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If x > 0, b > a, and 2x + 5 < 3x + 1,

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If x > 0, b > a, and 2x + 5 < 3x + 1, [#permalink] New post 07 Jun 2018, 05:35
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Question Stats:

50% (02:00) correct 50% (02:59) wrong based on 2 sessions
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If x > 0, b > a, and 2x + 5 < 3x + 1, then which of the following COULD be a value of x?

i) 4.39
ii) 7.17
iii) 9.27 


A) i and ii only
B) ii and iii only
C) i and iii only
D) iii only
E) i, ii and iii
[Reveal] Spoiler: OA

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Brent Hanneson – Creator of greenlighttestprep.com
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Last edited by Carcass on 09 Jun 2018, 08:47, edited 1 time in total.
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1 KUDOS received
GRE Instructor
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Joined: 10 Apr 2015
Posts: 1227
Followers: 45

Kudos [?]: 1105 [1] , given: 7

Re: If x > 0, b > a, and 2x + 5 < 3x + 1, [#permalink] New post 09 Jun 2018, 05:20
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GreenlightTestPrep wrote:
Image

If x > 0, b > a, and 2x + 5 < 3x + 1, then which of the following COULD be a value of x?

i) 4.39
ii) 7.17
iii) 9.27 


A) i and ii only
B) ii and iii only
C) i and iii only
D) iii only
E) i, ii and iii


Here's a useful triangle property:
Image

So, if b > a, then we know that 3x + 1 < 4x - 8
We're also told that 2x + 5 < 3x + 1

So, we can create the following 3-part inequality: 2x + 5 < 3x + 1 < 4x - 8
Subtract 2x from all 3 sides: 5 < x + 1 < 2x - 8
When we examine 5 < x + 1, we can conclude that 4 < x. So, x is greater than 4
When we examine x + 1 < 2x - 8, we can conclude that 9 < x. So, x is greater than 9

So, we know that x is greater than 4 AND x is greater than 9
So, it MUST be the case that x is greater than 9

Check the statements.....
Only statement iii works.

Answer: D

Cheers,
Brent
_________________

Brent Hanneson – Creator of greenlighttestprep.com
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Re: If x > 0, b > a, and 2x + 5 < 3x + 1,   [#permalink] 09 Jun 2018, 05:20
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