1. Freda typed 40 pages in 240 minutes, that is one every 6 minutes. Emily typed 40 pages in 200 minutes, that is one every 5 minutes. Emily's speed is 1.2 (=6/5) times faster than Freda's, so in order for them to finish at the same time, Emily will get 6/11 of the total number of pages, while Freda will get 5/11. For a total of 77 pages, Emily will get 42, Freda will get 35 and they will both finish at 210 minutes.

2. a. Tom asks if the number is greater than 50, Dick lies and says "No". Tom thinks the number is smaller than 50, when in fact it's greater.

b. Tom asks if it's a multiple of 4, Dick lies again and says "Yes". Tom thinks the number is a multiple of 4 smaller than 50, when in fact it's not a multiple of 4, and it's greater than 50.

c. Tom asks if it's a perfect square, Dick surprisingly decides to be truthful and says "Yes". Tom thinks the number is a perfect square, smaller than 50 (and greater than 8) and a multiple of 4, so either 16 or 36. However, the number is actually a perfect square greater than 50 (and less than or equal to 100) and not a multiple of 4, which means it can only be the number 81.

d. Tom asks if the first digit is a 3. If Dick says the truth ("No"), Tom will wrongly guess the number is 16. If Dick stays loyal to his name, Tom will wrongly again assume the number is 36. In either case, he should probably get a new friend.

*Edited by Gil_Galad (Tue Nov 11 2014 08:06 AM)*