Difference between revisions of "2021 AMC 12A Problems/Problem 3"

Revision as of 15:51, 11 February 2021

Problem

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?

$\textbf{(A)} ~10{,}272\qquad\textbf{(B)} ~11{,}700\qquad\textbf{(C)} ~13{,}362\qquad\textbf{(D)} ~14{,}238\qquad\textbf{(E)} ~15{,}426$

Solution

The units digit of a multiple of $10$ will always be $0$ . We add a $0$ whenever we multiply by $10$ . So, removing the units digit is equal to dividing by $10$ .

Let the smaller number (the one we get after removing the units digit) be $a$ . This means the bigger number would be $10a$ .

We know the sum is $10a+a = 11a$ so $11a=17402$ . So $a=1582$ . The difference is $10a-a = 9a$ . So, the answer is $9(1582) = 14238 = \boxed{\textbf{(D)}}$ .

--abhinavg0627

Video Solution by Punxsutawney Phil

https://youtube.com/watch?v=MUHja8TpKGw&t=143s

Video Solution by Hawk Math

https://www.youtube.com/watch?v=P5al76DxyHY

Video Solution

https://youtu.be/d2musztzDjw -pi_is_3.14

2021 AMC 12A (Problems • Answer Key • Resources)
Preceded by Problem 2	Followed by Problem 4
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All AMC 12 Problems and Solutions

The problems on this page are copyrighted by the Mathematical Association of America's American Mathematics Competitions.

@@ Line 17: / Line 17: @@
 ==Video Solution by Punxsutawney Phil==
 https://youtube.com/watch?v=MUHja8TpKGw&t=143s
+==Video Solution by Hawk Math==
+https://www.youtube.com/watch?v=P5al76DxyHY
 ==Video Solution==

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