# Aptitude - Problems on Numbers - Discussion

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"Success has many fathers, while failure is an orphan."
- (Proverb)
15.

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

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

Explanation:

Let the numbers be x and x + 2.

Then, (x + 2)2 - x2 = 84

4x + 4 = 84

4x = 80

x = 20.

The required sum = x + (x + 2) = 2x + 2 = 42.

 Sunil said: (Thu, Jul 7, 2011 01:29:42 AM) The questions is for sum of two consecutive "even numbers" So in your answer if x=1 then x+2=3 Both are odd numbers. Therefore i think the solution may be as follows:- Let the numbers be "2x" and "2x + 2". Then, (2x + 2)^2 - 2x^2 = 84 8x+4=84 x=10. The required sum = 2x + (2x + 2) = 42.

 Pratheep Msajce It said: (Wed, Jul 13, 2011 06:36:48 AM) The difference of the squares of the number is 84 So (a^2)-(b^2)=84 then (a+b)(a-b)=84 (a-b)=2[it is difference between consecutive even no] then (a+b)*(2)=84 A+B=42

 Arafath said: (Fri, Jul 6, 2012 05:51:01 PM) How does x square become 4x. ?

 Nivedha said: (Sun, Mar 17, 2013 11:55:36 AM) But, if we take x^2-(x+)^2 = 84, The answer changes to 46. Can anyone explain why they take (x+2)^2-x^2 = 84.

 Kranti said: (Sun, Jul 13, 2014 12:55:19 PM) @Nivedha ji, (x+2) is greater than x... and as it is for subtraction, he has taken larger number first, for getting a positive number.

 Jack said: (Thu, May 14, 2015 10:59:56 AM) I think it should be. (x^2) - (x+1)^2. (x+x+1)(x-x+1) = 84 //Using a^2 -b^2 formula. (2x+1)(1) = 84. 2x+1= 84. 2x = 83. x = 83/2.