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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: 28 Apr 2019, 17:19
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Difficulty:

  65% (hard)

Question Stats:

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

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Is \(x = 20?\)

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

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

Source: Experts Global
Difficulty Level: 700

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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.
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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, 20:08
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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, 01:07
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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]

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New post 25 Aug 2019, 11:39
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

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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 26 Aug 2019, 00:45
SajjadAhmad wrote:
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

Answer: A
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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 26 Aug 2019, 05:30
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
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Re: Is x = 20? (1) 20 < |x + 10| < 30 (2) 10 < |x + 5| < 30   [#permalink] 26 Aug 2019, 05:30
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