NEW HERE? LEARN MORE
closeclose
Last visit was: 25 Apr 2024, 12:16 It is currently 25 Apr 2024, 12:16
Decision Tracker
My Rewards
New posts
New comers' posts

Close
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
Your Progress

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.
Go to My Error Log Learn more
Close
Request Expert Reply
Confirm Cancel

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

SORT BY:
Date
Kudos
Tags:
Find Similar Topics 
Show Tags
Hide Tags
User avatar
L
Bunuel
Math Expert
Joined: 02 Sep 2009
Posts: 92914
Own Kudos [?]: 619000 [5]
Given Kudos: 81595
Send PM
CAT Tests Forum Quiz Mode
If x is an integer and |2x + 3| ≤ 12 then which of the following must [#permalink] New post   19 Oct 2018, 00:07
5
Bookmarks
Expert Reply
00:00
A
B
C
D
E

Difficulty:

65% (hard)

Question Stats:

58% (01:55) correct 42% (01:58) wrong based on 416 sessions
Hide Show 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
ShowHide Answer
Official Answer
C
User avatar
L
GMATinsight
GMAT Club Legend
GMAT Club Legend
Joined: 08 Jul 2010
Status:GMAT/GRE Tutor l Admission Consultant l On-Demand Course creator
Posts: 5960
Own Kudos [?]: 13387 [4]
Given Kudos: 124
Location: India
GMAT: QUANT+DI EXPERT
Schools: IIM (A) ISB '24
GMAT 1: 750 Q51 V41
WE:Education (Education)
Send PM
Reviews Badge
If x is an integer and |2x + 3| ≤ 12 then which of the following must [#permalink] New post   Updated on: 20 Oct 2018, 21:52
2
Kudos
2
Bookmarks
Expert Reply
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

Answer: Option C

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.
User avatar
G
saurabh9gupta
Senior Manager
Senior Manager
Joined: 10 Jan 2013
Posts: 267
Own Kudos [?]: 167 [0]
Given Kudos: 201
Location: India
Concentration: General Management, Strategy
Schools: Kenan-Flagler '24 (D)
GRE 1: Q163 V155
GPA: 3.95
Send PM
GMAT ToolKit User Reviews Badge
Re: If x is an integer and |2x + 3| ≤ 12 then which of the following must [#permalink] New post   19 Oct 2018, 00:42
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
User avatar
L
KarishmaB
Tutor
Joined: 16 Oct 2010
Posts: 14823
Own Kudos [?]: 64918 [1]
Given Kudos: 426
Location: Pune, India
Send PM
If x is an integer and |2x + 3| 12 then which of the following must [#permalink] New post   Updated on: 17 Oct 2022, 03:42
1
Kudos
Expert Reply
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.

Answer (C)

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.
avatar
B
HAPPYatHARVARD
Manager
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
Send PM
If x is an integer and |2x + 3| ≤ 12 then which of the following must [#permalink] New post   Updated on: 21 Oct 2018, 09:08
1
Kudos
Hi [url=https://gmatclub.com:443/forum/memberlist.php?mode=viewprofile&un=VeritasKarishma]VeritasKarishmaAnother way!
Attachments

IMG_20181021_115527.jpg
IMG_20181021_115527.jpg [ 1.45 MiB | Viewed 5050 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.
avatar
B
fogarasm
Intern
Intern
Joined: 25 Jan 2018
Posts: 10
Own Kudos [?]: 9 [0]
Given Kudos: 7
Location: United States
Schools: Ross '22 (A) Yale '22 (A) Haas '22 (A)
GMAT 1: 700 Q48 V38
GMAT 2: 750 Q49 V44
GPA: 3.56
Send PM
Re: If x is an integer and |2x + 3| ≤ 12 then which of the following must [#permalink] New post   20 Oct 2018, 09:22
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

Answer: Option C


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?
User avatar
L
GMATinsight
GMAT Club Legend
GMAT Club Legend
Joined: 08 Jul 2010
Status:GMAT/GRE Tutor l Admission Consultant l On-Demand Course creator
Posts: 5960
Own Kudos [?]: 13387 [0]
Given Kudos: 124
Location: India
GMAT: QUANT+DI EXPERT
Schools: IIM (A) ISB '24
GMAT 1: 750 Q51 V41
WE:Education (Education)
Send PM
Reviews Badge
Re: If x is an integer and |2x + 3| ≤ 12 then which of the following must [#permalink] New post   20 Oct 2018, 21:52
Expert Reply
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

Answer: Option C


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. :)
User avatar
L
GMATBusters
GMAT Tutor
Joined: 27 Oct 2017
Posts: 1905
Own Kudos [?]: 5582 [0]
Given Kudos: 236
WE:General Management (Education)
Send PM
GMAT ToolKit User
Re: If x is an integer and |2x + 3| ≤ 12 then which of the following must [#permalink] New post   20 Oct 2018, 22:04
Expert Reply
Graphical approach shall be as per attached sketch
Attachment:
WhatsApp Image 2018-10-21 at 10.32.28.jpeg
WhatsApp Image 2018-10-21 at 10.32.28.jpeg [ 60.94 KiB | Viewed 5068 times ]
User avatar
L
KarishmaB
Tutor
Joined: 16 Oct 2010
Posts: 14823
Own Kudos [?]: 64918 [1]
Given Kudos: 426
Location: Pune, India
Send PM
Re: If x is an integer and |2x + 3| ≤ 12 then which of the following must [#permalink] New post   23 Oct 2018, 03:49
1
Kudos
Expert Reply
HAPPYatHARVARD wrote:
Hi [url=https://gmatclub.com:443/forum/memberlist.php?mode=viewprofile&un=VeritasKarishma]VeritasKarishmaAnother way!


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.
avatar
B
shobhiitgupta
Intern
Intern
Joined: 02 Jun 2018
Posts: 8
Own Kudos [?]: 0 [0]
Given Kudos: 132
Location: India
Concentration: Finance
GPA: 4
Send PM
Re: If x is an integer and |2x + 3| ≤ 12 then which of the following must [#permalink] New post   11 Nov 2018, 18:26
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

Answer: Option C


I got the same range but won't x > -8 include values above 4.5 ?
User avatar
L
GMATinsight
GMAT Club Legend
GMAT Club Legend
Joined: 08 Jul 2010
Status:GMAT/GRE Tutor l Admission Consultant l On-Demand Course creator
Posts: 5960
Own Kudos [?]: 13387 [1]
Given Kudos: 124
Location: India
GMAT: QUANT+DI EXPERT
Schools: IIM (A) ISB '24
GMAT 1: 750 Q51 V41
WE:Education (Education)
Send PM
Reviews Badge
Re: If x is an integer and |2x + 3| ≤ 12 then which of the following must [#permalink] New post   12 Nov 2018, 04:37
1
Kudos
Expert Reply
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

Answer: Option C


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!!!
avatar
B
bhargaviUSMBA
Intern
Intern
Joined: 01 Dec 2018
Posts: 9
Own Kudos [?]: 0 [0]
Given Kudos: 21
Send PM
Re: If x is an integer and |2x + 3| ≤ 12 then which of the following must [#permalink] New post   13 Dec 2018, 22:48
VeritasKarishma 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


\(|2x+3|≤12\)

\(|x+3/2|≤6\)

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.

Answer (C)

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?
User avatar
bumpbot
Non-Human User
Joined: 09 Sep 2013
Posts: 32676
Own Kudos [?]: 822 [0]
Given Kudos: 0
Send PM
Re: If x is an integer and |2x + 3| ≤ 12 then which of the following must [#permalink] New post   27 Apr 2021, 03:59
Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
GMAT Club Bot
gmatclubot
Re: If x is an integer and |2x + 3| ≤ 12 then which of the following must [#permalink]
27 Apr 2021, 03:59
Moderators:
Bunuel
Math Expert
92914 posts
yashikaaggarwal
Senior Moderator - Masters Forum
3137 posts

Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne
Main navigation
GMAT Resources
Partners
MBA Resources
www.gmac.com|www.mba.com | | GMAT Club Rules | Terms and Conditions