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Is x > 0 ? (1) |x - 3| < 5 (2) |x + 2| > 5

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Bunuel
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Is x > 0 ? (1) |x - 3| < 5 (2) |x + 2| > 5 [#permalink] New post   28 Nov 2017, 05:12
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E

Difficulty:

65% (hard)

Question Stats:

50% (01:46) correct 50% (01:45) wrong based on 131 sessions
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Is x > 0 ?

(1) |x - 3| < 5

(2) |x + 2| > 5
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C
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TaN1213
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Is x > 0 ? (1) |x - 3| < 5 (2) |x + 2| > 5 [#permalink] New post   Updated on: 28 Nov 2017, 06:29
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Bunuel wrote:
Is x > 0 ?

(1) |x - 3| < 5

(2) |x + 2| > 5


imo C.
Question: is x positive?
1.
|x - 3| - 5 < 0
-2<x<8
Insufficient

2. |x + 2| > 5
|x + 2| - 5 > 0
x<-7 and x>3
insufficient

combining:
overlap region: 3<x<8
yes x is positive.

Originally posted by TaN1213 on 28 Nov 2017, 05:43.
Last edited by TaN1213 on 28 Nov 2017, 06:29, edited 1 time in total.
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Re: Is x > 0 ? (1) |x - 3| < 5 (2) |x + 2| > 5 [#permalink] New post   28 Nov 2017, 05:44
Bunuel wrote:
Is x > 0 ?

(1) |x - 3| < 5

(2) |x + 2| > 5


HI chetan2u,

(1) |x - 3| < 5

x=5 gives Yes x>0

x=-1 gives No x<0

(2) |x + 2| > 5

x=5 gives Yes x>0

x=-8 gives No x<0

Combining both gives x>0

Hence C

Is it correct? Where am I going wrong?
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Is x > 0 ? (1) |x - 3| < 5 (2) |x + 2| > 5 [#permalink] New post   28 Nov 2017, 06:15
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NandishSS wrote:
Bunuel wrote:
Is x > 0 ?

(1) |x - 3| < 5

(2) |x + 2| > 5


HI chetan2u,

(1) |x - 3| < 5

x=5 gives Yes x>0

x=-1 gives No x<0

(2) |x + 2| > 5

x=5 gives Yes x>0

x=-8 gives No x<0

Combining both gives x>0

Hence C

Is it correct? Where am I going wrong?


Yes, you are correct, but testing numbers may not get you correct always.

So let's see how do you do this..

1) |x-3|<5
Two areas..
x-3 is positive.....x-3<5....x<8
x-3 is NEGATIVE....-(x-3)<5....x-3>-5....x>-2.
Range -2<x<8
Insufficient

2) |x+2|>5
Again two cases as above
x+2>5....x>3
x+2<-5....x<-7....
(This is where you have gone wrong @TaN1213)
Insufficient

Combined..
In NEGATIVE, the two ranges are x>-2 and x<-7... Nothing in common
In POSITIVE, x>3 and x<8.... Common range 3< x<8
So sufficient
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Re: Is x > 0 ? (1) |x - 3| < 5 (2) |x + 2| > 5 [#permalink] New post   28 Nov 2017, 06:20
chetan2u wrote:
NandishSS wrote:
Bunuel wrote:
Is x > 0 ?

(1) |x - 3| < 5

(2) |x + 2| > 5


HI chetan2u,

(1) |x - 3| < 5

x=5 gives Yes x>0

x=-1 gives No x<0

(2) |x + 2| > 5

x=5 gives Yes x>0

x=-8 gives No x<0

Combining both gives x>0

Hence C

Is it correct? Where am I going wrong?


Yes, you are correct, but testing numbers may not get you correct always.

So let's see how do you do this..

1) |x-3|<5
Two areas..
x-3 is positive.....x-3<5....x<8
x-3 is NEGATIVE....-(x-3)<5....x-3>-5....x>-2.
Range -2<x<8
Insufficient

2) |x+2|>5
Again two cases as above
x+2>5....x>3
x+2<-5....x<-7....
(This is where you have gone wrong @TaN1213)
Insufficient

Combined..
In NEGATIVE, the two ranges are x>-2 and x<-7... Nothing in common
In POSITIVE, x>3 and x<8.... Common range 3< x<8
So sufficient


This Looks good :thumbup: Sirji :-)
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Is x > 0 ? (1) |x - 3| < 5 (2) |x + 2| > 5 [#permalink] New post   28 Nov 2017, 06:25
chetan2u wrote:
NandishSS wrote:
Bunuel wrote:
Is x > 0 ?

(1) |x - 3| < 5

(2) |x + 2| > 5


HI chetan2u,

(1) |x - 3| < 5

x=5 gives Yes x>0

x=-1 gives No x<0

(2) |x + 2| > 5

x=5 gives Yes x>0

x=-8 gives No x<0

Combining both gives x>0

Hence C

Is it correct? Where am I going wrong?


Yes, you are correct, but testing numbers may not get you correct always.

So let's see how do you do this..

1) |x-3|<5
Two areas..
x-3 is positive.....x-3<5....x<8
x-3 is NEGATIVE....-(x-3)<5....x-3>-5....x>-2.
Range -2<x<8
Insufficient

2) |x+2|>5
Again two cases as above
x+2>5....x>3
x+2<-5....x<-7....
(This is where you have gone wrong @TaN1213)
Insufficient

Combined..
In NEGATIVE, the two ranges are x>-2 and x<-7... Nothing in common
In POSITIVE, x>3 and x<8.... Common range 3< x<8
So sufficient


Thanks Chetan. I just re-did the sum and got it right this time. Wondering what was I thinking. Thank God this is a DS problem. :)
I will be editing the post.
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Re: Is x > 0 ? (1) |x - 3| < 5 (2) |x + 2| > 5 [#permalink] New post   28 Nov 2017, 07:27
Graphical approach to this question...

Provide kudos if u like my approach

NandishSS wrote:
Bunuel wrote:
Is x > 0 ?

(1) |x - 3| < 5

(2) |x + 2| > 5



HI chetan2u,

(1) |x - 3| < 5

x=5 gives Yes x>0

x=-1 gives No x<0

(2) |x + 2| > 5

x=5 gives Yes x>0

x=-8 gives No x<0

Combining both gives x>0

Hence C

Is it correct? Where am I going wrong?

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Re: Is x > 0 ? (1) |x - 3| < 5 (2) |x + 2| > 5 [#permalink] New post   26 Mar 2019, 10:44
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Re: Is x > 0 ? (1) |x - 3| < 5 (2) |x + 2| > 5 [#permalink]
26 Mar 2019, 10:44
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