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# Is the negative number x less than –1?

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Math Expert
Joined: 02 Sep 2009
Posts: 43853
Is the negative number x less than –1? [#permalink]

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14 May 2017, 11:24
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55% (hard)

Question Stats:

61% (01:17) correct 39% (01:19) wrong based on 48 sessions

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Is the negative number x less than –1?

(1) 1/x < 1/2
(2) 1/x^2 < 1/2
[Reveal] Spoiler: OA

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Director
Joined: 28 Mar 2017
Posts: 891
Re: Is the negative number x less than –1? [#permalink]

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14 May 2017, 11:35
Bunuel wrote:
Is the negative number x less than –1?

(1) 1/x < 1/2
(2) 1/x^2 < 1/2

E

1. stmt 1 will hold true for x=-2 and for x=-0.5
insufficient

2. for x<-2, the given condition holds true
for -2<x<-1, the given condition fails,
for -1<x<0, the condition condition fails
insufficient

1&2 clearly insufficient
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Manager
Joined: 04 Apr 2015
Posts: 101
Re: Is the negative number x less than –1? [#permalink]

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15 May 2017, 01:03
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IMO B

x has to be less than -1from statetment 2

waiting for the OA
Intern
Joined: 27 Dec 2012
Posts: 41
Re: Is the negative number x less than –1? [#permalink]

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15 May 2017, 01:25
Statement 1:
1/x-1/2<0
2-x/2x<0
As x<0
This gives us
x<2
No new information
Insufficient
Statement 2:
1/x^2-1/2<0
x^2>2
This confirms x<-1
Sufficient
B
Senior Manager
Joined: 23 Jun 2012
Posts: 344
Location: Pakistan
GPA: 3.76
Re: Is the negative number x less than –1? [#permalink]

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15 May 2017, 01:34
1
KUDOS
For me its B
if 1/x^2 < 1/2 then we can write this as
x^2 > 2...and it is only possible when x is > 1 and as we are given that x is negative this means x is negative number greater than 1
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Manager
Joined: 14 Oct 2015
Posts: 238
GPA: 3.57
Re: Is the negative number x less than –1? [#permalink]

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15 May 2017, 02:05
IMO its B -

1- $$1/x < 1/2$$
$$2/x < 1$$
$$x < 2$$ -- we flip signs because we know X is negative and we're taking negative to the other side, or so I think we should do.

2- $$1/x^2 < 1/2$$

flipping sides, sign remains the same since we're dealing with $$x^2$$

$$x^2 > 2$$ taking under root, we will be flipping the sign since we know x is negative.
$$x < 1.41$$ - Not sufficient.

Combining both, we know x < 2 and and less than 1.41 but its still not sufficient to determine if X is less than -1. Answer should be E IMO. I may be making a dumb mistake so would love it if someone can correct me.
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Director
Joined: 28 Mar 2017
Posts: 891
Re: Is the negative number x less than –1? [#permalink]

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15 May 2017, 03:29
gmatexam439 wrote:
Bunuel wrote:
Is the negative number x less than –1?

(1) 1/x < 1/2
(2) 1/x^2 < 1/2

E

1. stmt 1 will hold true for x=-2 and for x=-0.5
insufficient

2. for x<-2, the given condition holds true
for -2<x<-1, the given condition fails,
for -1<x<0, the condition condition fails
insufficient

1&2 clearly insufficient

I understand it should be "B" and not "E".
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Re: Is the negative number x less than –1?   [#permalink] 15 May 2017, 03:29
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