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 2 of 2.
Nang said:
8 years ago
Let two consecutive no. Be x, x+2,
Then ,x-x+2=84,
= 84/2,
= 42.
Then ,x-x+2=84,
= 84/2,
= 42.
(2)
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)
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)
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)
Anshu Saini said:
5 years ago
Two consecutive even numbers can only be 2x and 2x+2.
While x and x+2 are example of two consecutive odd numbers.
While x and x+2 are example of two consecutive odd numbers.
(1)
Punam Paswan said:
4 years ago
The consecutive no Be x, x+2,
Then, x-x+2=84,
= 84/2,
= 42.
Then, x-x+2=84,
= 84/2,
= 42.
(6)
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)
Xayoo said:
4 years ago
x^2 - y^2 = 84,
(x+y)(x-y) = 84,
(42 ) (2) = 84,
(22+20)(22-20) = 84.
x=22 , y = 20.
Therefore x + y = 22+ 20 = 42.
(x+y)(x-y) = 84,
(42 ) (2) = 84,
(22+20)(22-20) = 84.
x=22 , y = 20.
Therefore x + y = 22+ 20 = 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)
Abhinayeswari C said:
3 months ago
Very clear explanations. It helps me to understand clearly. Thanks all.
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