A fast approach is to apply rules for positive and negative numbers.

Quantity A: [2(negative) - positive]/negative
Quantity B: [2(positive) - negative]/negative

Quantity A: negative/negative
Quantity B: positive/negative

Quantity A: positive
Quantity B: negative

Answer:
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Another approach is use a property that says: (a - b)/x = a/x - b/x

Given:
Quantity A: (2x - y)/x
Quantity B: (2y - x)/x

Apply rule and rewrite:
Quantity A: 2x/x - y/x
Quantity B: 2y/x - x/x

Simplify:
Quantity A: 2 - y/x
Quantity B: 2y/x - 1

Add 1 to both quantities:
Quantity A: 3 - y/x
Quantity B: 2y/x

Add y/x to both quantities:
Quantity A: 3
Quantity B: 3y/x

Divide both quantities by 3 to get:
Quantity A: 1
Quantity B: y/x

Since x is NEGATIVE and y is POSITIVE, we know that y/x is NEGATIVE:
Quantity A: 1
Quantity B: NEGATIVE

Answer:

Cheers,
Brent
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