Difference between revisions of "1993 AHSME Problems/Problem 4"
(Created page with "== Problem == Define the operation "<math>\circ</math>" by <math>x\circ y=4x-3y+xy</math>, for all real numbers <math>x</math> and <math>y</math>. For how many real numbers <math...") |
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== Solution == | == Solution == | ||
| − | <math>\fbox{E}</math> | + | |
| + | Note that <math>3 \circ y = 4 \cdot 3 - 3y + 3y = 12</math>, so <math>3 \circ y = 12</math> is true for all values of <math>y</math>. Thus there are more than four solutions, and the answer is <math>\fbox{E}</math> | ||
== See also == | == See also == | ||
Latest revision as of 20:07, 27 May 2021
Problem
Define the operation "
" by 
, for all real numbers 
and 
. For how many real numbers does 
?
Solution
Note that 
, so 
is true for all values of . Thus there are more than four solutions, and the answer is 
See also
| 1993 AHSME (Problems • Answer Key • Resources) | ||
| Preceded by Problem 3 |
Followed by Problem 5 | |
| 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. 
