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

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Math Expert
Joined: 02 Sep 2009
Posts: 51218
Is x > 0 ? (1) |x - 3| < 5 (2) |x + 2| > 5  [#permalink]

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28 Nov 2017, 04:12
00:00

Difficulty:

55% (hard)

Question Stats:

53% (01:41) correct 47% (01:41) wrong based on 105 sessions

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Is x > 0 ?

(1) |x - 3| < 5

(2) |x + 2| > 5

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Director
Joined: 09 Mar 2017
Posts: 524
Location: India
Concentration: Marketing, Organizational Behavior
WE: Information Technology (Computer Software)
Is x > 0 ? (1) |x - 3| < 5 (2) |x + 2| > 5  [#permalink]

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Updated on: 28 Nov 2017, 05:29
1
1
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.
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Hit Kudus if this has helped you get closer to your goal, and also to assist others save time. Tq

Originally posted by TaN1213 on 28 Nov 2017, 04:43.
Last edited by TaN1213 on 28 Nov 2017, 05:29, edited 1 time in total.
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Re: Is x > 0 ? (1) |x - 3| < 5 (2) |x + 2| > 5  [#permalink]

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28 Nov 2017, 04:44
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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Math Expert
Joined: 02 Aug 2009
Posts: 7107
Is x > 0 ? (1) |x - 3| < 5 (2) |x + 2| > 5  [#permalink]

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28 Nov 2017, 05:15
2
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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1) Absolute modulus : http://gmatclub.com/forum/absolute-modulus-a-better-understanding-210849.html#p1622372
2)Combination of similar and dissimilar things : http://gmatclub.com/forum/topic215915.html
3) effects of arithmetic operations : https://gmatclub.com/forum/effects-of-arithmetic-operations-on-fractions-269413.html

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Re: Is x > 0 ? (1) |x - 3| < 5 (2) |x + 2| > 5  [#permalink]

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28 Nov 2017, 05:20
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 Sirji
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Director
Joined: 09 Mar 2017
Posts: 524
Location: India
Concentration: Marketing, Organizational Behavior
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Is x > 0 ? (1) |x - 3| < 5 (2) |x + 2| > 5  [#permalink]

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28 Nov 2017, 05:25
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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Hit Kudus if this has helped you get closer to your goal, and also to assist others save time. Tq

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Re: Is x > 0 ? (1) |x - 3| < 5 (2) |x + 2| > 5  [#permalink]

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28 Nov 2017, 06:27
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 &nbs [#permalink] 28 Nov 2017, 06:27
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