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

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

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New post Updated on: 10 Nov 2018, 21:24
1
5
00:00
A
B
C
D
E

Difficulty:

  55% (hard)

Question Stats:

52% (01:22) correct 48% (01:53) wrong based on 88 sessions

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Is x = 20?

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

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

Source: Experts Global
Difficulty Level: 650

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Originally posted by SajjadAhmad on 13 Oct 2018, 12:08.
Last edited by SajjadAhmad on 10 Nov 2018, 21:24, edited 2 times in total.
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Re: Is x = 20? (1) 20 < |x + 10| < 30 (2) 10 < |x + 5| < 30  [#permalink]

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New post 13 Oct 2018, 19:08
1
SajjadAhmad wrote:
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.
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Re: Is x = 20? (1) 20 < |x + 10| < 30 (2) 10 < |x + 5| < 30  [#permalink]

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New post 18 Oct 2018, 00:07
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
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Re: Is x = 20? (1) 20 < |x + 10| < 30 (2) 10 < |x + 5| < 30   [#permalink] 18 Oct 2018, 00:07
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