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Is x > 0?

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Expert Post
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Joined: 02 Sep 2009
Posts: 41873

Kudos [?]: 128603 [0], given: 12180

Is x > 0? [#permalink]

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New post 29 Apr 2016, 02:40
Expert's post
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Difficulty:

  25% (medium)

Question Stats:

71% (01:03) correct 29% (01:07) wrong based on 76 sessions

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Kudos [?]: 128603 [0], given: 12180

Expert Post
1 KUDOS received
Math Forum Moderator
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P
Joined: 02 Aug 2009
Posts: 4967

Kudos [?]: 5453 [1], given: 112

Re: Is x > 0? [#permalink]

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New post 29 Apr 2016, 02:54
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Expert's post
Is x > 0?

(1) |3x−30|<20..

If we want to explain the given MOD in ONE line..
IT IS : 3x lies less than 20 places from 30 on the number line..
so 3x lies between 30-20 and 30+20 OR between 10 and 50
or x lies between 10/3 and 50/3
so surely x>0..

we can solve it also
|3x−30|<20..
3x-30<20.. 3x<50
x<50/3

|3x−30|<20..
3x-30>-20..
3x>10 or x>10/3
x lies between 10/3 and 50/3
SUFF

(2) 3x – 30 is greater than zero.
3x-30>0 or 3x>30, that is x>10
so x>0
Suff

D
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Absolute modulus :http://gmatclub.com/forum/absolute-modulus-a-better-understanding-210849.html#p1622372
Combination of similar and dissimilar things : http://gmatclub.com/forum/topic215915.html

Kudos [?]: 5453 [1], given: 112

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Kudos [?]: 14 [0], given: 12

Re: Is x > 0? [#permalink]

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New post 29 Apr 2016, 12:31
Bunuel wrote:
Is x > 0?

(1) |3x−30|<20
(2) 3x – 30 is greater than zero.


The plot for |3x-30| will be a 'V' and the lowest possible co-ordinate will be at (10,0).

Now we just have to find the y co-ordinate upto which x co-ordinates remain positive.
3x-30 always remains in the 1st quadrant and -(3x-30) crosses the y-axis and goes into the 2nd quadrant at y = 30. So x remains positive for all values for 0<y<30.

Thus each condition is able to tell us that x>0.

Answer D.
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Kudos [?]: 14 [0], given: 12

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Re: Is x > 0? [#permalink]

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New post 11 Aug 2017, 22:08
Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

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Kudos [?]: 273 [0], given: 0

Re: Is x > 0?   [#permalink] 11 Aug 2017, 22:08
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