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# Given that 2x + 7 > 5 and 5x - 13 < 7, all values of x must be between

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Given that 2x + 7 > 5 and 5x - 13 < 7, all values of x must be between  [#permalink]

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18 Oct 2016, 02:24
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89% (00:52) correct 11% (01:16) wrong based on 91 sessions

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Given that 2x + 7 > 5 and 5x - 13 < 7, all values of x must be between which of the following pairs of integers?

A. -4 and -1
B. -1 and 4
C. -4 and 1
D. -2 and 5
E. 2 and 5

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Re: Given that 2x + 7 > 5 and 5x - 13 < 7, all values of x must be between  [#permalink]

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18 Oct 2016, 02:40
2x+7>5

2x>-2

x>-1

5x-13<7

5x<20

x<4

B

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Re: Given that 2x + 7 > 5 and 5x - 13 < 7, all values of x must be between  [#permalink]

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18 Oct 2016, 04:45
Bunuel wrote:
Given that 2x + 7 > 5 and 5x - 13 < 7, all values of x must be between which of the following pairs of integers?

A. -4 and -1
B. -1 and 4
C. -4 and 1
D. -2 and 5
E. 2 and 5

From the first inequality,

$$2x + 7 > 5$$

$$x > -1$$

From the second inequality,

$$5x - 13 < 7$$

$$x <$$ $$\frac{20}{5}$$

$$x < 4$$ approx

Therefor (B) $$-1 < x < 4$$
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Re: Given that 2x + 7 > 5 and 5x - 13 < 7, all values of x must be between  [#permalink]

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18 Oct 2016, 06:07
Bunuel wrote:
Given that 2x + 7 > 5 and 5x - 13 < 7, all values of x must be between which of the following pairs of integers?

A. -4 and -1
B. -1 and 4
C. -4 and 1
D. -2 and 5
E. 2 and 5

2x + 7 > 5
i.e 2x >5-7
i.e. 2x > -2
i.e. x > -1

Also, 5x - 13 < 7
i.e. 5x <7+13
i.e 5x < 20
i.e x < 4

i.e. -1 < x < 4

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Re: Given that 2x + 7 > 5 and 5x - 13 < 7, all values of x must be between  [#permalink]

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18 Oct 2016, 07:42
Bunuel wrote:
Given that 2x + 7 > 5 and 5x - 13 < 7, all values of x must be between which of the following pairs of integers?

A. -4 and -1
B. -1 and 4
C. -4 and 1
D. -2 and 5
E. 2 and 5

Min value of x in 2x + 7 > 5 must be -

2x > -2

Or, x > - 1

Max value of x in 5x - 13 < 7 must be -

5x < 20

Or, x < 4

So, x must be between -1 and 4 , and answer will hence be (B)

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Re: Given that 2x + 7 > 5 and 5x - 13 < 7, all values of x must be between  [#permalink]

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14 Jan 2018, 11:25
Bunuel wrote:
Given that 2x + 7 > 5 and 5x - 13 < 7, all values of x must be between which of the following pairs of integers?

A. -4 and -1
B. -1 and 4
C. -4 and 1
D. -2 and 5
E. 2 and 5

$$2x + 7 > 5$$

Or, $$2x > -2$$

Or, $$x > -1$$

$$5x - 13 < 7$$

Or, $$5x < 20$$

Or, $$x < 4$$

Finally we have : $$-1 < x < 4$$, among the given options only (B) satisfies, answer will be (B)
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Thanks and Regards

Abhishek....

PLEASE FOLLOW THE RULES FOR POSTING IN QA AND VA FORUM AND USE SEARCH FUNCTION BEFORE POSTING NEW QUESTIONS

How to use Search Function in GMAT Club | Rules for Posting in QA forum | Writing Mathematical Formulas |Rules for Posting in VA forum | Request Expert's Reply ( VA Forum Only )
Re: Given that 2x + 7 > 5 and 5x - 13 < 7, all values of x must be between   [#permalink] 14 Jan 2018, 11:25
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