# Problem from Queendom

1. Apr 21, 2004

### recon

I'm not able to solve this problem that appears as Question 23 on the queendom Classical IQ Test. Could someone please help?

One hundred businesspeople gather at a meeting. 85 of them carry a cellular phone, 80 of them have a beeper, 75 of them speak at least two languages and 70 of them wear a suit. Therefore, a certain number of them have all of the above: a cell phone AND a beeper AND speak at least two languages AND wear a suit. Out of these 100 businesspeople, what is the least possible number who have all of the above?

The choices are: 10 - 15 - 17 - 18 - 20.

2. Apr 21, 2004

### uart

I'll vote for 10 :)

3. Apr 21, 2004

### uart

Start with 85 and 80 and try to "squeeze them into a space of 100" with the minumum possible overlap. You find the minumum overlap of the tw oattributes is 85+80-100 = 65.

Now you have a new group of 65 which have both attributes. Try to combine this group of 65 with the group of 75 while keeping the overlap (corresponding to people possessing all three attributes) to a minimum. You get a minimum overlap of 65+75-100=40.

Finally try to combine this group of 40 with the group of 70 and you get a minimum overlap (corresponding to persons having all four attributes) of 70+40-100=10

4. Apr 21, 2004

### Njorl

15 have no cells, but have everything else
20 have no beeper, but have everything else
25 speak 1 language, but have all the other stuff
30 have no suits, but have all other stuff

add 'em up to 90, subtract from 100 and you get 10

Njorl