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x+y/n < x+z/n and x^2 - z + y < 0

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GRE Instructor
Joined: 10 Apr 2015
Posts: 2311
Followers: 73

Kudos [?]: 2208 [0], given: 27

x+y/n < x+z/n and x^2 - z + y < 0 [#permalink]  05 Aug 2019, 06:46
Expert's post
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Question Stats:

58% (01:19) correct 41% (00:26) wrong based on 12 sessions
$$\frac{x+y}{n}<\frac{x+z}{n}$$ and $$x^2-z+y<0$$

 Quantity A Quantity B n 0

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.
[Reveal] Spoiler: OA

_________________

Brent Hanneson – Creator of greenlighttestprep.com

Last edited by Carcass on 05 Aug 2019, 06:52, edited 1 time in total.
Edited by Carcass
GRE Instructor
Joined: 10 Apr 2015
Posts: 2311
Followers: 73

Kudos [?]: 2208 [0], given: 27

Re: x+y/n < x+z/n and x^2 - z + y < 0 [#permalink]  05 Aug 2019, 08:49
Expert's post
GreenlightTestPrep wrote:
$$\frac{x+y}{n}<\frac{x+z}{n}$$ and $$x^2-z+y<0$$

 Quantity A Quantity B n 0

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.

Given: $$\frac{x+y}{n}<\frac{x+z}{n}$$

Rewrite as: $$\frac{x}{n}+\frac{y}{n}<\frac{x}{n}+\frac{z}{n}$$

Subtract $$\frac{x}{n}$$ from both sides to get: $$\frac{y}{n}<\frac{z}{n}$$

Subtract $$\frac{y}{n}$$ from both sides to get: $$0<\frac{z}{n}-\frac{y}{n}$$

Simplify to get: $$0<\frac{z-y}{n}$$

In other words, $$\frac{z-y}{n}$$ is POSITIVE
------------------------------------------------------

Also given: $$x^2-z+y<0$$
Add z to both sides to get: $$x^2+y<z$$
Subtract y from both sides to get: $$x^2<z-y$$
Since 0 ≤ x², we can write 0 ≤ x² < z - y
This tells us that: 0 < z - y
In other words, z - y is POSITIVE
-------------------------------------------------------

If $$\frac{z-y}{n}$$ is POSITIVE and z-y is POSITIVE, then we can be certain that n is positive

We get:
Quantity A: Some positive number
Quantity B: 0

Cheers,
Brent
_________________

Brent Hanneson – Creator of greenlighttestprep.com

Re: x+y/n < x+z/n and x^2 - z + y < 0   [#permalink] 05 Aug 2019, 08:49
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