Difference between revisions of "1999 CEMC Gauss (Grade 8) Problems/Problem 3"
(Created page with "== Problem== Which one of the following gives an odd integer? <math>\text{(A)}\ 6^2 \qquad \text{(B)}\ 23-17 \qquad \text{(C)}\ 9\times 24 \qquad \text{(D)}\ 96\div 8 \qquad...") |
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The only odd number from the list is <math>\boxed {\textbf{(E) } 9 \times 41}</math>. | The only odd number from the list is <math>\boxed {\textbf{(E) } 9 \times 41}</math>. | ||
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| + | ~anabel.disher | ||
==Solution 2== | ==Solution 2== | ||
Without evaluating the answers, we can see that <math>6^2</math> is the square of an even number, <math>9 \times 24</math> involves multiplication with an even number, and <math>23 - 17</math> involves two odd numbers, so those are even. This means that we can eliminate those answers. | Without evaluating the answers, we can see that <math>6^2</math> is the square of an even number, <math>9 \times 24</math> involves multiplication with an even number, and <math>23 - 17</math> involves two odd numbers, so those are even. This means that we can eliminate those answers. | ||
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Thus, the answer is <math>\boxed {\textbf{(E) } 9 \times 41}</math>. | Thus, the answer is <math>\boxed {\textbf{(E) } 9 \times 41}</math>. | ||
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| + | ~anabel.disher | ||
Latest revision as of 14:34, 15 September 2025
Problem
Which one of the following gives an odd integer?
Solution 1
Evaluating all of the answer choices, we get:
The only odd number from the list is 
.
~anabel.disher
Solution 2
Without evaluating the answers, we can see that 
is the square of an even number, 
involves multiplication with an even number, and 
involves two odd numbers, so those are even. This means that we can eliminate those answers.
involves the multiplication of two odd numbers, meaning that it must be the odd number.
Thus, the answer is .
~anabel.disher
