A number (exactly not a four digit number and it starts with 7) is given. 9393…

Solution: 1

LCM of 12, 24, 32 and 54 = 864

Number is divisible by 864 when 9393 is added

CONFUSION POINT -

⇒ Number = k × 864 – 9393, for some integer k.

Given number is not a four digit integer. Assuming it to be five digit and using trial and error, we try with k = 91, 92 …

k = 91 ⇒ Number starts with 6

k = 92 ⇒ number = 70095 which starts with 7.

Validation :

The Number = 70095 (starts with 7)

When 9393 should be added to it

Now, the number becomes = (70095 + 9393) = 79488

If new number must be divisible by 12, 24, 32, 54.

So, it should be divisible by LCM of 12, 24, 32 and 54

LCM of 12, 24, 32 and 54 = 864

If we Divide the resultant number by 864, we get Quotient as 92.