1999 CEMC Gauss (Grade 7) Problems/Problem 5

Problem

Which one of the following gives an odd integer?

$\text{(A)}\ 6^2 \qquad \text{(B)}\ 23-17 \qquad \text{(C)}\ 9\times 24 \qquad \text{(D)}\ 96\div 8 \qquad \text{(E)}\ 9\times 41$

Solution 1

Evaluating all of the answer choices, we get:

$6^2 = 36$

$23 - 17 = 6$

$9 \times 24 = 216$

$96 \div 8 = 12$

$9 \times 41 = 369$

The only odd number from the list is $\boxed {\textbf{(E)} 9 \times 41}$ .

Solution 2

Without evaluating the answers, we can see that $6^2$ is the square of an even number, $9 \times 24$ involves multiplication with an even number, and $23 - 17$ involves two odd numbers, so those are even. This means that we can eliminate those answers.

$9 \times 41$ involves the multiplication of two odd numbers, meaning that it must be the odd number.

Thus, the answer is $\boxed {\textbf{(E)} 9 \times 41}$ .

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1999 CEMC Gauss (Grade 7) Problems/Problem 5

Problem

Solution 1

Solution 2