Difference between revisions of "1998 AHSME Problems/Problem 2"
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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. | 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. | ||
− | Checking to make sure the fraction is an integer, <math>\frac{A+B}{C+ | + | 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>. |
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== See also == | == See also == | ||
{{AHSME box|year=1998|num-b=1|num-a=3}} | {{AHSME box|year=1998|num-b=1|num-a=3}} |
Revision as of 15:47, 8 August 2011
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 |