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Re: If 0 < x < y, then which of the following MUST be true [#permalink]
All options are true..
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Re: If 0 < x < y, then which of the following MUST be true [#permalink]
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GreenlightTestPrep wrote:
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:
Show: ::
A, B and C


Let's examine each statement individually:

A) (x + 2)/(y + 2) > x/y
Since 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 > x
Perfect! This checks out with the given information that says 0 < x < y
So, statement A is TRUE

B) (x - y)/x < 0
Let'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) < 1
More 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,

Hi BrentGreenlightTestPrep, is it normal for GRE question as in this one not to say choose one or select all that apply? Got kind of confuse in this question.
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If 0 < x < y, then which of the following MUST be true [#permalink]
Expert Reply
Hi

Usually is ALWAYS indicateded. However, it is rare to have five answer choices in a multiple answer choice question.

The only case you do have five A >>> E are problem sovilng questions.

What you asked is legit but a bit trivial. You should be aware of the multiple choices as you should have in mind always the four answer choices A>>>>D in a quantitative comparison question.

It should be natural for a GRE test taker.

Regards

Posted from my mobile device
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Re: If 0 < x < y, then which of the following MUST be true [#permalink]
Noted thanks Carcass
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Re: If 0 < x < y, then which of the following MUST be true [#permalink]
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