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# Is the x-intercept of the non-horizontal line L negative?

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Is the x-intercept of the non-horizontal line L negative?  [#permalink]

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18 Feb 2019, 10:04
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Difficulty:

65% (hard)

Question Stats:

43% (01:40) correct 57% (01:34) wrong based on 56 sessions

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GMATH practice exercise (Quant Class 20)

Is the x-intercept of the non-horizontal line L negative?

(1) The slope of line L is equal to the y-intercept of line L.
(2) The slope of line L is positive.

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Fabio Skilnik :: GMATH method creator (Math for the GMAT)
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Re: Is the x-intercept of the non-horizontal line L negative?  [#permalink]

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19 Feb 2019, 04:54
1
fskilnik wrote:
GMATH practice exercise (Quant Class 20)

Is the x-intercept of the non-horizontal line L negative?

(1) The slope of line L is equal to the y-intercept of line L.
(2) The slope of line L is positive.

#1
y=mx+c
m=c;
x= always -ve
so for all values of either c being +ve or -ve we observe that lines passes through -ve horizontal axis ; i.e x= -ve
sufficient
#2
slope of L +ve can be + or -ve on horizontal axis..
in sufficient
IMO A
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Re: Is the x-intercept of the non-horizontal line L negative?  [#permalink]

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19 Feb 2019, 12:15
fskilnik wrote:
GMATH practice exercise (Quant Class 20)

Is the x-intercept of the non-horizontal line L negative?

(1) The slope of line L is equal to the y-intercept of line L.
(2) The slope of line L is positive.

$$c = {\left( {x - {\rm{intercept}}} \right)_{\rm{L}}}\,\,\mathop {\rm{ < }}\limits^? \,\,{\rm{0}}$$

$$L\,\,\,:\,\,\,{\rm{vertical}}\,\,{\rm{or}}\,\,{\rm{non - vertical}}\,\,{\rm{with}}\,\,m = {\rm{slop}}{{\rm{e}}_{\rm{L}}} \ne 0$$

$$\left( 1 \right)\,\,\,L\,\,{\rm{non - vertical}}\,\,{\rm{and}}\,\,L\,\,:\,\,\,y = mx + m = m\left( {x + 1} \right)$$

$$?\,\,\,:\,\,\,0 = m\left( {c + 1} \right)\,\,\,\,\,\mathop \Rightarrow \limits^{m\, \ne \,\,0} \,\,\,\,c + 1 = 0\,\,\,\,\, \Rightarrow \,\,\,\,\left\langle {{\rm{YES}}} \right\rangle$$

$$\left( 2 \right)\,\,\,{\rm{INSUFF}}.\,\,\,\,\left( {{\rm{trivial}}\,\,{\rm{geometric}}\,\,{\rm{bifurcation}}} \right)$$

We follow the notations and rationale taught in the GMATH method.

Regards,
Fabio.
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Re: Is the x-intercept of the non-horizontal line L negative?  [#permalink]

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04 Mar 2019, 21:18
fskilnik wrote:
GMATH practice exercise (Quant Class 20)

Is the x-intercept of the non-horizontal line L negative?

(1) The slope of line L is equal to the y-intercept of line L.
(2) The slope of line L is positive.

(1) If the slope is 4 the line is-
y = 4x + 4
Slope is positive that means line is going up and cutting y axis at 4, it can only cut X axis at a -ve value.

if the slope is -2
y = -2x - 2
Slope is negative that means line is going down and cutting Y axis at -2, it can only cut X axis at a -ve value.

(2) Slope is positive doesn't tell me anything about X intercept.
Re: Is the x-intercept of the non-horizontal line L negative?   [#permalink] 04 Mar 2019, 21:18
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