Bunuel wrote:
If g and h are integers and g/h > 1, which of the following could illustrate the position of g and h on the number line?
Attachment:
2017-07-14_1156.png
Method I - Choose numbers
1. Pick an integer quotient greater than 1. Use 2.
Let g = 4, so h must = 2.
The answer choices should signal scenario two:
g = -4, in which case h must = -2.
So g = 4 and h = 2, OR g = -4 and h = -2
Chosen values are +/+ and -/-, i.e., same sign, and must be that way. 4/-2, e.g., equals -2. Our quotient is positive.
2. Eliminate C and D; opposite signs won't work.
3. Answers B and E have the variables in the wrong order.
For B, 4 is not less than 2.
For E, -4 is not greater than -2.
Eliminate B and E.
3. Check variables' placement in A. -4 is less than -2. Correct.
Method II - Mostly algebra
1. We need two positive or two negative values.
If \(\frac{g}{h}\) > 1, either both are positive or both are negative because their quotient is positive.
2. Determine relative size of variables.
When both are
positive:
\(\frac{+g}{+h}\) > 1, multiply by h
g > h
When both are
negative:
\(\frac{-g}{-h}\) > 1, multiply by h and reverse the sign
-g < -h
(When dealing with variables, it's easy to get this one wrong. That's what trap answer E is for. So: g is more negative than h, farther left on number line).
3. Eliminate C and D; g and h have different signs.
4. B, both variables positive, says g < h. From above, false. When positive, g > h. Eliminate B.
5. A or E? In both choices, both variables are negative.
E is backwards, says -g > - h (g is not, as it should be, farther left on number line). Eliminate E.
A says -g < - h. (g is farther left than h on number line.) Correct.
Answer A
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