### Brain Teasers

# The Dishonest Grocer

Quinn, Ralph, and Steve work at a grocery store that sells apples, bananas, and oranges. Quinn says, "Seven apples and five bananas cost the same as six oranges." Ralph says, "Four apples and nine oranges cost the same as five bananas." Steve says, "Six oranges and three bananas cost the same as four apples." Only one is lying...but who?

### Hint

The three values equivalents must be considered in pairs. The one false equivalent leads to two impossible situations, while the pair of true equivalents is a possible situation.### Answer

Quinn is lying.Let a equal the price of apples, b equal the price of bananas, and o equal the price of oranges. Quinn is saying that 7a + 5b = 6o. Ralph is saying that 4a + 9o = 5b. Steve is saying that 6o + 3b = 4a.

Combining Quinn's and Ralph's statements, we get 11a = -6o. This is impossible.

Combining Ralph's and Steve's statements, we get 15o = 2b. This is possible.

Combining Quinn's and Steve's statements, we get 8b = -3a. This is impossible.

This means that either Quinn is lying, or Ralph and Steve are both lying. But there only can be one liar: obviously Quinn.

Hide Hint Show Hint Hide Answer Show Answer

## What Next?

View a Similar Brain Teaser...

If you become a registered user you can vote on this brain teaser, keep track of which ones you have seen, and even make your own.

### Solve a Puzzle

Comments hidden to avoid spoilers.

## Follow Braingle!