What is 100(100-3)-(100 × 100-3)?

2010 AMC 10B Problem 1 — Solution

2010 AMC 10B Problem 1

Attempt Problem 1 of the 2010 AMC 10B below, then check your answer against the professionally curated solution from LIVE by Po-Shen Loh. You can also try the full timed exam, view all 2010 AMC 10B solutions, or check the answer key.

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

$-20,000$

$-10,000$

$-297$

$-6$

$0$

Answer: C

Concepts:order of operations whole number operations

Difficulty rating: 560

Solution:

We have that $\begin{align*}100(100 - 3) &= 100 \cdot 97 \\&= 9700\end{align*}$ and $\begin{align*}100 \cdot 100 - 3 &= 10000 - 3\\ &= 9997.\end{align*}$

As such, their difference is: $9700 - 9997 = - 297.$

Thus, C is the correct answer.

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