What is the sum of two consecutive even numbers, the difference of whose squares is 84?

A. 34 B. 38
C. 42 D. 46

• Sum of two consecutive even Nos. are 2n+2n+2=4n+2
  Given (2n+2)^2-(2n)^2=8n+4=84
  Solving, we get n =10
  Sum of two consecutive even no. is 42(answer option is C)
• 13 years agoHelpfull: Yes(22) No(1)
• Let first no=x
  hence,next even no=x+2
  we have to find X+X+2=2X+2=?
  =>
  (X+2)^2-(x)^2=84 ...Given
  solving above equation x=20
  therefore answer is 2*20+2=42
  option c.42
• 11 years agoHelpfull: Yes(5) No(2)
• let an even no be 2n so consecutive even no is (2n+2 )......now the difference of their squares is equal to (2n+2)^2-2n^2....[greater no-smaller no......].......this is equal to 84 .........solving this we get 8n=80 or n=10 which makes 2n=20 and (2n+2)=22 .therefore their sum is 20 + 22 =42 which is in option (C)
• 9 years agoHelpfull: Yes(2) No(2)
• (x*x)-(x-2)*(x-2)=84
  x=22;
  x-2=20;
  then their sum =42
• 9 years agoHelpfull: Yes(0) No(0)
• let frst no be x n second even no be x+2,
  then (x+2)^2-x^2=84
  x2+4x+4-x2=84
  x=20 ,x+2=22
  sum=20+22=42(c)
• 9 years agoHelpfull: Yes(0) No(0)
• Let two even numbers be 2x and 2(x+1).
  So, sum of two consecutive even numbers will be:
  2x+2(x+1)=2x+2x+2=4x+2
  
  Now, difference of their squares is:
  (2x)^2-[2(x+1)]^2=84
  [2x+2(x+1)][2x-2(x+1)]=84
  because, a^2-b^2=(a+b)(a-b)
  [4x+2][2]=84
  [4x+2]=84/2=42
  Ans. C
• 9 years agoHelpfull: Yes(0) No(0)
• Option verification
  Answer:3
• 8 years agoHelpfull: Yes(0) No(0)
• result : 44
• 7 years agoHelpfull: Yes(0) No(3)