Aptitude - Numbers - Discussion

Discussion Forum : Numbers - General Questions (Q.No. 28)
28.
If n is a natural number, then (6n2 + 6n) is always divisible by:
6 only
6 and 12 both
12 only
by 18 only
Answer: Option
Explanation:

(6n2 + 6n) = 6n(n + 1), which is always divisible by 6 and 12 both, since n(n + 1) is always even.

Discussion:
27 comments Page 1 of 3.

Ajay said:   8 months ago
@All.

Let us assume n ( it can be any number)
I'm taking n as 1.
6n² + 6n = 6 × 1² + 6×1 = 12
So, 12 is divisible by both 6 and 12.
Answer: Option B
(1)

Shruti said:   2 years ago
If we assume that n = 1.
Then,
6n^2+6n,
6*1*1+6*1 = 12,
So from the given options, 6 and 12 is always divisible.
(3)

Bapan mondal said:   3 years ago
Solve with prove
(6n2 + 6n).

1st
6n(n+1) put the value n=6.
66(6+1)= 66(7)=462/6=77 clearly divisible.

2nd
6n(n+1)= put the value n=12.
612(12+1)=612(13)=7956/12=633 clearly divisible.

Exception
6n(n+1)= put the value 18.
618(18+1)=618(19) = 11742/18 it's not divisible.
(5)

Hemanth said:   3 years ago
6n^2 + 6n = 6 n(n+1) ->n(n+1) is always even
= 6 2(2+1), Ex:2(2+1) = 6.
= 36.
->I think everyone knows divisibility of 6 and 12.
(1)

Habib said:   4 years ago
@Onkar @Narra Rakesh @Emi.

If n is odd then (n+1) is even and if n is even then (n+1) is odd.
Multiplication of an odd and an even number is always even.
So that the number is divisible by 6 and 12.
(2)

Onkar said:   5 years ago
When N is odd. Then it's not divisible by 12.

So, it's divisible by only 6.

Fhici said:   5 years ago
Assume n is a odd number then n-1 will be even and if odd number multiply with even it will be even. So that's for n(n-1) is a even number.

If you assume n is an even number then (n-1) will be odd number..Then multiplication of odd and even number will be also even number. So n(n-1) is always even.

Narra Rakesh said:   5 years ago
If N is even number given expression is divisible by 6 and 12.
But, here N is a natural number.
The given expression is divisible by 6 only.

Sid said:   7 years ago
@Niranjan.

It would be 8,
because 18x25=450,
And then so, 18x26=468,
So, N would be 8.

Priyanka said:   7 years ago
6n^2+6n= 6n(n+1).

Now the number above will always be divisible by 6
And it will be divisible by 12 only when n(n+1) part is even
Eg.6*2=12 ,6*6=36,6*5=30 when we used odd number to multiply with 6 its resultant was not divisible by 12 whereas with even number multiplies by 6 is always divisible by 12.

In case of n*(n+1) always one of the numbers will be odd and another one will be even, Multiplication of odd and even number always results into even number hence it will always be divisible by 12.


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