Math Problem Statement
Solution
The problem states:
"If the difference between the largest and smallest number from a set of five numbers is 0, what is the difference between the second largest and the third largest numbers?"
Solution:
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Key observation:
If the difference between the largest and smallest numbers is 0, all the numbers in the set must be equal. Let the common value of all five numbers be . -
Second largest and third largest numbers:
Since all the numbers are equal (), the second largest and the third largest numbers are also . -
Difference between the second largest and the third largest numbers:
Final Answer:
The difference between the second largest and the third largest numbers is 0.
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5 Related Questions:
- What happens if the largest and smallest numbers differ by a nonzero value?
- How would this problem change if the set contained only three numbers?
- What is the difference between the median and the smallest number in this scenario?
- If one number in the set is increased, how does it affect the differences?
- How is this property (all numbers being equal) useful in other math problems?
Tip:
When dealing with differences in sets, always check whether the given condition implies uniformity or variability in the numbers.
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Math Problem Analysis
Mathematical Concepts
Number Theory
Properties of Equal Numbers
Formulas
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Theorems
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Suitable Grade Level
Grades 6-8
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