BARC Quiz 4: Solution and Q&A

Quiz 4 - Part 1

1. The product of two consecutive negative even integers is 24. Find the sum of the numbers.
2. The sum of the digits of a two-digit number is 11. When the digits are reversed, the new number exceeds the original number by 9. From the original number, calculate the product of tens digit to the square of the units digit.
3. Find two consecutive positive even integers such that the square of the second, decreased by twice the first is 124. Find the smaller number.
4. One number is 25 greater than a second number. If the lesser number is subtracted from 3 times the greater number, the difference is 195. Find the product of the two numbers.

Quiz 4 - Part 2

1. Today, I am one more than eleven times as old as my son. Nine years from now, I will be seven more than three times as old as him. How old is my son?
2. Three times Dick's age plus Tom's age equals twice Harry's age. Double the cube of Harry's age is equal to three times the cube of Dick's age added to the cube of Tom's age. Their respective ages are relatively prime to each other. How old is Harry?
3. Twice the larger of two numbers is three more than five times the smaller, and the sum of four times the larger and three times the smaller is 71. What is the smaller number?

Quiz 4 - Part 3

1. At what time between three and four o’clock is the minute hand the same distance from VIII as the hour hand is from XII?
2. It is now between 9 am and 10 o'clock am. In 4 minutes, the hour hand of the clock will be directly opposite the position occupied by the minute hand 3 minutes ago. What time is it?
3. Dr. Reed, arriving late at the lab one morning, pulled out his watch and said, “I must have it seen to. I have noticed that the minute and the hour hand are exactly together every 65 minutes.” Does Dr. Reed’s watch gain or lose, and how much per hour?