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

 It is currently 14 Dec 2019, 10:52

### 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

# If x is a real number, then the quantity (1 − |x|)(1 + x) is positive

Author Message
TAGS:

### Hide Tags

Manager
Status: students
Joined: 08 Mar 2019
Posts: 93
GPA: 3.9
WE: Account Management (Accounting)
If x is a real number, then the quantity (1 − |x|)(1 + x) is positive  [#permalink]

### Show Tags

15 Mar 2019, 10:12
1
3
00:00

Difficulty:

95% (hard)

Question Stats:

43% (02:18) correct 57% (02:06) wrong based on 67 sessions

### HideShow timer Statistics

If x is a real number, then the quantity (1 − |x|)(1 + x) is positive if and only if

(A) |x| < 1

(B) |x| > 1

(C) x < −1 or − 1 < x < 1

(D) x < 1

(E) x < −1
Manager
Joined: 29 Nov 2016
Posts: 175
Location: India
GMAT 1: 750 Q50 V42
Re: If x is a real number, then the quantity (1 − |x|)(1 + x) is positive  [#permalink]

### Show Tags

16 Mar 2019, 11:36
chetan2u can you confirm if the OA is correct? Shouldnt the OA be D?
Director
Joined: 28 Jul 2016
Posts: 679
Location: India
Concentration: Finance, Human Resources
GPA: 3.97
WE: Project Management (Investment Banking)
Re: If x is a real number, then the quantity (1 − |x|)(1 + x) is positive  [#permalink]

### Show Tags

16 Mar 2019, 11:44
Mudit27021988 wrote:
chetan2u can you confirm if the OA is correct? Shouldnt the OA be D?

Answer should not be D since x<1 means lets take -2
That will 1+x negative.
However still C is also not correct.
Bunuel can you comment
Manager
Joined: 29 Nov 2016
Posts: 175
Location: India
GMAT 1: 750 Q50 V42
Re: If x is a real number, then the quantity (1 − |x|)(1 + x) is positive  [#permalink]

### Show Tags

16 Mar 2019, 11:57
globaldesi wrote:
Mudit27021988 wrote:
chetan2u can you confirm if the OA is correct? Shouldnt the OA be D?

Answer should not be D since x<1 means lets take -2
That will 1+x negative.
However still C is also not correct.
Bunuel can you comment

globaldesi
if you take x=-2 then 1+x is negative and so is (1-|x|). making the expression positive.
Intern
Joined: 11 Mar 2019
Posts: 1
Re: If x is a real number, then the quantity (1 − |x|)(1 + x) is positive  [#permalink]

### Show Tags

17 Mar 2019, 02:20
If X=-1 the expression is not positive but it's equal to zero, so C is the correct answer.
Math Expert
Joined: 02 Aug 2009
Posts: 8320
If x is a real number, then the quantity (1 − |x|)(1 + x) is positive  [#permalink]

### Show Tags

18 Mar 2019, 07:10
1
Rubina11 wrote:
If x is a real number, then the quantity (1 − |x|)(1 + x) is positive if and only if

(A) |x| < 1

(B) |x| > 1

(C) x < −1 or − 1 < x < 1

(D) x < 1

(E) x < −1

You could do it two ways..

(I) Algebraic/inequality way..
We are told (1 − |x|)(1 + x) >0
Two cases..
A) Both (1 − |x|) and (1 + x) are positive..
1-|x|>0, or |x|<1, that is -1<x<1
1+x>0, or x>-1
OVERLAP -1<x<1
B) Both (1 − |x|) and (1 + x) are negative..
1-|x|<0, or |x|>1, that is -1>x or x>1
1+x<0, or x<-1
OVERLAP x<-1

Thus answer is x<-1 and -1<x<1
C

Next is making use of choices..
(A) |x| < 1 ... Clearly at -2, (1 − |x|)(1 + x)=(1-|-2|)(1-2)=(-1)(-1)=1.. positive but NOT included in this choice

(B) |x| > 1 ..... at 2, (1 − |x|)(1 + x)=(1-|2|)(1+2)=(-1)(3)-31..NO

(C) x < −1 or − 1 < x < 1...YES

(D) x < 1 .......Clearly at -1, (1 − |x|)(1 + x)=(1-|-1|)(1-1)=0.. no

(E) x < −1........At x=0, (1 − |x|)(1 + x)=(1-|0|)(1+0)=(1)(0)=1.. positive but NOT included in this choice

Hence C
_________________
If x is a real number, then the quantity (1 − |x|)(1 + x) is positive   [#permalink] 18 Mar 2019, 07:10
Display posts from previous: Sort by