Aptitude - Problems on Numbers - Discussion
Discussion Forum : 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?
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.
Discussion:
20 comments Page 1 of 2.
Sunil said:
1 decade ago
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.
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:
1 decade ago
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
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:
1 decade ago
How does x square become 4x. ?
Nivedha said:
1 decade ago
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.
The answer changes to 46.
Can anyone explain why they take (x+2)^2-x^2 = 84.
Kranti said:
1 decade ago
@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:
1 decade ago
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.
(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:
9 years ago
if we took like that (x)^2-(x+2)^2 = 84, answer is changed i.e.46.
Is it correct?
Is it correct?
Sankarilakshmi said:
9 years ago
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).
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:
8 years ago
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.
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.
(1)
Sundar DS said:
8 years ago
(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.
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.
(1)
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