## Monday, January 16, 2006

### Only three are good friends

Four friends were shown a number. Here's what they had to say:

Andy: It has two digits
Betty: It goes evenly into 150
Cathy: It is not 150
David: It is divisible by 25

It turns out that one (and only one) of the friends is lying. Which friend lied?

1. OK, I'll take a stab at this one. David is lying. Both 15 and 30 are factors of 150, less than 150, and 2 digits, but they are not divisible by 25.

2. You got it. David is lying, dirty butter.

If A was lying, the number would have three digits (1 digit would not be divisible by 25). But the only number with 3 digits that goes evenly into 150 is 150. So either B or C would by lying as well.

If B was lying, then the number does not go evenly into 150. But then either A or D must be lying, because that leaves 25, 50, 75, etc...

If C was lying, then the number is 150. But then A would also by lying as 150 has three digits, not two.

So that leaves D. For example if the number was 10, then D would be lying, but everything else works out.

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