1. Emily and Freda are two typists working in the same office. One day they are given 80 pages for typing. They divide the work equally and start typing. Emily is more experienced, and therefore types faster, and so she finishes 40 minutes before Freda, who takes four hours to do the work. The next day they are given 77 pages for typing. How should the work be divided so that the two girls finish at the same time?

2. Tom is trying to find out where his friend Dick lives. All he knows is that it is in a street where the houses are numbered from 8 to 100 inclusive. Tom asks: "Is it greater than 50?" Dick answers, but he lies. Tom then asks: "Is it a multiple of 4?" Again Dick answers, and again he lies. Then Tom says: "Is it a perfect square?" Dick answers and this time he tells the truth. Finally Tom asks: "Is the first digit a 3?"
After Dick replies (truthfully or not, we don't know), Tom tells him the number, but he is wrong. But you know, don't you?

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.

Quite correct, Gil Galad. Well reasoned.

1. Freda takes 4 hours (240 mins) to type 80 pages = 240/40 = 6 mins a page.
Emily takes 3 hours 20 mins (200 mins) = 200/40 = 5 mins a page.

So the work must be divided in the ratio 5 : 6 to achieve parity. Divide 77 into 11 parts, 7 pages per part.
5 parts (35 pages) to Freda, and 6 parts (42 pages) to Emily.
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2. Begin by listing multiples of 4: list 1a - under 50; list 1b - over 50.
Then list squares: 2a - under 50; list 2b - over 50.
Then circle which numbers appear on both list 1s, and both list 2s.
Then decide what Dick's answers must have been, and how Tom
arrived at thinking the number might begin with 3.