View source for 1991 AHSME Problems/Problem 13

== Problem ==

Horses <math>X,Y</math> and <math>Z</math> are entered in a three-horse race in which ties are not possible. The odds against <math>X</math> winning are <math>3:1</math> and the odds against <math>Y</math> winning are <math>2:3</math>, what are the odds against <math>Z</math> winning? (By "odds against <math>H</math> winning are <math>p:q</math>" we mean the probability of <math>H</math> winning the race is <math>\frac{q}{p+q}</math>.)

<math>\text{(A) } 3:20\quad
\text{(B) } 5:6\quad
\text{(C) } 8:5\quad
\text{(D) } 17:3\quad
\text{(E) } 20:3</math>

== Solution ==
<math>\fbox{E}</math>

== See also ==
{{AHSME box|year=1991|num-b=12|num-a=14}}  

[[Category: Introductory Algebra Problems]]
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