GreenlightTestPrep wrote:

If 0 < x < y, then which of the following MUST be true?

A) \(\frac{x + 2}{y + 2} > x/y\)

B) \(\frac{x - y}{x} < 0\)

C) \(\frac{2x}{x + y} < 1\)

Answer:

Let's examine each statement individually:

A) (x + 2)/(y + 2) > x/ySince y is POSITIVE, we can safely take the given inequality and multiply both sides by y to get: (y)(x+2)/(y+2) > x

Also, if y is POSITIVE, then (y+2) is POSITIVE, which means we can safely multiply both sides by (y+2) to get: (y)(x+2) > x(y+2)

Expand: xy + 2y > xy + 2x

Subtract xy from both sides: 2y > 2x

Divide both sides by 2 to get: y > 2

Perfect! This checks out with the given information that says 0 < x < y

So, statement A is TRUE

B) (x - y)/x < 0Let's use number sense here.

If x < y, then x - y must be NEGATIVE

We also know that x is POSITIVE

So, (x - y)/x = NEGATIVE/POSITIVE = NEGATIVE

In other words, it's TRUE that (x - y)/x < 0

Statement B is TRUE

C) 2x/(x + y) < 1More number sense...

If x is positive, then 2x is POSITIVE

If x and y are positive, then x + y is POSITIVE

If x < y, then we know that x + x < x + y

In other words, we know that 2x < x + y

If 2x < x + y, then the FRACTION 2x/(x + y) must be less than 1

Statement C is TRUE

Answer: A, B, C

Cheers,

Brent

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Brent Hanneson – Creator of greenlighttestprep.com

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