Additions of Variables

topspin360 wrote:

An eccentric casino owner decides that his casino should only use chips in $5 and $7 denominations. Which of the following amounts cannot be paid out using these chips?

A) $31
B) $29
C) $26
D) $23
E) $21

To determine the amount that CANNOT be paid out, we'll eliminate the amounts that CAN be paid out.

When we scan the 5 answer choices, we can see that we can eliminate 3 of them almost immediately.
We can pay out $21 using three $7 chips, so ELIMINATE E.
Since $26 is $5 greater than $21, we can pay out $26 using three $7 chips and one $5 chip. ELIMINATE C.
Since $31 is $10 greater than $21, we can pay out $31 using three $7 chips and two $5 chips. ELIMINATE A.

This leaves us with B and D.
We can pay out $29 using two $7 chips, and three $5 chips so ELIMINATE B.

By the process of elimination (POE), the correct answer must be D

Cheers,
Brent