Aptitude - Numbers - Discussion

See it has given that no. Should be divisible by 12

We have 2 factors of 12
2 | 12
2 | 6
3 | 3
x | 1
So, 12 = 2 * 2 * 3,
= 4 * 3.

We can see that there are 2 numbers 4864 and 9P2.

4864 * 9P2 are divisible by 12 it means they should be divisible by 3 and 4 also,
4864 is divisible by 4 because its last 2 digit is divisible by 4.

And if the sum of the no is a factor of 3 then it is divisible by 3 so we can see 9 + p + 2 = 11p.
So, if we put 1 we get 12 which is divisible by 3 so answer is 1.

I think you all got my point

@Arul.

For the divisibility rule of 12 we must take rule 3 and rule 4 because 3*4 = 12.

So, it must satisfy both rule.
1. Let's take p = 1.
9 + p + 1 = 9 + 1 + 1 = 12.
We can divide 12 by both 3 and 4. So the condition is satisfied.

2. If p = 4
9 + p + 1 = 9 + 4 + 1 = 14 .
It is not divisible by both 3 and 4 . So that's why we take p = 1.
Thank you.

Even p=4 is satisfying the condition. Because 9+4+2 is a multiple of 3. So if the option 1 is not given but 4 is in the option we should be selecting it. Not only 4, other numbers which satisfy the condition (sum of digits a multiple of 3).

Suppose we can ignore the 4864x because we need only p-value so I write;
9+p+2=11p (what we add in this to get divided from 12).
9+1+2=12 .........

So the p of value is 1.

I think you all understand now.

Why don't we take p=4 if we take p=4 it is also satisfying the condition right?

What if in the option both p=1 and p=4 is given?

Anyone, please explain.

Because 3 and 4 is the factors of 12 and if the number is divisible by 4 then it should be divisible by 3 as well to get divisible by 12 completely.

If in the case of 48 if it has to be divisible by 12 then 4, 3 both should divide it if in que it is in form of 24*2 then how we will approach.

I don't understand that how we get p=1. Because if we consider p=1 then it becomes 9+1+1=11 not 12. Then how can we take the value of p=1.

9 + p + 2 =11p.

If we add any number it must be divisible by 12.
So, if we add 1 then we get 11 + 1 = 12 is divisible by 12.

Clearly 4864 is divided by 4.

Then 9p2 is also divided by 4 and 3.

(Solution = 9+p+1=12 (where p =1)).

So answer is 1.