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

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

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New post 15 Mar 2019, 10:12
1
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A
B
C
D
E

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  95% (hard)

Question Stats:

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

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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
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Re: If x is a real number, then the quantity (1 − |x|)(1 + x) is positive  [#permalink]

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New post 16 Mar 2019, 11:36
chetan2u can you confirm if the OA is correct? Shouldnt the OA be D?
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Re: If x is a real number, then the quantity (1 − |x|)(1 + x) is positive  [#permalink]

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New post 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
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Re: If x is a real number, then the quantity (1 − |x|)(1 + x) is positive  [#permalink]

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New post 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.
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Re: If x is a real number, then the quantity (1 − |x|)(1 + x) is positive  [#permalink]

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New post 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.
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If x is a real number, then the quantity (1 − |x|)(1 + x) is positive  [#permalink]

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New post 18 Mar 2019, 07:10
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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
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If x is a real number, then the quantity (1 − |x|)(1 + x) is positive   [#permalink] 18 Mar 2019, 07:10
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