Sample Problem

I’m thinking of a three-digit number X3Y, in which the tens digit is 3. (Where X and Y present unknown digits.)

(a)   What is the largest number?

(b)   What is the smallest number?

(c)   What number is closest to 400?


(a)  To make a largest number, replace X and Y with the largest digit 9. The result is 939;

(b)  To make a smallest number, replace X with 1, which is the smallest digit possible for a three-digit number.

The result is 130;

(c)  We can try to replace X with 3 or 4, and replace Y with 9 and 0; and get 339 and 430;

400 – 339 = 61

430 – 400 = 30

Thus, the closest number (to 400) we can get is 430.