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# If |2x-1| < 5, is |x|<2 ?

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Manager
Status: Quant Expert Q51
Joined: 02 Aug 2014
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If |2x-1| < 5, is |x|<2 ?  [#permalink]

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19 Dec 2018, 02:12
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65% (hard)

Question Stats:

58% (02:10) correct 42% (02:26) wrong based on 103 sessions

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If $$|2x-1| < 5$$, is $$|x|<2$$ ?

(1) $$x^3 < x^2$$

(2) $$x < 0$$

Kudos for the best explanation

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Joined: 11 Jun 2018
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Schools: DeGroote "22 (S)
GMAT 1: 500 Q39 V21
Re: If |2x-1| < 5, is |x|<2 ?  [#permalink]

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19 Dec 2018, 07:59

Can the experts please throw some light on this DS Question
Math Expert
Joined: 02 Aug 2009
Posts: 7984
If |2x-1| < 5, is |x|<2 ?  [#permalink]

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19 Dec 2018, 08:14
Manat wrote:

Can the experts please throw some light on this DS Question

If $$|2x-1| < 5$$, is $$|x|<2$$ ?

(1) $$x^3 < x^2$$

(2) $$x < 0$$

We are given $$|2x-1| < 5$$, which is $$-5<2x-1 < 5 =>-5+1<2x-1+1<5+1........-4<2x<6......-2<x<3$$.
So, this range is certain.

We are asked $$|x|<2........-2<x<2$$?
Ofcourse this translates into 'Is $$2\leq{x}<3$$?', as we know 2<x<3

(1) $$x^3 < x^2$$...
$$x^3 < x^2....x^3-x^2<0....x^2(x-1)<0$$
x^2 is surely positive, so x-1<0 or x<0
so ans is YES, as $$2\leq{x}<3$$ is not true.
Sufficient

(2) $$x < 0$$
This means ans is YES, as $$2\leq{x}<3$$ is not true.
Sufficient

D
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Re: If |2x-1| < 5, is |x|<2 ?  [#permalink]

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20 Dec 2018, 01:48
Manat Is that clear now ?
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Re: If |2x-1| < 5, is |x|<2 ?  [#permalink]

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20 Dec 2018, 23:12
chetan2u wrote:
If $$|2x-1| < 5$$, is $$|x|<2$$ ?

(1) $$x^3 < x^2$$

(2) $$x < 0$$

We are given $$|2x-1| < 5$$, which is $$-5<2x-1 < 5 =>-5+1<2x-1+1<5+1........-4<2x<6......-2<x<3$$.
So, this range is certain.

We are asked $$|x|<2........-2<x<2$$?
Ofcourse this translates into 'Is $$2\leq{x}<3$$?', as we know 2<x<3

D

I am not sure I got this: as we know 2<x<3
You wrote:

We are given $$|2x-1| < 5$$, which is $$-5<2x-1 < 5 =>-5+1<2x-1+1<5+1........-4<2x<6......-2<x<3$$.
So, this range is certain.

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If |2x-1| < 5, is |x|<2 ?  [#permalink]

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20 Apr 2019, 15:32
Yes/No Question: If |2x-1|<5 , is |x|<2?
-5<2x-1<5
-4<2x<6
-2<x<3
Rephrase: is x more than -2 or less than 2 (-2<x<2)?
We know from the stem that -2<x so the question becomes is x<2 (or as above, can x be 2<=x<3)?

(1) x³ < x²
This tests knowledge of numbers around -1, 0, 1 raised to even/odd powers...
The statement is true in all cases except when x>1 (if in doubt, you can test -3/2, -1/2, 1/2 and 3/2)
So, if x must be <1, it is <2 (in other words, since x cannot be >1, it cannot be 2<=x<3).
Definite YES, sufficient.

(2) x < 0
If we know x<0 then it is <2. Definite YES, Sufficient.
It's helpful to draw a number line to visualize.
If |2x-1| < 5, is |x|<2 ?   [#permalink] 20 Apr 2019, 15:32
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