Problem Solving

swerve wrote:On a weekend, 6 college friends went skiing and evenly split the cost of their cabin. If the amount paid by each person was an integer, which of the following could not have been the cost of the cabin?

A. $126
B. $156
C. $218
D. $648
E. $1,728

If the total cost is divisible by 6, then each of the 6 friends will pay an integer amount.

Take answer choice A ($126) for example.
126 is divisible by 6
$126/6 = $31
So, each person pays an integer amount ($31 each)
ELIMINATE A

The question is basically asking us to find the answer choice that is NOT divisible by 6

CONCEPT #1: A number is divisible by 6 if that number is divisible by 2 AND by 3
We can see that all 5 answer choices are divisible by 2.

CONCEPT #2: A number is divisible by 3 if the SUM OF THE DIGITS of that number is divisible by 3
Take answer choice B ($156) for example.
The sum of the digits = 1 + 5 + 6 = 12
Since 12 is divisible by 3, we can conclude that 156 is divisible by 3
ELIMINATE B

Answer choice C ($218)
The sum of the digits = 2 + 1 + 8 = 11
Since 11 is NOT divisible by 3, we can conclude that 218 is NOT divisible by 3
If 218 is NOT divisible by 3, then 218 is also NOT divisible by 6

Answer: C

Cheers,
Brent