The number line above represents which of the following

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swerve: Legendary Member; Posts: 2535; Joined: Sun Oct 29, 2017 2:04 pmFollowed by: 6 members

by swerve » Mon Nov 19, 2018 8:44 am

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The number line above represents which of the following inequalities?

A. x < 1
B. -6 < 2x < 2
C. -9 < 3x < 6
D. 1 < 2x < 3
E. x > -3

The OA is B

Source: Manhattan Prep

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fskilnik@GMATH: GMAT Instructor; Posts: 1449; Joined: Sat Oct 09, 2010 2:16 pmFollowed by: 33 members; Thanked: 59 times

by fskilnik@GMATH » Mon Nov 19, 2018 10:26 am

swerve wrote:

The number line above represents which of the following inequalities?

A. x < 1
B. -6 < 2x < 2
C. -9 < 3x < 6
D. 1 < 2x < 3
E. x > -3
Source: Manhattan Prep

$$?\,\,\,:\,\,\, - 3 < x < 1\,\,\,\, \Leftrightarrow \,\,\,\, - 6 < 2x < 2\,\,\,\,\,\,\,\,\,\,\,\, \Rightarrow \,\,\,\,\,\,\left( {\rm{B}} \right)$$

This solution follows the notations and rationale taught in the GMATH method.

Regards,
Fabio.

Fabio Skilnik :: GMATH method creator ( Math for the GMAT)
English-speakers :: https://www.gmath.net
Portuguese-speakers :: https://www.gmath.com.br

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[email protected]: Elite Legendary Member; Posts: 10392; Joined: Sun Jun 23, 2013 6:38 pmFollowed by: 511 members; Location: Palo Alto, CA; Thanked: 2867 times; GMAT Score:800

by [email protected] » Mon Nov 19, 2018 10:56 am

Hi All,

The given Number line shows us a set of numbers from -3 to +1, NOT inclusive. We can TEST VALUES against the 5 answer choices to find the answer that includes JUST that range of numbers...

To start, both Answer A and Answer E include an open-ended range of values, so neither of those is correct.

With X=0, we can eliminate Answer D.

Answer B and C both include all of the values in the Number Line range, but Answer C includes some additional values (such as X = 1.5), that are NOT in the range defined by the Number Line. Eliminate Answer C.

Final Answer: B

GMAT assassins aren't born, they're made,
Rich

Contact Rich at [email protected]

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

by Brent@GMATPrepNow » Mon Nov 19, 2018 10:57 am

swerve wrote:

The number line above represents which of the following inequalities?

A. x < 1
B. -6 < 2x < 2
C. -9 < 3x < 6
D. 1 < 2x < 3
E. x > -3

We can also solve the question by testing the answer choices
Here's what I mean:

The diagram tells us that x= 0 is a solution to the inequality.
When we check the answer choices, we see that answer choice D (1 < 2x < 3) does NOT have x = 0 as a solution.
When we let x = 0, the inequality becomes 1 < 2(0) < 3. In other words, 1 < 0 < 3
No good! ELIMINATE D

The diagram also tells us that x= 1.5 is NOT a solution to the inequality.
When we check the answer choices, we see that answer choices C and E say that x = 1.5 IS a solution.
C. -9 < 3x < 6. Replace x with 1.5 to get: -9 < 4.5 < 6. Works! Since answer C says that x COULD equal 1.5, we can eliminate answer choice C
E. x > -3. Replace x with 1.5 to get: 1.5 > -3. Works! Since answer E says that x COULD equal 1.5, we can eliminate answer choice E.

We're down to answer choices A and B
The diagram tells us that x= -5 is NOT a solution to the inequality.
When we check the answer choices, we see that answer choice A say that x = -5 IS a solution.
A. x < 1. Replace x with -5 to get: -5 < 1. Works! Since answer A says that x COULD equal -5, we can eliminate answer choice A

By the process of elimination, we're left with...

Answer: B

Cheers,
Brent

Brent Hanneson - Creator of GMATPrepNow.com

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