CAT Exam Model Paper 8 with solutions for free online practice

The value of a three digit number in base 10 will be from 10${}^2$to 10${}^3$ -1 .
Similarly, the value of a three digit number in base 7 will be from 7${}^2$ to7${}^3$-1 .
And the value of a three digit number in base 13 will be from 13${}^2$ to 13${}^3$- 1.
So the common numbers are from 13${}^2$ to 7${}^3$ -1 . → 169 to 342
Hence, 174 such numbers would be there.