Aptitude  Problems on Numbers  Discussion




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 Albert Einstein

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 
Answer: Option
Explanation:
Let the numbers be x and x + 2.
Then, (x + 2)^{2}  x^{2} = 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)(ab)=84
(ab)=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)^2x^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)(xx+1) = 84 //Using a^2 b^2 formula.
(2x+1)(1) = 84.
2x+1= 84.
2x = 83.
x = 83/2. 

