What is the sum of two consecutive even numbers, the difference of whose…
20252024
What is the sum of two consecutive even numbers, the difference of whose squares is 84 ?
- A.
34
- B.
38
- C.
42
- D.
46
Attempted by 35 students.
Show answer & explanation
Correct answer: C
Answer: 42
Let the two consecutive even numbers be 2n and 2n+2.
Compute the difference of squares: (2n+2)^2 - (2n)^2 = 8n + 4.
Set it equal to 84: 8n + 4 = 84. Solve: 8n = 80, so n = 10.
The numbers are 2n = 20 and 2n+2 = 22, so their sum is 20 + 22 = 42.
Key idea: express consecutive even numbers as 2n and 2n+2 so the difference of squares simplifies neatly to a linear equation.