If two numbers have a sum of 100 and a difference of 20, what are the numbers?

If two numbers have a sum of 100 and a difference of 20, what are the numbers?

• A. 80 and 20
• B. 60 and 40
• C. 50 and 50
• D. 70 and 30

Answer: (B)

Knowing both the sum and the difference lets you find the numbers by using the average and half the difference. The sum is 100, so the average of the two numbers is 100/2 = 50. The difference is 20, so half the difference is 10. The numbers are centered around the average: one is 50 plus 10, the other is 50 minus 10, giving 60 and 40. They add up to 100 and their difference is 20. Among the options, only 60 and 40 fit both conditions. The other pairs don’t match the required sum and/or difference.

Knowing both the sum and the difference lets you find the numbers by using the average and half the difference. The sum is 100, so the average of the two numbers is 100/2 = 50. The difference is 20, so half the difference is 10. The numbers are centered around the average: one is 50 plus 10, the other is 50 minus 10, giving 60 and 40. They add up to 100 and their difference is 20. Among the options, only 60 and 40 fit both conditions. The other pairs don’t match the required sum and/or difference.