# Aptitude - Problems on Numbers - Discussion

### Discussion :: Problems on Numbers - General Questions (Q.No.15)

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: (Jul 7, 2011) 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: (Jul 13, 2011) 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: (Jul 6, 2012) How does x square become 4x. ?

 Nivedha said: (Mar 17, 2013) 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: (Jul 13, 2014) @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: (May 14, 2015) 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.

 Pooja said: (Nov 6, 2016) if we took like that (x)^2-(x+2)^2 = 84, answer is changed i.e.46. Is it correct?

 Sankarilakshmi said: (Nov 17, 2016) Hi @Pooja. If we took like that (x)^2 - (x+2)^2 = 84. Then, x^2-(x^2+4x+4) = 84, x^2-x^2-4x-4 = 84, -4x = 88, x = -22. The required sum = x + (x + 2). = -22 + (-22 + 2), =-22 - 20 = -42 (same answer but negative integer so we taken the large number first).

 Pranshu Yadav said: (May 10, 2017) In this case; Consecutive even no x, x+2. According to the question. (x)^2 - (x+2)^2 = 84. (x+x+2)(x-x+2) = 84. (2x + 2)2 = 84. 4x + 4 = 84. 4x =84-4. 4x=80. x=80/4. x=20. Then; = x +x+2. = 20+20+2. = 42. This is the correct answer = 42.

 Sundar Ds said: (May 23, 2017) (x+2)2/x2 = 84, x2 + 4 + 4x/x2 = 84, 4x+4 = 84, 4x = 84 - 4, 4x = 80, x = 20. The required sum=x + (x+2) 2x + 2, 2 * 20+2 = 42.

 Nang said: (Jul 1, 2017) Let two consecutive no. Be x, x+2, Then ,x-x+2=84, = 84/2, = 42.

 Soumya said: (Mar 28, 2018) Let two consecutive even numbers be 2x,2(x+1)[taking x is not valid] so (2x+2)^2-4x^=84. or, 8x-4=84. or, x=11. So two numbers are 2*11,2*12= 22,24. Sum = 22+24= 46.