2020 AMC 10B Problems/Problem 1

Problem

What is the value of $1-(-2)-3-(-4)-5-(-6)?$

$\textbf{(A)}\ -20 \qquad\textbf{(B)}\ -3 \qquad\textbf{(C)}\ 3 \qquad\textbf{(D)}\ 5 \qquad\textbf{(E)}\ 21$

Solution 1

We know that when we subtract negative numbers, $a-(-b)=a+b$ .

The equation becomes $1+2-3+4-5+6 = \boxed{\textbf{(D)}\ 5}$ .

~quacker88

Solution 2

Like Solution 1, we know that when we subtract $a-(-b)$ , that will equal $a+b$ as the opposite/negative of a negative is a positive. Thus, $1-(-2)-3-(-4)-5-(-6)=1+2-3+4-5+6$ . We can group together a few terms to make our computation a bit simpler. $1+(2-3)+4+(-5+6)= 1+(-1)+4+1=\boxed{\textbf{(D)}\ 5}$ .

~BakedPotato66

Solution 3

Notice $1-(-2)-3-(-4)-5-(-6)$ has three groups: $1-(-2)$ , $-3-(-4)$ , $-5-(-6)$

The first group, $1-(-2)$ , can be expressed as $a-[-(a+1)]$ .

Simplify,

$a-[-(a+1)]$ is $2a+1$

The second and third groups can be expressed as $-c-[-(c+1)]$ .

Simplify,

$-c-[-(c+1)]$ is $1$

Thus, the sum of the three groups is $2 \cdot 1 + 1 + 1 + 1 = 5$ or $\boxed{\textbf{(D)}\ 5}$

Video Solutions

Video Solution by Education, the study of everything

https://www.youtube.com/watch?v=NpDVTLSi-Ik

~Education, the Study of Everything

Video Solution by TheBeautyofMath

https://youtu.be/Gkm5rU5MlOU

~IceMatrix

Video Solution by WhyMath

https://youtu.be/-wciFhP5h3I

~savannahsolver

Video Solution by Alex Explains

https://www.youtube.com/watch?v=GNPAgQ8fSP0&t

~AlexExplains

2020 AMC 10B (Problems • Answer Key • Resources)
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All AMC 10 Problems and Solutions

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

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