolate costs exactly Rs. 2.50 (Assume that the only cost of a box of chocolates is that of the chocolates in it)
The railroad bridge across the Futile Mire has a northbound track and a southbound track. The tracks are parallel and exactly 2 miles long. Anyone attempting to cross the bridge on foot must stay between the rails on the chosen track. It is not possible to step outside the rails or to jump to the other track.
One day Tom and Sue try to walk across the bridge, Tom heading north on the northbound track, and Sue heading south on the southbound track. The athletic Sue can run twice as fast as the portly Tom. All trains run at the same constant speed.
When Tom and Sue are 1 mile apart they both hear trains whistles behind them. Trains are approaching on both tracks. Tom and Sue can just escape by running to either end of the bridge. How far is each train from the tunnel?
Q. In the middle of a vast prairie, a truck is stationed at the intersection of two perpendicular straight highways.
The truck travels at 50 miles per hour along the highways and at 14 miles per hour across the prairie.
Consider the set of points that can be reached by the firetruck within six minutes. The area of this region is m/n square miles, where m and n are relatively prime positive integers.
Q. There is a grid of 20 squares by 10 squares each having unit edge length. How many rectangles are there having area 'x' sq units,where x is an odd integer?
Note that square is a rectangle.
Solution
total number of rectangles including squares of odd area
= (20+18+16+14+12+10+8+6+4+2)(10+8+6+4+2) = 110*30 = 3300