Difference between revisions of "2010 AMC 10B Problems/Problem 1"

Latest revision as of 15:58, 1 August 2022

What is $100(100-3)-(100\cdot100-3)$ ?

$\textbf{(A)}\ -20,000 \qquad \textbf{(B)}\ -10,000 \qquad \textbf{(C)}\ -297 \qquad \textbf{(D)}\ -6 \qquad \textbf{(E)}\ 0$

$100(100-3)-(100\cdot{100}-3)=10000-300-10000+3=-300+3=\boxed{\textbf{(C)}\ -297}$ .

~Education, the Study of Everything

~IceMatrix

2010 AMC 10B (Problems • Answer Key • Resources)
Preceded by First Problem	Followed by Problem 2
1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15 • 16 • 17 • 18 • 19 • 20 • 21 • 22 • 23 • 24 • 25
All AMC 10 Problems and Solutions

@@ Line 1: / Line 1: @@
 == Problem ==
-. What is <math>100(100-3)-(100\cdot100-3)</math>?
+What is <math>100(100-3)-(100\cdot100-3)</math>?
 <math>
-\mathrm{(A)}\ -20,000
+\textbf{(A)}\ -20,000
 \qquad
-\mathrm{(B)}\ -10,000
+\textbf{(B)}\ -10,000
 \qquad
-\mathrm{(C)}\ -297
+\textbf{(C)}\ -297
 \qquad
-\mathrm{(D)}\ -6
+\textbf{(D)}\ -6
 \qquad
-\mathrm{(E)}\ 0
+\textbf{(E)}\ 0
 </math>
 == Solution ==
-We first expand the first term, simplify, and then compute to get an answer of {{boxed}}<math>(C) -297</math>{{/boxed}}.
+<math>100(100-3)-(100\cdot{100}-3)=10000-300-10000+3=-300+3=\boxed{\textbf{(C)}\ -297}</math>.
+==Video Solution==
+https://youtu.be/mvMGV8tpqGs
+~Education, the Study of Everything
+==Video Solution==
+https://youtu.be/uAc9VHtRRPg
+~IceMatrix
+==See Also==
+{{AMC10 box|year=2010|ab=B|before=First Problem|num-a=2}}
+{{MAA Notice}}