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The number line above represents which of the following inequalities?

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by BTGModeratorVI » Sat Mar 14, 2020 6:31 am

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Answers

A

B

C

D

E

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Difficulty—

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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

Answer: B
Source: Manhattan Prep
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Re: The number line above represents which of the following inequalities?

by Brent@GMATPrepNow » Sun Mar 15, 2020 4:45 am
BTGModeratorVI wrote: ↑
Sat Mar 14, 2020 6:31 am
 Image

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

Answer: B
Source: Manhattan Prep
A quick approach here is to test 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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Re: The number line above represents which of the following inequalities?

by Scott@TargetTestPrep » Sat Mar 21, 2020 3:15 pm
BTGModeratorVI wrote: ↑
Sat Mar 14, 2020 6:31 am
 Image

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

Answer: B
Source: Manhattan Prep
Looking at answer choice B, we have:

-6 < 2x < 2

Dividing by 2, we have:

-3 < x < 1

Thus, we see this matches the given number line.

Answer: B

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