Question

The sum of two natural numbers is $17,402.$ One of the two numbers is divisible by $10.$ If the units digit of that number is erased, the other number is obtained. What is the difference of these two numbers?

$10,272$

$11,700$

$13,362$

$14,238$

$15,426$

Answer: D

Concepts:place value linear equation

Difficulty rating: 900

Video solution:

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Written solution:

Let $x$ and $y$ be the two numbers. WLOG, let $x$ be divisible by $10.$ Then the units digit of $x$ is $0.$

If we erase the units digit, then we are essentially dividing $x$ by $10.$ The problem statement also gives us that $\dfrac{x}{10} = y.$

Therefore, $\begin{aligned} \dfrac{x}{10} + x &= 17,402 \\ \dfrac{11x}{10} &= 17,402 \\ x &= 15,820. \end{aligned}$ Then $x - \dfrac{x}{10} = 14,238.$

Thus, D is the correct answer.

2021 AMC 10A Spring Problem 3

Answer: D

Difficulty rating: 900

Video solution:

Written solution:

Problem 3 in Other Years