1999 CEMC Gauss (Grade 7) Problems/Problem 1

Problem

$1999 - 999 + 99$ equals

$\text{(A)}\ 901 \qquad \text{(B)}\ 1099 \qquad \text{(C)}\ 1000 \qquad \text{(D)}\ 199 \qquad \text{(E)}\ 99$

Solution 1

$1999 - 999 + 99 = 1000 + 99 = \boxed{\textbf{(B) }1099}$

~anabel.disher

Solution 2

$1999$ is approximately $2000$ , $999$ is approximately $1000$ , and $99$ is approximately $100$ . This means we can approximate the solution as: $2000 - 1000 + 100 = 1100$

The closest answer is $\boxed{\textbf{(B) }1099}$ .

~anabel.disher

Solution 3 (answer choices)

Subtracting $99$ from the answer choices and then adding $999$ , or simply adding $900$ to the answer choices, should give $1999$ .

Adding $900$ to each answer gives: $\text{(A)}\ 1801 \qquad \text{(B)}\ 1999 \qquad \text{(C)}\ 1900 \qquad \text{(D)}\ 1099 \qquad \text{(E)}\ 999$

Thus, the answer is $\boxed{\textbf{(B) }1099}$

~anabel.disher

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1999 CEMC Gauss (Grade 7) Problems/Problem 1

Contents

Problem

Solution 1

Solution 2

Solution 3 (answer choices)