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?
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.
ReplyDeleteYou got it. David is lying, dirty butter.
ReplyDeleteIf 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.