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A) Quantity A is greater. B) Quantity B is greater. C) The two quantities are equal. D) The relationship cannot be determined from the information given.

Let's see what happens if we rewrite Quantity A as one big fraction. First get common denominators... Quantity A: 5y/2xy - 2x/2yx Quantity B: (5y-2x)/(2x-2y)

Combine to get: Quantity A: (5y-2x)/2yx Quantity B: (5y-2x)/(2x-2y)

NICE!! This numerators are the same for both fractions. This gives me the opportunity to use a strategy I call "Looking for Equality" (see our video below for more on this) I can see that if I choose an x- and y-value that makes the numerators both zero, this will speed up my solution. You'll see why shortly.

I can see that, if x = 5 and y = 2, then we can plug these values into the quantities to get: Quantity A: [5(2)-2(5)]/(2)(2)(5) Quantity B: [5(2)-2(5)]/[2(5)-2(2)]

Evaluate: Quantity A: 0 Quantity B: 0

So, when x = 5 and y = 2 the quantities are EQUAL. The correct answer is EITHER C or D

At this point, every pair of x- and y-values will either yield equal quantities or not. Let's plug in super-easy numbers. We'll plug in x = 1 and y = 1 We get: Quantity A: [5(1)-2(1)]/(2)(1)(1) Quantity B: [5(1)-2(1)]/[2(1)-2(1)]

Evaluate: Quantity A: 3/2 Quantity B: 3/0 These quantities are definitely NOT EQUAL.

From the given condition, x and y have to both positive or negative. Now putting value x=1, y=1 Q.A 3/2 Q.B undefined Now putting x=1,y=2 Q.A 2 Q.B -4 , Q.A>Q.B Now putting x=-1,y=-1 Q.A -3/2 Q.B undefined