Math Problem Statement

If the difference between the largest and the smallest number from a set of five numbers is 0, what is the difference between the second largest and the third largest numbers?

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:

  1. 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 xx.

    Largest number=Smallest number=x\text{Largest number} = \text{Smallest number} = x

  2. Second largest and third largest numbers:
    Since all the numbers are equal (x,x,x,x,xx, x, x, x, x), the second largest and the third largest numbers are also xx.

  3. Difference between the second largest and the third largest numbers:
    xx=0x - x = 0


Final Answer:

The difference between the second largest and the third largest numbers is 0.


Would you like further clarification or examples? 😊


5 Related Questions:

  1. What happens if the largest and smallest numbers differ by a nonzero value?
  2. How would this problem change if the set contained only three numbers?
  3. What is the difference between the median and the smallest number in this scenario?
  4. If one number in the set is increased, how does it affect the differences?
  5. 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.