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

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AnisMURR
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If |2x-1| < 5, is |x|<2 ? [#permalink] New post   19 Dec 2018, 02:12
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If \(|2x-1| < 5\), is \(|x|<2\) ?


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

(2) \(x < 0\)

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Re: If |2x-1| < 5, is |x|<2 ? [#permalink] New post   19 Dec 2018, 07:59
chetan2u VeritasKarishma Bunuel amanvermagmat gmatbusters

Can the experts please throw some light on this DS Question
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If |2x-1| < 5, is |x|<2 ? [#permalink] New post   19 Dec 2018, 08:14
Expert Reply
Manat wrote:
chetan2u VeritasKarishma Bunuel amanvermagmat gmatbusters

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

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

Can you please explain?
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If |2x-1| < 5, is |x|<2 ? [#permalink] New post   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.
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If |2x-1| < 5, is |x|<2 ? [#permalink]
20 Apr 2019, 15:32
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