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.
Ezhili said:
2 years ago
The two consecutive even number formula is: x + x+2... = 84.
Difference of squares is:x^2-(x+2)^2 = 84,
X^2 -(x+2) (x+2) = 84,
X^2 - x^2 + 2x + 2x + 4 = 84.
Thus (+ x^2 - x^2) are cancel,
4x + 4 = 84,
4x = 84 - 4.
X = 80/4 = 20.
The consecutive even num formula is:
X + X+2.. =20 + 20 + 2 = 42.
Difference of squares is:x^2-(x+2)^2 = 84,
X^2 -(x+2) (x+2) = 84,
X^2 - x^2 + 2x + 2x + 4 = 84.
Thus (+ x^2 - x^2) are cancel,
4x + 4 = 84,
4x = 84 - 4.
X = 80/4 = 20.
The consecutive even num formula is:
X + X+2.. =20 + 20 + 2 = 42.
(3)
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)
Pavinesh said:
6 years ago
TAKE 2x ,2x+2 be the two consecutive numbers:
Then as per given condition, (2x+2)^2-(2x)^2=84.
(4x^2+4+8x)-(4x^2)=84
8x=80
x=10;
If you substitute this to 2x+2x+2.
20+20+2=42.
I hope you get a clear solution.
Then as per given condition, (2x+2)^2-(2x)^2=84.
(4x^2+4+8x)-(4x^2)=84
8x=80
x=10;
If you substitute this to 2x+2x+2.
20+20+2=42.
I hope you get a clear solution.
(2)
Subas said:
4 years ago
Let first even number is (x)
and the second even number is (x+2).
According to question;
(x+2)^2-x^2 = 84.
(x+2-x)(x+2+x) = 84,
2(2x+2) = 42,
2x+2 = 42,
2x = 40,
x = 20.
Next no.= 20 + 2 = 22,
Sum = 20 + 22 + 42.
and the second even number is (x+2).
According to question;
(x+2)^2-x^2 = 84.
(x+2-x)(x+2+x) = 84,
2(2x+2) = 42,
2x+2 = 42,
2x = 40,
x = 20.
Next no.= 20 + 2 = 22,
Sum = 20 + 22 + 42.
(2)
Tushar said:
6 years ago
Let two consecutive number Be x, x+2.
Then, x^2 - (x+2)^2 = 84;
So put (a+b)^2 formulae,
Then x^2-(x^2+2*x*2+2^2)=84;
cut x^2,remaining is 4x+4=84;
x=20;
And put this in equation 2x+2=2*20+2=42.
Then, x^2 - (x+2)^2 = 84;
So put (a+b)^2 formulae,
Then x^2-(x^2+2*x*2+2^2)=84;
cut x^2,remaining is 4x+4=84;
x=20;
And put this in equation 2x+2=2*20+2=42.
(1)
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
Soumya said:
7 years ago
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.
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.
(1)
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.
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