### Brain Teasers

# Some Old Books

The local library decided to hand out some of its old books to its 1400 borrowers. To each of the female borrowers they gave 6 books and to each male borrower they gave 4 books. If only half of the females in town and three quarters of the males in town accepted the books how many books were given away?

### Hint

Choose a random number of girls and then work it out.### Answer

4200 books.Since each female was offered 6 books but only half of them accepted, on an average, each of them got 3 books. Also, since each male was offered 4 books and three quarters accepted, again an average male got 3 books. Since females and males got the same number of books per person, it doesn't matter how many females there actually are.

So, total books given away = 1400 x 3 = 4200.

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## Comments

you're going to have to give a little more info than "choose a random number of girls". also, according to the info you have given, the only way to arrive at your answer is if all 1400 borrowers were female and there are no men in town.

you can come up with almost any answer to this.

The answer is correct no matter how many women there are. If x=number of women, then (1400-x)= number of men. Therefore the number of books given out to women is 6*(0.5x) or 3x. The number of books given to men is 4*0.75*(1400-x) or 4200-3x. The total of books is therefore always 4200!

yeah, what he said..

R

Oops! I pressed "Add comment" too soon. I was going to say... Really hard teaser, 10 out of 10.

I say it's the best teaser I've seen so far!! I thought there was nowhere enough information; it's BRILLIANT!

If there are 1000 females amongst the 1400 borrowers offered the deal, and half accepted, the females received 3000 books (500 x 6), leaving 400 men, of which 300 accepted, thus giving the males 900 books (300 x 3) for a total of 3900 books, sorry, a poorly written riddle.

Horseman the males got 4 books each! Thats 300 x 4 = 1200. 3000 + 1200 = 4200.

The only thing misleading about the teaser is the assumption that the 1400 borrowers were the entire population of the town. I think deleting the reference to the town and replacing it with a reference to borrowers would make it clearer.

Great teaser because of the misdirection involved. I read the clues and immediately said to myself 'there's not enough information to solve this' Then I read the first couple of comments about a random number of girls and it suddenly struck me that it might work for any number. I tried the algebraic approach an realised that x+y = 1400 people and 3x+3y = number of books. Very cute!!!

The only thing misleading about the teaser is the assumption that the 1400 borrowers were the entire population of the town. I think deleting the reference to the town and replacing it with a reference to borrowers would make it clearer.

Great teaser because of the misdirection involved. I read the clues and immediately said to myself 'there's not enough information to solve this' Then I read the first couple of comments about a random number of girls and it suddenly struck me that it might work for any number. I tried the algebraic approach an realised that x+y = 1400 people and 3x+3y = number of books. Very cute!!!

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