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Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.  If x is an integer and |2x + 3| ≤ 12 then which of the following must

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Math Expert V
Joined: 02 Sep 2009
Posts: 55804
If x is an integer and |2x + 3| ≤ 12 then which of the following must  [#permalink]

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Difficulty:   85% (hard)

Question Stats: 53% (01:56) correct 47% (01:57) wrong based on 407 sessions

HideShow timer Statistics If x is an integer and $$|2x+3|≤12$$, then which of the following must be true?

A. x < -9
B. x < -8
C. x > -8
D. x < 4
E. x > 4

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If x is an integer and |2x + 3| ≤ 12 then which of the following must  [#permalink]

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1
Bunuel wrote:
If x is an integer and $$|2x+3|≤12$$, then which of the following must be true?

A. x < -9
B. x < -8
C. x > -8
D. x < 4
E. x > 4

$$|2x+3|≤12$$

i.e. $$-12 ≤ 2x+3 ≤ 12$$

i.e. $$-12-3 ≤ 2x ≤ 12-3$$

i.e. $$-15 ≤ 2x ≤ 9$$

i.e. $$-7.5 ≤ x ≤ 4.5$$

Out of all options we see

A. x < -9 Is INCORRECT as all values of x are greater than -9
B. x < -8 Is INCORRECT as all values of x are greater than -8
C. x > -8 Is CORRECT because all values of x in the calculated range of values of x are greater than -8
D. x < 4 Is INCORRECT because x may be 4 which is NOT less than 4
E. x > 4 Is INCORRECT as x may be less than 4 as well

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Originally posted by GMATinsight on 19 Oct 2018, 00:24.
Last edited by GMATinsight on 20 Oct 2018, 21:52, edited 1 time in total.
Manager  G
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Re: If x is an integer and |2x + 3| ≤ 12 then which of the following must  [#permalink]

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Bunuel wrote:
If x is an integer and $$|2x+3|≤12$$, then which of the following must be true?

A. x < -9
B. x < -8
C. x > -8
D. x < 4
E. x > 4

use this link to solve - https://gmatclub.com/forum/inequalities ... 06653.html
Veritas Prep GMAT Instructor D
Joined: 16 Oct 2010
Posts: 9369
Location: Pune, India
Re: If x is an integer and |2x + 3| ≤ 12 then which of the following must  [#permalink]

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1
Bunuel wrote:
If x is an integer and $$|2x+3|≤12$$, then which of the following must be true?

A. x < -9
B. x < -8
C. x > -8
D. x < 4
E. x > 4

$$|2x+3|≤12$$

$$|x+3/2|≤6$$

So x is a point that is a distance of 6 or less from -1.5
So x would be less than 4.5 or more than -7.5

$$-7.5 \leq x \leq 4.5$$

<------------------------ (-7.5) ================== (4.5) ---------------------->

x can take any value in the "===" region. For each value in this region, x is definitely greater than -8.

For more, check: https://www.veritasprep.com/blog/2011/0 ... edore-did/
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If x is an integer and |2x + 3| ≤ 12 then which of the following must  [#permalink]

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Attachments IMG_20181021_115527.jpg [ 1.45 MiB | Viewed 1900 times ]

Originally posted by HAPPYatHARVARD on 20 Oct 2018, 06:53.
Last edited by HAPPYatHARVARD on 21 Oct 2018, 09:08, edited 2 times in total.
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Joined: 25 Jan 2018
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Re: If x is an integer and |2x + 3| ≤ 12 then which of the following must  [#permalink]

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Quote:
A. x < -9 Is INCORRECT as all values of x are greater than -9
B. x < -8 Is INCORRECT as all values of x are greater than -8
C. x > -8 Is CORRECT because all values of x in the calculated range of values of x are greater than -8
D. x < 4 Is INCORRECT because x may be 4.25 which is greater than 4
E. x > 4 Is INCORRECT as x may be less than 4 as well

Quick clarification question - with regard to answer D, x is an integer—so 4.25 being greater than 4 is not the reason why the choice is wrong. It's because x could be 4, which is not included by x < 4. Is that correct?
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Re: If x is an integer and |2x + 3| ≤ 12 then which of the following must  [#permalink]

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fogarasm wrote:
Quote:
A. x < -9 Is INCORRECT as all values of x are greater than -9
B. x < -8 Is INCORRECT as all values of x are greater than -8
C. x > -8 Is CORRECT because all values of x in the calculated range of values of x are greater than -8
D. x < 4 Is INCORRECT because x may be 4.25 which is greater than 4
E. x > 4 Is INCORRECT as x may be less than 4 as well

Quick clarification question - with regard to answer D, x is an integer—so 4.25 being greater than 4 is not the reason why the choice is wrong. It's because x could be 4, which is not included by x < 4. Is that correct?

fogarasm Thank you for pointing out the mistake in the mistake. I missed the information in quick solving the question. _________________
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Re: If x is an integer and |2x + 3| ≤ 12 then which of the following must  [#permalink]

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Graphical approach shall be as per attached sketch
Attachment: WhatsApp Image 2018-10-21 at 10.32.28.jpeg [ 60.94 KiB | Viewed 1968 times ]

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Re: If x is an integer and |2x + 3| ≤ 12 then which of the following must  [#permalink]

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HAPPYatHARVARD wrote:

Yes, this method uses the definition of absolute values. The method I have shown is based on the concept of looking at absolute value in terms of distance.
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Re: If x is an integer and |2x + 3| ≤ 12 then which of the following must  [#permalink]

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GMATinsight wrote:
Bunuel wrote:
If x is an integer and $$|2x+3|≤12$$, then which of the following must be true?

A. x < -9
B. x < -8
C. x > -8
D. x < 4
E. x > 4

$$|2x+3|≤12$$

i.e. $$-12 ≤ 2x+3 ≤ 12$$

i.e. $$-12-3 ≤ 2x ≤ 12-3$$

i.e. $$-15 ≤ 2x ≤ 9$$

i.e. $$-7.5 ≤ x ≤ 4.5$$

Out of all options we see

A. x < -9 Is INCORRECT as all values of x are greater than -9
B. x < -8 Is INCORRECT as all values of x are greater than -8
C. x > -8 Is CORRECT because all values of x in the calculated range of values of x are greater than -8
D. x < 4 Is INCORRECT because x may be 4 which is NOT less than 4
E. x > 4 Is INCORRECT as x may be less than 4 as well

I got the same range but won't x > -8 include values above 4.5 ?
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Status: GMATINSIGHT Tutor
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Re: If x is an integer and |2x + 3| ≤ 12 then which of the following must  [#permalink]

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1
shobhiitgupta wrote:
GMATinsight wrote:
Bunuel wrote:
If x is an integer and $$|2x+3|≤12$$, then which of the following must be true?

A. x < -9
B. x < -8
C. x > -8
D. x < 4
E. x > 4

$$|2x+3|≤12$$

i.e. $$-12 ≤ 2x+3 ≤ 12$$

i.e. $$-12-3 ≤ 2x ≤ 12-3$$

i.e. $$-15 ≤ 2x ≤ 9$$

i.e. $$-7.5 ≤ x ≤ 4.5$$

Out of all options we see

A. x < -9 Is INCORRECT as all values of x are greater than -9
B. x < -8 Is INCORRECT as all values of x are greater than -8
C. x > -8 Is CORRECT because all values of x in the calculated range of values of x are greater than -8
D. x < 4 Is INCORRECT because x may be 4 which is NOT less than 4
E. x > 4 Is INCORRECT as x may be less than 4 as well

I got the same range but won't x > -8 include values above 4.5 ?

The logic is,

When it's known that $$-7.5 ≤ x ≤ 4.5$$ then for all possible values of x we can say that each value will certainly be greater than -8

on the other hand you can prove all other options incorrect as per the following explanation (already mentioned in previous solutions)

A. x < -9 Is INCORRECT as all values of x are greater than -9
B. x < -8 Is INCORRECT as all values of x are greater than -8
C. x > -8 Is CORRECT because all values of x in the calculated range of values of x are greater than -8
D. x < 4 Is INCORRECT because x may be 4 which is NOT less than 4
E. x > 4 Is INCORRECT as x may be less than 4 as well

I hope this helps!!!
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GMATinsight
Bhoopendra Singh and Dr.Sushma Jha
e-mail: info@GMATinsight.com I Call us : +91-9999687183 / 9891333772
Online One-on-One Skype based classes and Classroom Coaching in South and West Delhi
http://www.GMATinsight.com/testimonials.html

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Intern  B
Joined: 01 Dec 2018
Posts: 11
Re: If x is an integer and |2x + 3| ≤ 12 then which of the following must  [#permalink]

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Bunuel wrote:
If x is an integer and $$|2x+3|≤12$$, then which of the following must be true?

A. x < -9
B. x < -8
C. x > -8
D. x < 4
E. x > 4

$$|2x+3|≤12$$

$$|x+3/2|≤6$$

So x is a point that is a distance of 6 or less from -1.5
So x would be less than 4.5 or more than -7.5

$$-7.5 \leq x \leq 4.5$$

<------------------------ (-7.5) ================== (4.5) ---------------------->

x can take any value in the "===" region. For each value in this region, x is definitely greater than -8.

For more, check: https://www.veritasprep.com/blog/2011/0 ... edore-did/

But this satisfies option D too.. X<4, if its <4.5, it could be less that 4 too right? Re: If x is an integer and |2x + 3| ≤ 12 then which of the following must   [#permalink] 13 Dec 2018, 22:48
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