Question

The hundreds digit of a three-digit number is $2$ more than the units digit. The digits of the three-digit number are reversed, and the result is subtracted from the original three-digit number. What is the units digit of the result?

$0$

$2$

$4$

$6$

$8$

Answer: E

Concepts:place value digits

Difficulty rating: 1260

Solution:

Let the units digit be $u,$ and let the tens digit be $t.$ This makes the hundreds digit be $u+2.$ This makes the number equal to $100(u+2) +10t+u$ $=101u+200+10t$ and the reversed number is $100u +10t+(u+2)$ $=101u+2+10t.$ This makes the difference equal to $(101u+10t+200)-$ $(101u+10t+2)=198.$ This makes the units digit $8.$

Therefore, the units digit is E .

2010 AMC 8 Problem 22

Answer: E

Difficulty rating: 1260

Solution:

Problem 22 in Other Years