June 2021

If a pair of dice is tossed 6 times, what is the probability of obtaining a total of 7 or 11 twice, a matching pair once, and any other combination 3 times?

To encourage Elmer’s promising tennis career, his father offers him a prize if he wins (at least) two tennis sets in a row in a three-set series to be played with his father and the club champion alternately:

according to Elmer’s choice. The champion is a better player than his father. Which series should Elmer choose?

During the last election, the total number of votes in a certain municipality was 12,400. Had 2/5 of the supporters of administration candidate stayed away from the polls and 1/2 of the supporters of opposition candidate behaved likewise, the administration candidate’s majority over the other would have been reduced by 100. How many votes did administration candidate received?

Stations A and B are 120 miles apart on a single-track railroad. At the same time that a train leaves A for B at 25 mph, a train leaves B for A at 15 mph. Just as the train leaves A, a botfly flies from the front of the engine straight toward the other train at 100 mph. On meeting the second train it immediately turns back and flies straight for the first train. It continuous to fly back and forth with undiminished speed until it is crushed in the eventual collision.

At an ordinary rate a man can row the distance from Pasig to Manila, about 15km, in 5 hours less time than it takes him to return. Could he double his rate, his time to Manila would only be one hour less than his time to Pasig. What is the rate of Pasig River?

The geometric mean of two numbers is 8 and the arithmetic mean is 17. Find one of the numbers.

The king’s minter boxes his coins 100 to a box. In each box he puts 1 false coin. The king suspects the minter and from each of 100 boxes draws a random coin and has it tested. What is the chance the minter’s peculations go undetected?

What time between 2 and 3 o’clock will the angle between the hands of the clock be bisected by the line connecting the center of the clock and the 3 o’clock mark?

A contractor has 50 men of the same capacity at work on a job. They can complete the job in 30 days, but the contract expired in 20 days. He decides to put 20 additional men. If all the men get P600/day for a full or part day and if the liquidated damages are P50,000 for every full or part of the day he requires over his contract time. How much money he saves or loss by putting 20 additional men?

Find the values of b for which the line y = 3x + b and the parabola y² = 5x will have no common point.