1996 AJHSME Problems/Problem 5
Contents
Problem 5
The letters , , , , and represent numbers located on the number line as shown.
Which of the following expressions represents a negative number?
Solution 1
First, note that . Thus, and are negative, while , , and are positive.
Option is the difference of two numbers. If the first number is lower than the second number, the answer will be negative. In this case, , so , and is thus indeed a negative number. So option is correct.
Option is the product of two negatives, which is always positive.
Option starts with the quotient of a positive and a negative. This is negative. But this negative quotient is then multiplied by a negative number, which gives a positive number.
Option has the product of two negatives in the denominator. Thus, the denominator is positive. Additionally, the numerator is (barely) positive. A positive over a positive will be positive.
Option has the sum of two positives in the numerator. That will be positive. The denominator is also positive. Again, the quotient of two positives is positive.
Solution 2
Estimate the numbers, and calculate.
For option , the value of . Thus is the right answer.
For option ,
For option ,
For option ,
For option ,
See also
1996 AJHSME (Problems • Answer Key • Resources) | ||
Preceded by Problem 4 |
Followed by Problem 6 | |
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