2001 AMC 8 竞赛试题/第02题
Problem
I'm thinking of two whole numbers. Their product is 24 and their sum is 11. What is the larger number?
Solution 1
Let the numbers be 
and 
. Then we have 
and 
. Solving for in the first equation yields 
, and substituting this into the second equation gives 
. Simplifying this gives 
, or 
. This factors as 
, so 
or 
, and the corresponding values are 
and 
. These are essentially the same answer: one number is 
and one number is 
, so the largest number is 
.
Solution 2
Use the answers to attempt to "reverse engineer" an appropriate pair of numbers. Looking at option 
, guess that one of the numbers is . If the sum of two numbers is 
and one is , then other must be 
. The product of those numbers is 
, which is the second condition of the problem, so our number are and .
However, is the smaller of the two numbers, so the answer is or 
.
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