Aptitude - Numbers - Discussion

Discussion :: Numbers - General Questions (Q.No.65)

65. 

If the number 42573 * is exactly divisible by 72, then the minimum value of * is:

[A]. 4
[B]. 5
[C]. 6
[D]. 7
[E]. 8

Answer: Option C

Explanation:

72 = 9 x8, where 9 and 8 are co-prime.

The minimum value of x for which 73x for which 73x is divisible by 8 is, x = 6.

Sum of digits in 425736 = (4 + 2 + 5 + 7 + 3 + 6) = 27, which is divisible by 9.

Required value of * is 6.


Soniya said: (Jul 1, 2011)  
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.

Faizal said: (Feb 24, 2012)  
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.

Rajasekar said: (Nov 7, 2014)  
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.

Ashith said: (Jan 9, 2015)  
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.

Rampavan said: (Mar 8, 2015)  
Good problem and Easy for solving is also available.

Ritvik said: (Aug 12, 2015)  
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.

Koti Ch said: (Mar 4, 2016)  
May I know about co prime numbers?

Saravanan said: (Mar 4, 2016)  
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.

Atul said: (Jul 21, 2016)  
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.

Shree said: (Jul 5, 2017)  
425736/72 =6.

Pankaj Verma 9041939259 said: (Nov 15, 2017)  
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.

Vinod said: (Feb 7, 2019)  
Why should a take 6 and 73x?

Arun Prasanth V said: (Feb 9, 2019)  
42573* รท 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.

Post your comments here:

Name *:

Email   : (optional)

» Your comments will be displayed only after manual approval.