GMAT Question of the Day - Daily to your Mailbox; hard ones only

 It is currently 16 Sep 2019, 21:33 ### 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. ### Request Expert Reply # Is x = 20? (1) 20 < |x + 10| < 30 (2) 10 < |x + 5| < 30

 new topic post reply Question banks Downloads My Bookmarks Reviews Important topics
Author Message
TAGS:

### Hide Tags

Senior RC Moderator V
Joined: 02 Nov 2016
Posts: 3736
GPA: 3.39
Is x = 20? (1) 20 < |x + 10| < 30 (2) 10 < |x + 5| < 30  [#permalink]

### Show Tags

1
8 00:00

Difficulty:   65% (hard)

Question Stats: 52% (01:30) correct 48% (02:00) wrong based on 122 sessions

### HideShow timer Statistics

Is $$x = 20?$$

(1) $$20 < |x + 10| < 30$$

(2) $$10 < |x + 5| < 30$$

Source: Experts Global
Difficulty Level: 700

_________________
For new project RC Butler 2019: Click here
New! Need for an RC strategy and practice? Click here
Patterns among those who have scored 750+(2019 Edition) Click here
For all GMAT Flashcards => Click here

Originally posted by SajjadAhmad on 13 Oct 2018, 13:08.
Last edited by SajjadAhmad on 28 Apr 2019, 17:19, edited 3 times in total.
VP  D
Status: Learning stage
Joined: 01 Oct 2017
Posts: 1030
WE: Supply Chain Management (Energy and Utilities)
Re: Is x = 20? (1) 20 < |x + 10| < 30 (2) 10 < |x + 5| < 30  [#permalink]

### Show Tags

1
1
Is x = 20?

(1) 20 < lx+10l < 30

(2) 10 < lx+5l < 30

EG

St1:- 20 < lx+10l < 30

You know, |x+10| is always positive. Also, (a) |x+10|=x+10 when $$x+10\geq{0}$$ or, $$x\geq{-10}$$ (b) |x+10|=-(x+10) when $$(x+10)<{0}$$ or, $$x<{-10}$$

Case-I:- When x< -10 then |x+10|=-(x+10)

We can write 20 < lx+10l < 30 =$$20<\left(-\left(x+10\right)\right)<30$$
On solving, we have, -40 < x < -30---------------(1)

Case-II:- When $$x+10\geq{0}$$ then |x+10|=x+10
We can write 20 < lx+10l < 30 =20 < x+10 < 30
On solving, we have, 10<x<20------------------------(2)
From (1) & (2) , we have range of x: -40 < x < -30 or 10<x<20
Answer to question stem is NO.
Sufficient.

St2:- 10 < lx+5l < 30

Applying the same procedures as we have applied in st1, we have

-35 < x < -15 or 5 < x < 25
Question stem is inconsistent.
Insufficient.

Ans. (A)

PS:- We can solve this question using graphical method too.
_________________
Regards,

PKN

Rise above the storm, you will find the sunshine
Manager  G
Joined: 07 Aug 2018
Posts: 108
Location: United States (MA)
GMAT 1: 560 Q39 V28 GMAT 2: 670 Q48 V34 Re: Is x = 20? (1) 20 < |x + 10| < 30 (2) 10 < |x + 5| < 30  [#permalink]

### Show Tags

1
1
1
x=20?

S(1) $$20<|x+10|<30$$

Case 1: x>0

$$20<x+10<30$$
$$=10<x<20$$
We know x is not equal to 20.

Case 2: x<0

$$20<-(x+10)<30$$
$$20<-x-10<30$$
$$-30>x>-40$$
We know x is not equal to 20. SUFFICIENT!

S(2) $$10<|x+5|<30$$

Case 1: x>0

$$10<x+5<30$$
$$=5<x<25$$
x can equal 20 or any number between 5 and 25.

Case 2: x<0

$$10<-(x+5)<30$$
$$10<-x-5<30$$
$$-15>x>-35$$
We know x is not equal to 20. BUT since first case 1 gives an yes and no answer: INSUFFCIENT

Hence, A
_________________
Intern  B
Joined: 10 May 2018
Posts: 39
Re: Is x = 20? (1) 20 < |x + 10| < 30 (2) 10 < |x + 5| < 30  [#permalink]

### Show Tags

I have one query regarding this question.though I had solved this question by absolute method but can't we just try to put the value of X =20 and confirm
In the first case it can not be equal to 20 as it will make X+10 as 30 and it is not smaller than 30 so the answer is No

For the second scenario X can be 20 or something else also eg 20 or 21.

Is this method correct or should we stick to absolute method

Posted from my mobile device
SVP  V
Joined: 26 Mar 2013
Posts: 2324
Re: Is x = 20? (1) 20 < |x + 10| < 30 (2) 10 < |x + 5| < 30  [#permalink]

### Show Tags

Is $$x = 20?$$

(1) $$20 < |x + 10| < 30$$

(2) $$10 < |x + 5| < 30$$

Source: Experts Global
Difficulty Level: 700

(1) $$20 < |x + 10| < 30$$

Take 20 and apply in the above, you will find that x can't equal to 20. Answer is always NO.

Sufficient

(2) $$10 < |x + 5| < 30$$

Take 20 and apply in the above, you will find that x can equal to 20. Answer is NO.

Take 21 and apply in the above, you will find that x can't equal to 20. Answer is Yes.

Insufficient

Senior Manager  G
Joined: 19 Nov 2017
Posts: 254
Location: India
Schools: ISB
GMAT 1: 670 Q49 V32 GPA: 4
Re: Is x = 20? (1) 20 < |x + 10| < 30 (2) 10 < |x + 5| < 30  [#permalink]

### Show Tags

Statement 1
$$20 < |x + 10| < 30$$

Case 1
$$20 < x + 10 < 30$$
$$20 - 10 < x + 10 - 10 < 30 - 10$$
$$10 < x < 20$$

Case 2
$$20 + 10 < - x - 10 + 10 < 30 + 10$$
$$30< - x < 40$$
$$- 40< x < - 30$$

From the two cases we can conclude x < 20. This means x ≠ 20
Sufficient

Statement 1
$$10 < |x + 5| < 30$$

Case 1
$$10 < x + 5 < 30$$
$$10 - 5< x + 5 - 5< 30 - 5$$
$$5< x < 25$$

Case 2
$$10 < - x - 5 < 30$$
$$10 + 5 < - x - 5 + 5 < 30 + 5$$
$$15 < - x < 35$$
$$- 35 < x < - 15$$

From the two cases we can conclude x < 25. This means x ≠ 20 or x = 20
Insufficient

Hence, A
_________________

Vaibhav

Sky is the limit. 800 is the limit.

~GMAC Re: Is x = 20? (1) 20 < |x + 10| < 30 (2) 10 < |x + 5| < 30   [#permalink] 26 Aug 2019, 05:30
Display posts from previous: Sort by

# Is x = 20? (1) 20 < |x + 10| < 30 (2) 10 < |x + 5| < 30

 new topic post reply Question banks Downloads My Bookmarks Reviews Important topics

 Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne  