Aptitude - Numbers - Discussion

Hi paavani..

Principle: If a number is divisible by 3 means, sum of the digits also divisible by 3.

For eg: take 12. we know that 12 is divisible by 3
sum of digits i.e 1+2 = 3 ,3 is divisible by 3.

First u clear about this?

We cum to problem then..
517*324 is completely divisible by 3
so sum of the digits also divisible by 3.

Then, 5+1+7+x+3+2+4 = 22+x

We hav given the options 0, 1 , 2

If x=0, sum= x+22= 0+22 = 22 is not divisible by 3
If x=1, Sum =x+22 = 1+22 = 23 is not divisible by 3
If x=2, Sum =x+22 = 2+22 = 24 is divisible by 3
So answer is 2

Hope you understand this..

Simple method-->divide the left-hand side number by 3, the remainder will be 1, then divide RHS number by 3 the remainder will be 0 as the number is divided by 3 so, place 2 before remainder 1, it will be 21 and divide by 3. That's solved.

Ex: 517/3 = 1 (remainder) * 324/3 = 0, So place 2 before 1 (remainder) = 21/3 = 7 (all are divided).

@Ram, Sonakshi.

The adding of digits to check divisibility can be done only for 3 which is rule for test of divisibility for 3.

Similarly,To check divisibility of 9 the sum of digits should be 9.

Ex: 45 => 4+5=9 . So 45 is divisible by 9.

Each digit has its own Divisibility rule to check whether it exactly divides the given or not.

Hi @Pavani..

If a number(for example take xyzpqr) is divisible by 3, then the sum(x+y+z+p+q+r) is also divisible by 3 and vice versa..

ex: 243 is divisible by 3
2+4+3=9 is also divisible by 3..

So if u want to check dat a number is divisible by 3 then it is enough to see whether the sum of digits in the number is divisible by 3..

@Divya.

We don't divide (22+x) by 3, it is an equation form. It means what you add in 22 so it can be divided by 3.

Ex

=> 22+x/3.

=> If we assume smallest number 0, 1 then we got sum is 22, 23 which is not divided by 3, so we add 3(x) , and we get 24 which is divisible by 3.

Hope you understand.

517*324 its divided by 3.

5+1+7+X+3+2+4 = 22+X.

X = 0, 1, 2, 3, .

22+0 = 22. Its not divided by three.

22+1 = 23. Its not divided by three.

22+2 = 24(8*3) = 24 is divided by three.

So, the x value is 2. The two will be added. So the number is divided by three. So the answer is three.

According to you guys if a number is divisible by another number then sum of its all digits also divisible. But it's not true in all cases.

e.g. The number is 625 which is divisible by 5. But if we add all its digits 6+2+5=13 which is not divisible by 5.

So this principle is wrong.

@Suresh @Mariya

Yeah, let's assume if
SAM is divisible by 3
S+A+M is also divisible by 3.

5 + 1 + 7 + x + 3 + 2 + 4 if we add this it would be 22+x.

So 22 is not divisible by 3.
If we add 2 in place of x i.e, 22+2 = 24 then it is divisible by 3.
So the answer is "2".

hi..
the rule for division for 3 is the total of the given number should be divided by 3..
so when add 517x324=22 which can't be divided by 3, so we have to add 2, to make it dividable by 3.

after adding 2 it becomes 24 which can be divided by 3.

hope it helps u..

It's quite simple. Consider * as x and add all the numbers which will become (22+x). Now choose the number from options one by one and put in place of x and then try to divide it by 3. As I put the first option in place of x = (22+2) = 24 which is divided by 3.