If g and h are integers and g/h > 1, which of the following could

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