from: category_eng |
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Let be a positive integer such that is an integer. Which of the following statements is not true: ' |
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3. | ' ' |
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4. | ' ' |
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Which of the following is equal to the product
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6. | ' ' |
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7. | ' ' |
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9. | ' ' |
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From which it follows that and . Thus the answer is . |
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We can rewrite the given fraction as: |
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We also know that because and are of opposite sign. Therefore, is maximized when is minimized, which occurs when is the largest and is the smallest. |
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Multiplying the numerator and the denominator by the same value does not change the value of the fraction. Alternately, we can directly compute that the numerator is , the denominator is , and hence their ratio is . |
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Solution 1Solution 2Notice that everything cancels out except for in the numerator and in the denominator. Thus, the product is , and the answer is . |
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We compute: |
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First, simplify the fractions. |
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First, simplify the fractions. |
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The number halfway between is the average. |