Difference between revisions of "1998 AHSME Problems/Problem 2"
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<math> \mathrm{(A) \ }13 \qquad \mathrm{(B) \ }14 \qquad \mathrm{(C) \ } 15\qquad \mathrm{(D) \ }16 \qquad \mathrm{(E) \ } 17 </math> | <math> \mathrm{(A) \ }13 \qquad \mathrm{(B) \ }14 \qquad \mathrm{(C) \ } 15\qquad \mathrm{(D) \ }16 \qquad \mathrm{(E) \ } 17 </math> | ||
| − | + | ==Solution== | |
| + | |||
| + | If we want <math>\frac{A+B}{C+D}</math> to be as large as possible, we want to try to maximize the numerator <math>A+B</math> and minimize the denominator <math>C+D</math>. Picking <math>A=9</math> and <math>B=8</math> will maximize the numerator, and picking <math>C=0</math> and <math>D=1</math> will minimize the denominator. | ||
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| + | Checking to make sure the fraction is an integer, <math>\frac{A+B}{C+D} = \frac{17}{1} = 17</math>, and so the values are correct, and <math>A+B = 17</math>, giving the answer <math>\boxed{E}</math>. | ||
| + | |||
| + | == See also == | ||
| + | {{AHSME box|year=1998|num-b=1|num-a=3}} | ||
| + | {{MAA Notice}} | ||
Latest revision as of 13:28, 5 July 2013
Problem 2
Letters 
and 
represent four different digits selected from 
If 
is an integer that is as large as possible, what is the value of 
?
Solution
If we want 
to be as large as possible, we want to try to maximize the numerator and minimize the denominator 
. Picking 
and 
will maximize the numerator, and picking 
and 
will minimize the denominator.
Checking to make sure the fraction is an integer, 
, and so the values are correct, and 
, giving the answer 
.
See also
| 1998 AHSME (Problems • Answer Key • Resources) | ||
| Preceded by Problem 1 |
Followed by Problem 3 | |
| 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 • 26 • 27 • 28 • 29 • 30 | ||
| All AHSME Problems and Solutions | ||
The problems on this page are copyrighted by the Mathematical Association of America's American Mathematics Competitions. 
