2010 AMC 10B Problem 1

Problem 1 of 25EasierAlgebra

What is the value of the following expression?

100(100-3)-(100 \cdot 100-3)

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Solution

We have that

\begin{aligned}100(100 - 3) &= 100 \cdot 97 \\&= 9700\end{aligned}

and

\begin{aligned}100 \cdot 100 - 3 &= 10000 - 3\\ &= 9997.\end{aligned}

As such, their difference is:

9700 - 9997 = - 297.

Thus, C is the correct answer.

Concepts: order of operations · whole number operations

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