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The number line above shows the position of a point that has coordinat

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The number line above shows the position of a point that has coordinat [#permalink]

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New post 12 Jul 2017, 01:49
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The number line above shows the position of a point that has coordinate x. Which of the following statements about x must be true?

I. 2 < x < 4
II. – x < – 3
III. 0 < 2x – 3 < 1

(A) I only
(B) II only
(C) III only
(D) I and II
(E) I and III


[Reveal] Spoiler:
Attachment:
2017-07-12_1248.png
2017-07-12_1248.png [ 2.76 KiB | Viewed 548 times ]
[Reveal] Spoiler: OA

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Re: The number line above shows the position of a point that has coordinat [#permalink]

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New post 12 Jul 2017, 02:21
Bunuel wrote:
Image
The number line above shows the position of a point that has coordinate x. Which of the following statements about x must be true?

I. 2 < x < 4
II. – x < – 3
III. 0 < 2x – 3 < 1

(A) I only
(B) II only
(C) III only
(D) I and II
(E) I and III


[Reveal] Spoiler:
Attachment:
2017-07-12_1248.png


It should be A.

I - pretty obvious from the graph line.
II - From the graph we know, 2 < x < 3

multiplying by - 1 would flip signs.

-2 > x > -3

so x cannot be smaller than -3.

III -

0 < 2x - 3 < 1

adding 3 to all 3.

3 < 2x < 4

dividing by 2

3/2 < x < 2

but we know x is between 2 and 3 and not 1.5 and 2.
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Re: The number line above shows the position of a point that has coordinat [#permalink]

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New post 12 Jul 2017, 06:49
Bunuel wrote:
Image
The number line above shows the position of a point that has coordinate x. Which of the following statements about x must be true?

I. 2 < x < 4
II. – x < – 3
III. 0 < 2x – 3 < 1

(A) I only
(B) II only
(C) III only
(D) I and II
(E) I and III


[Reveal] Spoiler:
Attachment:
2017-07-12_1248.png


From the graph given ,
2<x<3
=> 2<x< 4

II. – x < – 3
=> x > 3 , this is false

III. 0 < 2x – 3 < 1
=> 3< 2x < 4
=> 3/2 < x < 2 , this is false

Answer A
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Re: The number line above shows the position of a point that has coordinat [#permalink]

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New post 06 Aug 2017, 10:49
Bunuel wrote:
Image
The number line above shows the position of a point that has coordinate x. Which of the following statements about x must be true?

I. 2 < x < 4
II. – x < – 3
III. 0 < 2x – 3 < 1

(A) I only
(B) II only
(C) III only
(D) I and II
(E) I and III


[Reveal] Spoiler:
Attachment:
2017-07-12_1248.png


I. From the number line, 2<x<4. True
II. x < 3, flipping the sign gives -x > -3. Not true.
III. Pick a number closest to 2, say 2.1
2x - 3 = 2*2.1 - 3 = 4.2 - 3 = 1.2 > 1
So, 0 < 2x - 3 < 1 Not true.

Ans A. I only.

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Re: The number line above shows the position of a point that has coordinat   [#permalink] 06 Aug 2017, 10:49
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