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Odd Sums, Even Sums

Problem #23
Deadline to submit the solution: January 5th, 2001

 

The sum A is equal to the sum of all odd numbers between 1 and 99:
A = 1 + 3 + 5 + 7 + . . . + 99

The sum B is equal to the sum of all even numbers between 2 and 100:
B = 2 + 4 + 6 + 8 + 10 + . . . . + 100.

 

Q1: Which sum is larger: A or B?

Q2: By how much is one of the sums larger than the other?

 

The Solutions

 


Question 1: B
   Because all the numbers in group B are bigger than group A.

Question 2: 50
    Each group has 50 numbers.
    Each number in group B is one ahead of group A.
    1 * 50 = 50

School: King Elementrary School
Name: justin
Age: 7
Grade: 2
State: Michigan


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