Last visit was: 18 Jul 2024, 10:56 It is currently 18 Jul 2024, 10:56
Toolkit
GMAT Club Daily Prep
Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History
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

SORT BY:
Tags:
Show Tags
Hide Tags
Math Expert
Joined: 02 Sep 2009
Posts: 94406
Own Kudos [?]: 642014 [7]
Given Kudos: 85997
GMAT Club Legend
Joined: 08 Jul 2010
Status:GMAT/GRE Tutor l Admission Consultant l On-Demand Course creator
Posts: 6020
Own Kudos [?]: 13804 [5]
Given Kudos: 125
Location: India
GMAT: QUANT+DI EXPERT
Schools: IIM (A) ISB '24
GMAT 1: 750 Q51 V41
WE:Education (Education)
General Discussion
Senior Manager
Joined: 10 Jan 2013
Posts: 266
Own Kudos [?]: 167 [0]
Given Kudos: 201
Location: India
Concentration: General Management, Strategy
GRE 1: Q163 V155
GPA: 3.95
Tutor
Joined: 16 Oct 2010
Posts: 15124
Own Kudos [?]: 66714 [1]
Given Kudos: 436
Location: Pune, India
If x is an integer and |2x + 3| 12 then which of the following must [#permalink]
1
Kudos
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.

Originally posted by KarishmaB on 19 Oct 2018, 01:42.
Last edited by KarishmaB on 17 Oct 2022, 03:42, edited 1 time in total.
Manager
Joined: 07 Apr 2018
Posts: 80
Own Kudos [?]: 58 [1]
Given Kudos: 271
Location: United States
Concentration: General Management, Marketing
GMAT 1: 600 Q45 V28
GPA: 3.8
If x is an integer and |2x + 3| ≤ 12 then which of the following must [#permalink]
1
Kudos
Attachments

IMG_20181021_115527.jpg [ 1.45 MiB | Viewed 6067 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.
Intern
Joined: 25 Jan 2018
Posts: 10
Own Kudos [?]: 9 [0]
Given Kudos: 7
Location: United States
GMAT 1: 700 Q48 V38
GMAT 2: 750 Q49 V44
GPA: 3.56
Re: If x is an integer and |2x + 3| ≤ 12 then which of the following must [#permalink]
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?
GMAT Club Legend
Joined: 08 Jul 2010
Status:GMAT/GRE Tutor l Admission Consultant l On-Demand Course creator
Posts: 6020
Own Kudos [?]: 13804 [0]
Given Kudos: 125
Location: India
GMAT: QUANT+DI EXPERT
Schools: IIM (A) ISB '24
GMAT 1: 750 Q51 V41
WE:Education (Education)
Re: If x is an integer and |2x + 3| ≤ 12 then which of the following must [#permalink]
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.
GMAT Tutor
Joined: 27 Oct 2017
Posts: 1895
Own Kudos [?]: 5791 [0]
Given Kudos: 238
WE:General Management (Education)
Re: If x is an integer and |2x + 3| ≤ 12 then which of the following must [#permalink]
Graphical approach shall be as per attached sketch
Attachment:

WhatsApp Image 2018-10-21 at 10.32.28.jpeg [ 60.94 KiB | Viewed 6060 times ]
Tutor
Joined: 16 Oct 2010
Posts: 15124
Own Kudos [?]: 66714 [1]
Given Kudos: 436
Location: Pune, India
Re: If x is an integer and |2x + 3| ≤ 12 then which of the following must [#permalink]
1
Kudos
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.
Intern
Joined: 02 Jun 2018
Posts: 8
Own Kudos [?]: 0 [0]
Given Kudos: 132
Location: India
Concentration: Finance
GPA: 4
Re: If x is an integer and |2x + 3| ≤ 12 then which of the following must [#permalink]
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 ?
GMAT Club Legend
Joined: 08 Jul 2010
Status:GMAT/GRE Tutor l Admission Consultant l On-Demand Course creator
Posts: 6020
Own Kudos [?]: 13804 [1]
Given Kudos: 125
Location: India
GMAT: QUANT+DI EXPERT
Schools: IIM (A) ISB '24
GMAT 1: 750 Q51 V41
WE:Education (Education)
Re: If x is an integer and |2x + 3| ≤ 12 then which of the following must [#permalink]
1
Kudos
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!!!
Intern
Joined: 01 Dec 2018
Posts: 9
Own Kudos [?]: 0 [0]
Given Kudos: 21
Re: If x is an integer and |2x + 3| ≤ 12 then which of the following must [#permalink]
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.gmatclub.com/forum/veritas-prep-resource-links-no-longer-available-399979.html#/2011/0 ... edore-did/

But this satisfies option D too.. X<4, if its <4.5, it could be less that 4 too right?
GMAT Club Legend
Joined: 03 Jun 2019
Posts: 5307
Own Kudos [?]: 4220 [0]
Given Kudos: 161
Location: India
GMAT 1: 690 Q50 V34
WE:Engineering (Transportation)
Re: If x is an integer and |2x + 3| 12 then which of the following must [#permalink]
If x is an integer and $$|2x+3|≤12$$, then which of the following must be true?

-12 <= 2x+3 <= 12
-7.5 <= x <= 4.5

A. x < -9
B. x < -8
C. x > -8: MUST BE TRUE
D. x < 4
E. x > 4

IMO C

Posted from my mobile device
Re: If x is an integer and |2x + 3| 12 then which of the following must [#permalink]
Moderator:
Math Expert
94404 posts