Last visit was: 23 Jul 2024, 04:17 It is currently 23 Jul 2024, 04:17
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.

# Is |x - 3| < 7 ? (1) x > 0 (2) x < 10

SORT BY:
Tags:
Show Tags
Hide Tags
Math Expert
Joined: 02 Sep 2009
Posts: 94578
Own Kudos [?]: 643197 [10]
Given Kudos: 86728
GMAT Club Legend
Joined: 03 Jun 2019
Posts: 5311
Own Kudos [?]: 4244 [3]
Given Kudos: 161
Location: India
GMAT 1: 690 Q50 V34
WE:Engineering (Transportation)
Senior Moderator - Masters Forum
Joined: 19 Jan 2020
Posts: 3128
Own Kudos [?]: 2815 [0]
Given Kudos: 1511
Location: India
GPA: 4
WE:Analyst (Internet and New Media)
Intern
Joined: 28 Jan 2019
Posts: 24
Own Kudos [?]: 8 [0]
Given Kudos: 360
Location: India
Re: Is |x - 3| < 7 ? (1) x > 0 (2) x < 10 [#permalink]
yashikaaggarwal wrote:
Is |x - 3| < 7 ?

(1) x > 0
Case 1: put x= 1
|1-3|<7
2<7 (sufficient)

Case 2: put x = 12
|12-3|>7
9>7 (insufficient)

Case 3: put x=9
|9-3|=7
7=7(insufficient)

Statement 1: (insufficient alone)

(2) x < 10
Case 1: x=9
|9-3|=7
7=7 (insufficient)

Case 2: put x= 1
|1-3|<7
2<7 (sufficient)

Case 3: put x = -12
|-12-3|>7
15>7 (insufficient)
Statement 2 is insufficient alone.

Statement 1 and 2:
0<x<10
Case 1: x=9
|9-3|=7
7=7 (insufficient)

Case 2: put x= 1
|1-3|<7
2<7 (sufficient)

(Not sufficient)

Posted from my mobile device

Statement 1 and 2:
0<x<10
Case 1: x=9
|9-3|=7
7=7 (insufficient)

|9-3| is 6 - it's sufficient
Senior Moderator - Masters Forum
Joined: 19 Jan 2020
Posts: 3128
Own Kudos [?]: 2815 [0]
Given Kudos: 1511
Location: India
GPA: 4
WE:Analyst (Internet and New Media)
Re: Is |x - 3| < 7 ? (1) x > 0 (2) x < 10 [#permalink]
Anuragjn wrote:
yashikaaggarwal wrote:
Is |x - 3| < 7 ?

(1) x > 0
Case 1: put x= 1
|1-3|<7
2<7 (sufficient)

Case 2: put x = 12
|12-3|>7
9>7 (insufficient)

Case 3: put x=9
|9-3|=7
7=7(insufficient)

Statement 1: (insufficient alone)

(2) x < 10
Case 1: x=9
|9-3|=7
7=7 (insufficient)

Case 2: put x= 1
|1-3|<7
2<7 (sufficient)

Case 3: put x = -12
|-12-3|>7
15>7 (insufficient)
Statement 2 is insufficient alone.

Statement 1 and 2:
0<x<10
Case 1: x=9
|9-3|=7
7=7 (insufficient)

Case 2: put x= 1
|1-3|<7
2<7 (sufficient)

(Not sufficient)

Posted from my mobile device

Statement 1 and 2:
0<x<10
Case 1: x=9
|9-3|=7
7=7 (insufficient)

|9-3| is 6 - it's sufficient

Yes got my mistake
Thank you.
Retired Moderator
Joined: 05 May 2016
Posts: 766
Own Kudos [?]: 696 [0]
Given Kudos: 1316
Location: India
Re: Is |x - 3| < 7 ? (1) x > 0 (2) x < 10 [#permalink]
Bunuel wrote:
Is |x - 3| < 7 ?

(1) x > 0
(2) x < 10

DS21224

Is |x - 3| < 7

We get 2 cases.

Case 1: if x - 3 > 0
=> x- 3 < 7
=> x < 10.

Case 2: if x - 3 < 0
=> - x + 3 < 7
=> - x < 4
=> x > -4.

Thus we get : -4 < x < 10.
Now,

Statement 1: x > 0.
It satisfies x< 10.
but what if x > = 10. The the inequality wont hold true.

So Insufficient.

Statement 2: x < 10
It satisfies both : x < 10 x > -4.
But what if x < -4 also,

So this statement is also Insufficient.

Statement 1 + Statement 2:
0 < x < 10.
It satisfies both the sides of Inequality.
Thus Sufficient.

IESE School Moderator
Joined: 11 Feb 2019
Posts: 270
Own Kudos [?]: 173 [0]
Given Kudos: 53
Is |x - 3| < 7 ? (1) x > 0 (2) x < 10 [#permalink]
Given: |x - 3| < 7
Lets analyze the qtn statement: x is 7 points away from 3 on the number line
=> -4<x<10

Let analyze the statemnets:
I: x > 0 i.e x can be 3,5,10 or even 20 but we know x<10 NOT SUFFICIENT
II: x < 10 i.e. x can be 5,3,0 ,-4 or even -10 but we know -4<x NOT SUFFICIENT

Lets combine both:

from I: x>0
from II: x<10
==> 0<x<10

This is well within the range from out initial analysis of -4<x<10. Hence SUFFICIENT

C
Intern
Joined: 17 May 2020
Posts: 2
Own Kudos [?]: 6 [1]
Given Kudos: 43
Location: Viet Nam
Concentration: General Management, Economics
GPA: 4
WE:General Management (Energy and Utilities)
Re: Is |x - 3| < 7 ? (1) x > 0 (2) x < 10 [#permalink]
1
Bookmarks
|x - 3| < 7 can be re-written as below:

~ -7<x-3 < 7
~ -4 < x < 10

(1): x>0: x>10 does not make the inequality correct >> INSUFFICIENT
(2): x<10: if x<-4 >> does not make the inequality correct >> INSUFFICIENT
(1) + (2): 0<x<10 (within the range from -4 to 10) is totally Sufficient.

Hence C
VP
Joined: 11 Aug 2020
Posts: 1245
Own Kudos [?]: 208 [0]
Given Kudos: 332
Re: Is |x - 3| < 7 ? (1) x > 0 (2) x < 10 [#permalink]
Is |x - 3| < 7 ?

Rephrased: -4 < x < 10?

(1) x > 0
Clearly insufficient.
e.g. x = 11 or 100 then the answer is NO.
e.g. x = 5 then YES

(2) x < 10
Clearly insufficient.
x = 5 then YES
x = -100 then NO

C: Sufficient b/c 0 < x < 10 overlaps with the defined region.
Non-Human User
Joined: 09 Sep 2013
Posts: 34046
Own Kudos [?]: 853 [0]
Given Kudos: 0
Re: Is |x - 3| < 7 ? (1) x > 0 (2) x < 10 [#permalink]
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.
Re: Is |x - 3| < 7 ? (1) x > 0 (2) x < 10 [#permalink]
Moderator:
Math Expert
94578 posts