Aptitude - Numbers - Discussion

Option C IS CORRECT OPTION.

Solution:

If the number 653 xy is divisible by 90, then (x + y) = ?

90 = 10*9.
10 = 2*5 and 9=3*3.
So the number 653xy should be such that it should be divisible by "2,5 and 3.".

1) For the number divisible by 2 it should be even.
2) For the number divisible by 5 it should end with 0 or 5.
3) For the number divisible by 3 the total sum of the number should be divisible by 3.

So checked for all condition.
653xy y=0(to get even number and also divisible by 5)-----> eq(1)
From eq(1) 653x0 now when x = 4 then 6 + 5 + 3 + 4 + 0 = 18 which is divisible by 3.

653xy is divisible 90. It means 9*10 or 10*9.

Here we take 9*10. Therefore take x multiple as 9 and why multiple 10.
If the number is a multiple of 10 means the unit digit should be 0.
Therefore take y=0.

Now, x multiple is 9 then the sum of 653xy should be divisible by 3.
653xy= 6+5+3+x+y=14+x+0 (. Y=0).

Then 14+x then is take x=0 then x=14 not 3 divisible, x=1 then x=14+1==15 not 3 divisible,
Then x=14+2=16 not 3 divisible,
x=14+3=17 not 3 divisible, x=14+4=18 divisible of 3,
Therefore x=3.
The answer is x+y=3+0=3.

Because a number is said to be divisible by only when it divides the number correctly.

In order to make 14+x divisible by 9. Substitute some numeric values in x and make sure that it is divisible by 9.

14+2=16 not divisible by 9.

14+4=28 is divisible so x=4.

Simple method.

In divisibility rule of 9, if all the sum of digits is divisible by 9 then the whole number is divisible by 9.

So put 4, i.e 6534 and add 6 + 5 + 3 + 4 = 18, So the number is divisible by 9.
Hence option 3 is right.

Let put x=0 and y=0 in 653 xy this become 65300.

Now divide 65300 by 90 = 725.55.

Now multiple and add 90 in 725(725À-90+90 = 65340). Here last two digits are 40 .

Its means x = 4 & y = 0.
So x+y = 4+0=4 Ans.

The answer to this question should be 6 and not 4.

let me explain how;
3xy should be divisible by 90.
so by hit and trial, we get 360 which is completely divisible by 90.
so the sum of x+y should be 6+0=6 and not 4.

No. divisible by 9 is also divisible by 90,

Apply the divisibility rule of 9 and consider the simplest value of x and y which should be divided by 9.
eg. divisibility rule of 9 (x=2,y=2).
6+5+3+2+2 = 18
2+2 = 4 Ans.

@ Vishnu murthy

I have doubt
6534 / 90
72.6

Then how is your method correct?

I think answer is wrong.
The correct answer is 6.

Why we distribute 90 = 9 * 10 or how y become 0?

Please explain.

I don't understand that equation. Please someone explain.