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.
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)
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)
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.
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)
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.
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)
Saymon said:
8 years ago
Is it applicable?
x & x+2
so, (x+x+2)^2 =x^2+2.x(x+2)+(x+2)^2 =x^2+2x^2+4x+x^2+2x2+4 = 4x^2+8x+4 = 4(x^2+2x+1).
x & x+2
so, (x+x+2)^2 =x^2+2.x(x+2)+(x+2)^2 =x^2+2x^2+4x+x^2+2x2+4 = 4x^2+8x+4 = 4(x^2+2x+1).
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)
Payal said:
10 years ago
But again if we take for odd integers and where x=1 then again the answer is 8 which does not come.
Swetha said:
1 decade ago
Why can't we can take consecutive even integers as x, x+2, x+4....where x=2.
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