House Cleaning

Leo's mom asks Dr. Hong, Leo and Angela to clean up the house. If Dr. Hong and Leo work together, they can complete the task in 1.5 hours. If Dr. Hong and Angela work together, it would take them 1.75 hours. If Leo and Angela work together, it would take them 4.2 hours. If all three of them work together, how long does it take to clean up the house?  

Favorite Math Subjects

30 CMM students get together and discuss their favorite math subjects. 23 of them like geometry; 29 of them like algebra; 19 of them like probability. At most how many students like all three subjects?

Logo Shot

In the expression LOGO + SHOT = HARD, each letter represents a single digit number from 0 to 9. Different letters represent different numbers. L, S and H cannot be zero. What's the difference between the largest and smallest values of HARD?