Aptitude - Numbers - Discussion

Standard form of 72 = 3^2 * 2^3.

i.e. 72 = 9*8.

If a number is divisible by a number a and a number b, and both a and b are co-primes i.e. they have no common factor other than 1. then the number is divisible by a*b. e.g. if 120 is divisible by 2 and 3 therefore 120 is divisible by 2*3.

Also 120 is divisible by 8 and 2, but it won't be divisible by 8 * 2 because 8 and 2 are not co-primes.

In the above case 9 and 8 are coprime therefore check for divisibility by 8 and 9.

For divisibility by 8 : the last digit must be even and the last 3 digits must be divisible by 8.
for divisibility by 9: sum of all digit must be divisible by 9.

Therefore check 4+2+5+7+3+x such that x is even first, then the sum is divisible by 9 and lastly, last 3 digits are divisible by 8.

You won't have to do the last step though since the only even number making the sum of digits divisible by 9 is 6: 4+2+5+7+3+6 = 27.

Hence 6 is the answer

Easy method:

72 is always divisible by(9*8),

Note: always take the minimum value here min value is : 8.

Now take the last 3 digits and place 8 in place of 'x'.

Then use all the given options,

Ex: 73* => 738/4 it will not give. So by the way we can get only by using 6.
i.e: 738/6 = 123.

Hence the answer: 6.

Thank you.

There is a simple way:-

72 is a multiple of 3, since 42573x is divisible by 72 (given).

Hence: 4+2+5+7+3+x = 21+x (which must be a divisible by 3).

From the given options 6 is the only option which fits in place of x to satisfy the above criteria.

Hope you understood.

42573* ÷ 72,
First we do,
72 = 9*8.
Then,
The sum of num 42573* is divisible are not divisible by 9,
4+2+5+7+3+x = 21+x,
Now see we take 6 to add and then the number is divisible,
21+6= 27 now it is divided so the x =6.

If you count the digits except * it comes to be 21. Now place one by one options and add it up and check the divisibility by 3.

Only option C and D satisfies but option D doesn't satisfy divisibility rule of 9. Clearly answer is 6 i.e. option C.

72 is known that is divisible by 3.

And any number, multiplied by 72 will be even.

And, 4 + 2 + 5 + 7 + 3 = 21, which is divisible by 3 "known".

We need to find an option from rest of the options which is even and divided by 3.

73x is divisible by 8 is, x = ?
First divide 73/8.
8x9 = 72 remainder 1.

73 1 X we need 6(1 is remainder while dividing 73 with 8 after remainder we have to put the value of X).

1X/8 as we know 16/8 so X is 6.

The divisibility rule for 8 is :

You have to take the last 3 digit no and divide it by 8 if it is divisible by then the no will be divisible by 8.

Hope you understood.

72 = 2^3+3^2.

Apply divisibility rule of 2 and 3 on 42573x.

4+2+5+7+3+x = 21+x should be divisible by 3 if and only if x is 6.

Sir, I am unable to solve this, because when x=6 then we get 27 which is divided by 9 not by 8, then how answer is x=6.