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Logic Systems |
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# Logic Systems

(1) Gary got 40% off.

(2) Gary did not buy a computer.

(3) Bob bought a movie.

(4) Jen did not buy a computer.

(5) Jen got 35% off.

(6) The television had a 60% markdown.

(7) Barb did not get 55% off.

(8) The computer did not have a 20% markdown.

(9) The CD did not have a 35% markdown.

## Step 1:

You know that Gary got 40% off (1), that Jen got 35% off (5), and that Bob bought a movie (3), so you can begin by putting this information into three of the spots.Gary | Item | 40% |

Jen | Item | 35% |

Bob | movie | Markdown |

Person | Item | Markdown |

Person | Item | Markdown |

## Step 2:

You also know that the television had a 60% markdown (6). Since you know that neither Gary nor Jen bought a television since they did not get 60% off (step 1) and that Bob did not buy a television (3), you can fill in this information in one of the remaining two spots.Gary | Item | 40% |

Jen | Item | 35% |

Bob | movie | Markdown |

Person | television | 60% |

Person | Item | Markdown |

## Step 3:

You know that neither Gary (2) nor Jen (4) bought a computer. Since the other two spaces are for the Movie and the Television, you can put the Computer in the last space.Gary | Item | 40% |

Jen | Item | 35% |

Bob | movie | Markdown |

Person | television | 60% |

Person | computer | Markdown |

## Step 4:

The computer did not have a 20% markdown (8), since there are only two possible markdowns left (20% or 55%), you know that the computer must have had a 55% markdown. Therefore, the movie must have had a 20% markdown.Gary | Item | 40% |

Jen | Item | 35% |

Bob | movie | 20% |

Person | television | 60% |

Person | computer | 55% |

## Step 5:

Since Barb did not get 55% off (7), she could not have bought the computer. There is only one other spot left, so Barb must have bought the television.Gary | Item | 40% |

Jen | Item | 35% |

Bob | movie | 20% |

Barb | television | 60% |

Person | computer | 55% |

## Step 6:

There is one person and one item that you weren’t given any information about. Since all of the other names have been used, you know that Amanda must have bought the computer.Gary | Item | 40% |

Jen | Item | 35% |

Bob | movie | 20% |

Barb | television | 60% |

Amanda | computer | 55% |

## Step 7:

Since the CD didn’t have a 35% markdown (9), Gary must have bought the CD for 40% less. Therefore, Jen must have bought the last remaining item, the videogame.Gary | CD | 40% |

Jen | videogame | 35% |

Bob | movie | 20% |

Barb | television | 60% |

Amanda | computer | 55% |