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Is x > 0? (1) |3x30|<20 (2) 3x 30 is greater than zero.

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Bunuel
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Is x > 0? (1) |3x30|<20 (2) 3x 30 is greater than zero. [#permalink] New post   29 Apr 2016, 02:40
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Is x > 0?

(1) |3x−30|<20
(2) 3x – 30 is greater than zero.
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D
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chetan2u
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Re: Is x > 0? (1) |3x30|<20 (2) 3x 30 is greater than zero. [#permalink] New post   29 Apr 2016, 02:54
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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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Re: Is x > 0? (1) |3x30|<20 (2) 3x 30 is greater than zero. [#permalink] 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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Re: Is x > 0? (1) |3x30|<20 (2) 3x 30 is greater than zero. [#permalink] New post   14 Jun 2019, 20:44
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A.

1.|3x−30|<20..
3x-30<20.. 3x<50
x<50/3


2. |3x−30|<20..
3x-30>-20..
3x>10 or x>10/3
x lies between 10/3 and 50/3
SUFF

B.

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

D is answer
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Is x > 0? (1) |3x30|<20 (2) 3x 30 is greater than zero. [#permalink] New post   14 Jun 2019, 21:51
Bunuel wrote:
Is x > 0?

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


Formula:
If lxl < a
—> -a < x < a

(1) |3x−30|<20
—> -20 < 3x - 30 < 20
—> -20 + 30 < 3x - 30 + 30 < 20 + 30
—> 10 < 3x < 50
—> 10/3 < x < 50/3

So, x is always positive - Sufficient

(2) 3x – 30 is greater than zero
—> 3x - 30 > 0
—> 3x > 30
—> x > 10

So, x is always positive - Sufficient

IMO Option D
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Is x > 0? (1) |3x30|<20 (2) 3x 30 is greater than zero. [#permalink] New post   17 Apr 2022, 22:02
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Bunuel wrote:
Is x > 0?

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


First recall what absolute values mean.
|x| < 20 means x is a point on the number line at a distance less than 20 from 0. So x lies between -20 and 20 (exclusive).
|x - 4| < 20 means x is a point on the number line at a distance less than 20 from 4. So x lies between -16 and 24 (exclusive).
etc

Question: Is x positive?

(1) |3x−30|<20

|x - 10| < 20/3

This means, x is a point such that it is at a distance of less than 6.66 from 10. So x lies between 3.33 to 16.66.
Then x must be positive.

(2) 3x – 30 is greater than zero.
3x - 30 > 0
x > 10
Then x must be positive.

Answer (D)

For another example, check: https://anaprep.com/algebra-inequalitie ... in-action/
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Is x > 0? (1) |3x30|<20 (2) 3x 30 is greater than zero. [#permalink]
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