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

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Brent@GMATPrepNow: GMAT Instructor; Posts: 16207; Joined: Mon Dec 08, 2008 6:26 pm; Location: Vancouver, BC; Thanked: 5254 times; Followed by:1268 members; GMAT Score:770

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

by Brent@GMATPrepNow » Thu Jun 07, 2018 5:28 am

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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

Answer: D
Difficulty level: 600 - 650
Source: www.gmatprepnow.com

Brent Hanneson - Creator of GMATPrepNow.com

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Source: Beat The GMAT — Problem Solving | Thu Jun 07, 2018 5:28 am

GMAT/MBA Expert

Brent@GMATPrepNow: GMAT Instructor; Posts: 16207; Joined: Mon Dec 08, 2008 6:26 pm; Location: Vancouver, BC; Thanked: 5254 times; Followed by:1268 members; GMAT Score:770

by Brent@GMATPrepNow » Sat Jun 09, 2018 5:14 am

Brent@GMATPrepNow wrote:
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:

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 GMATPrepNow.com