Aptitude - Numbers - Discussion
Discussion Forum : Numbers - General Questions (Q.No. 81)
81.
The difference of the squares of two consecutive even integers is divisible by which of the following integers ?
Answer: Option
Explanation:
Let the two consecutive even integers be 2n and (2n + 2). Then,
(2n + 2)2 = (2n + 2 + 2n)(2n + 2 - 2n)
= 2(4n + 2)
= 4(2n + 1), which is divisible by 4.
Discussion:
15 comments Page 1 of 2.
Rumpa said:
1 decade ago
Let two consecutive even integer as x and x+2.
= (x+2)^2-x^2.
= x^2+4x+4-x^2.
= 4x+4.
= 4(x+4).
Divisible by 4.
= (x+2)^2-x^2.
= x^2+4x+4-x^2.
= 4x+4.
= 4(x+4).
Divisible by 4.
(4)
Shamili said:
1 decade ago
(2n+2)^2!=(2n+2+2n)(2n+2-2n)
It can be write as
(2n+2)^2-(2n)^2=(2n+2+2n)(2n+2-2n)
=(8n+4)
=4(2n+1)
Which is divisible by 4
It can be write as
(2n+2)^2-(2n)^2=(2n+2+2n)(2n+2-2n)
=(8n+4)
=4(2n+1)
Which is divisible by 4
(1)
Satyendra said:
10 years ago
If we taking two consecutive number as 2 and 4.
Then, we get 12 which is divisible by 3 and 6 also then.
Why we choose 4 only.
16- 4 = 12.
12/3 = 0.
Please clear this doubt.
Then, we get 12 which is divisible by 3 and 6 also then.
Why we choose 4 only.
16- 4 = 12.
12/3 = 0.
Please clear this doubt.
(1)
Sobhit Kumar Sah said:
9 years ago
@Satyendra.
According to your opinion, there are two answers. Since we take next consecutive even integers 4 & 6.
According to your opinion, there are two answers. Since we take next consecutive even integers 4 & 6.
(1)
Marthandan said:
1 decade ago
Please explain (2n+2) ^2 = (2n+2+2n) (2n+2-2n).
Balaji said:
1 decade ago
Please explain (2n+2) ^2 = (2n+2+2n) (2n+2-2n).
Prabhu said:
1 decade ago
The difference between two consecutive even no
(2n+2)^2-(2n)^2= (2n+2+2n) (2n+2-2n) (that is a^2-b^2=(a+b)(a-b))
=(4n+2)2
=4(2n+1)
(2n+2)^2-(2n)^2= (2n+2+2n) (2n+2-2n) (that is a^2-b^2=(a+b)(a-b))
=(4n+2)2
=4(2n+1)
Naveen said:
1 decade ago
Here missing it should be (2n+2)^2-(2n)^2
Priya said:
1 decade ago
(2n+2)^2 - (2n)^2 = 4n^2+8n+4 - 4n^2
= (8n+4)
= 4(2n+1)
Which is divisible by 4.
= (8n+4)
= 4(2n+1)
Which is divisible by 4.
Anusha said:
1 decade ago
Eg: Two consecutive even numbers are 6, 8 and 2, 4.
36-64 = 28.
28 is divisible by 4.
4-16 = 12.
12 is divisible by 4.
36-64 = 28.
28 is divisible by 4.
4-16 = 12.
12 is divisible by 4.
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