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.

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

Please explain.

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.

(14+x) is divisible by 9. But how can we get x=4?

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.

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.

Not understand the derivation. Please help me to get it.

Please help me to find the co factors.

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.

@ 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.