Aptitude - Numbers - Discussion

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.

Why should a take 6 and 73x?

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.

How 6 will be the answer? please explain.

How 73x will came in solving x = 6? Please explain this step.

I got confused, Could anyone please explain clearly?

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