Difference between revisions of "1998 AJHSME Problems/Problem 10"
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Each of the letters <math>\text{W}</math>, <math>\text{X}</math>, <math>\text{Y}</math>, and <math>\text{Z}</math> represents a different integer in the set <math>\{ 1,2,3,4\}</math>, but not necessarily in that order. If <math>\dfrac{\text{W}}{\text{X}} - \dfrac{\text{Y}}{\text{Z}}=1</math>, then the sum of <math>\text{W}</math> and <math>\text{Y}</math> is | Each of the letters <math>\text{W}</math>, <math>\text{X}</math>, <math>\text{Y}</math>, and <math>\text{Z}</math> represents a different integer in the set <math>\{ 1,2,3,4\}</math>, but not necessarily in that order. If <math>\dfrac{\text{W}}{\text{X}} - \dfrac{\text{Y}}{\text{Z}}=1</math>, then the sum of <math>\text{W}</math> and <math>\text{Y}</math> is | ||
Revision as of 11:50, 23 December 2012
Problem
Each of the letters 
, 
, 
, and 
represents a different integer in the set 
, but not necessarily in that order. If 
, then the sum of and is
Solution
There are different ways to approach this problem, and I'll start with the different factor of the numbers of the set .
has factor .
has factors and
has factors and
has factors , , and .
From here, we note that even though all numbers have the factor , only has another factor other than in the set (ie. )
We could therefore have one fraction be 
and another 
.
The sum of the numerators is 
See also
| 1998 AJHSME (Problems • Answer Key • Resources) | ||
| Preceded by Problem 9 |
Followed by Problem 11 | |
| 1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15 • 16 • 17 • 18 • 19 • 20 • 21 • 22 • 23 • 24 • 25 | ||
| All AJHSME/AMC 8 Problems and Solutions | ||
