Question

how many positive integer X are there such that 4x has four digit and 5x has five digit

Answer 1

X also has only one one digit

Answer 2

Number of positive integers ‘x’ where 3x has 3 digits

The smallest 3-digit multiple of 3 = 102 (3x). So ‘x’ is 34.

The largest 3-digit multiple of 3 = 999 (3x). So ‘x’ is 333.

So there are 300 (333–34+1) positive integers for which ‘3x’ has 3 digits

They are from 34 to 333.

Number of positive integers ‘x’ where 4x has 4 digits

The smallest 4-digit multiple of 4 = 1000 (4x). So ‘x’ is 250.


The largest 4-digit multiple of 4 = 9996 (4x). So ‘x’ is 2499.

So there are 2250 (2499–250+1) positive integers for which ‘4x’ has 4 digits

They are from 250 to 2499.

So the number of integers satisfying both the conditions would be

333–250+1 = 84.