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

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Joined: 02 Nov 2016
Posts: 4136
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Is x = 20? (1) 20 < |x + 10| < 30 (2) 10 < |x + 5| < 30  [#permalink]

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Updated on: 28 Apr 2019, 17:19
1
8
00:00

Difficulty:

65% (hard)

Question Stats:

52% (01:32) correct 48% (01:58) wrong based on 126 sessions

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Is $$x = 20?$$

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

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

Source: Experts Global
Difficulty Level: 700

_________________

Last edited by SajjadAhmad on 28 Apr 2019, 17:19, edited 3 times in total.
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Status: Learning stage
Joined: 01 Oct 2017
Posts: 1012
WE: Supply Chain Management (Energy and Utilities)
Re: Is x = 20? (1) 20 < |x + 10| < 30 (2) 10 < |x + 5| < 30  [#permalink]

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13 Oct 2018, 20:08
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.
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PKN

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Joined: 07 Aug 2018
Posts: 107
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]

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18 Oct 2018, 01:07
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]

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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

Posted from my mobile device
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Joined: 26 Mar 2013
Posts: 2343
Re: Is x = 20? (1) 20 < |x + 10| < 30 (2) 10 < |x + 5| < 30  [#permalink]

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26 Aug 2019, 00:45
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

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

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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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Vaibhav

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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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