Drexel dragonThe Math ForumDonate to the Math Forum

Ask Dr. Math - Questions and Answers from our Archives
_____________________________________________
Associated Topics || Dr. Math Home || Search Dr. Math
_____________________________________________

Math Logic


Date: 6/5/96 at 9:32:19
From: Jim Marone
Subject: Math logic

This is a problem about logic.

Sally, Ron, Jim, and Meghan are President, VP, Treasurer, and Captain 
of the cheerleading squad, but not necessarily in that order. Who is 
what?

Clues

Sally loves money.
Meghan thinks she could not handle a whole class
Jim was elected
Ron is Jim's partner


Date: 6/14/96 at 0:49:40
From: Doctor Jeffrey
Subject: Re: math logic

Sally    Treasurer
Ron      Vice President
Jim      President
Meghan   Captain

This is how I got it:

The first thing I did was make a chart (they usualy help with logic 
problems). The chart I made had the names in the rows and the 
positions in the columns. If I know that someone has a certain 
position, I put an o in that part of the chart. If I know that someone 
doesn't hold a certain position, I put an x there. This is the chart I 
started with:

     P     V     T     C
  -------------------------
S |     |     |     |     | 
  -------------------------
R |     |     |     |     | 
  -------------------------
J |     |     |     |     |
  -------------------------
M |     |     |     |     |
  -------------------------

From this point I started using the clues.  The first clue I used was 
the fact that Meghan wouldn't have gone for President since she didn't 
want to lead the whole class. After using this piece of information, 
the chart looks like this:


     P     V     T     C
  -------------------------
S |     |     |     |     |
  -------------------------
R |     |     |     |     | 
  -------------------------
J |     |     |     |     |
  -------------------------
M |  x  |     |     |     |
  -------------------------

Next, since Sally loves money, she was probably the Treasurer.

     P     V     T     C
  -------------------------
S |  x  |  x  |  o  |  x  | 
  -------------------------
R |     |     |  x  |     | 
  -------------------------
J |     |     |  x  |     |
  -------------------------
M |  x  |     |  x  |     |
  -------------------------

I was able to fill in the additional x's because I know Sally can only 
hold one position and only one person can be treasurer.

Since Ron and Jim are partners they had better be the President and 
Vice President, so Meghan must be the Captain.  So now it looks like 
this:

     P     V     T     C
  -------------------------
S |  x  |  x  |  o  |  x  | 
  -------------------------
R |     |     |  x  |  x  | 
  -------------------------
J |     |     |  x  |  x  |
  -------------------------
M |  x  |  x  |  x  |  o  |
  -------------------------

This leaves President and Vice President for Ron and Jim.  Since 
Presidents are elected and Vice Presidents are not, Jim must be 
President and Ron must be Vice President.

-Doctor Jeffrey,  The Math Forum
 Check out our web site!  http://mathforum.org/dr.math/   
    
Associated Topics:
Elementary Word Problems
High School Logic
Middle School Logic
Middle School Word Problems

Search the Dr. Math Library:


Find items containing (put spaces between keywords):
 
Click only once for faster results:

[ Choose "whole words" when searching for a word like age.]

all keywords, in any order at least one, that exact phrase
parts of words whole words

Submit your own question to Dr. Math

[Privacy Policy] [Terms of Use]

_____________________________________
Math Forum Home || Math Library || Quick Reference || Math Forum Search
_____________________________________

Ask Dr. MathTM
© 1994-2013 The Math Forum
http://mathforum.org/dr.math/