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Aptitude - Problems on Numbers - Discussion

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"Act well your part; there all honor lies."
- Alexander Pope
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 - 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.

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