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# In xy plane, a certain line L1 has how many intersections

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In xy plane, a certain line L1 has how many intersections  [#permalink]

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Updated on: 03 Oct 2012, 03:59
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Difficulty:

45% (medium)

Question Stats:

65% (01:40) correct 35% (01:44) wrong based on 141 sessions

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In xy plane, a certain line L1 has how many intersections with y = x^2 +2?

(1) Line L1 does not intersect the X- Axis
(2) The point Q (2,1) lies on line L1

Originally posted by shivanigs on 03 Oct 2012, 00:25.
Last edited by Bunuel on 03 Oct 2012, 03:59, edited 1 time in total.
Renamed the topic and edited the question.
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Re: In xy plane, a certain line L1 has how many intersections  [#permalink]

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03 Oct 2012, 04:20
6
8
In xy plane, a certain line L1 has how many intersections with y = x^2 +2?

Probably the best way to deal with this question is to make diagrams.

(1) Line L1 does not intersect the X- Axis. This statement implies that line L1 is parallel to x-axis. We can have 0, 1, or 2 intersection points:
Attachment:

Parabola.png [ 10.82 KiB | Viewed 6774 times ]
Not sufficient.

(2) The point Q (2,1) lies on line L1. Again, we can have 0, 1, or 2 intersection points:
Attachment:

Parabola2.png [ 10.18 KiB | Viewed 6774 times ]
Not sufficient.

(1)+(2) Line L1 is parallel to x-axis and passes through the point (2, 1):
Attachment:

Parabola3.png [ 10.83 KiB | Viewed 6767 times ]
As we can see the line does not intersect the parabola. Sufficient.

Hope it's clear.
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Re: In xy plane, a certain line L1 has how many intersections wi  [#permalink]

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Updated on: 03 Oct 2012, 06:26
In xy plane, a certain line L1 has how many intersections with y = x^2 +2?

1. Line L1 does not intersect the X- Axis
2. The point Q (2,1) lies on line L1

STAT1
tells us that the line is parallel to x axis. So the equation of the line will be y = k (where k is a constant)
For every value of:
k >2 we have two point of intersections. (x^2= k -2 will give two values of x)
For k =2 we have one point of intersection only point of intersection is (0,2)
and for k < 2 we Dont have any point of intersection (x^2= -ve, which is not possible)

So, 1 is insufficient

STAT2:
Statement2 by itself is nOt sufficient as we do not know the equation of the line. the line can intersect the given curve at 0 ,1 or two points.

STAT1 and STAT2 combined we have:
y=1 as the equation of the line. So we have 0 points of intersection.

Hope it helps!
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Originally posted by BrushMyQuant on 03 Oct 2012, 00:38.
Last edited by BrushMyQuant on 03 Oct 2012, 06:26, edited 1 time in total.
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Re: In xy plane, a certain line L1 has how many intersections wi  [#permalink]

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03 Oct 2012, 04:23
nktdotgupta wrote:
In xy plane, a certain line L1 has how many intersections with y = x^2 +2?

1. Line L1 does not intersect the X- Axis
2. The point Q (2,1) lies on line L1

STAT1
tells us that the line is parallel to x axis. So the equation of the line will be y = k (where k is a constant)
For every value of:
k >2 we have two point of intersections. (x^2= k -2 will give two values of x)
For k =2 we have one point of intersection only point of intersection is (0,2)
and for k < 2 we Dont have any point of intersection (x^2= -ve, which is not possible)

So, 1 is insufficient

STAT2:
Statement2 by itself is nOt sufficient as we do not know the equation of the line. the line can intersect the given curve at 1 or two points.

STAT1 and STAT2 combined we have:
y=2 as the equation of the line. So we have only one point of intersection which is (0,2)

Hope it helps!

Check the solution above. Your answer is correct but some parts of the solution are not.
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Re: In xy plane, a certain line L1 has how many intersections wi  [#permalink]

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03 Oct 2012, 06:26
Bunuel wrote:
nktdotgupta wrote:
In xy plane, a certain line L1 has how many intersections with y = x^2 +2?

1. Line L1 does not intersect the X- Axis
2. The point Q (2,1) lies on line L1

STAT1
tells us that the line is parallel to x axis. So the equation of the line will be y = k (where k is a constant)
For every value of:
k >2 we have two point of intersections. (x^2= k -2 will give two values of x)
For k =2 we have one point of intersection only point of intersection is (0,2)
and for k < 2 we Dont have any point of intersection (x^2= -ve, which is not possible)

So, 1 is insufficient

STAT2:
Statement2 by itself is nOt sufficient as we do not know the equation of the line. the line can intersect the given curve at 1 or two points.

STAT1 and STAT2 combined we have:
y=2 as the equation of the line. So we have only one point of intersection which is (0,2)

Hope it helps!

Check the solution above. Your answer is correct but some parts of the solution are not.

@Bunuel: Thanks.. edited.
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Re: In xy plane, a certain line L1 has how many intersections  [#permalink]

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03 Oct 2012, 14:22
bunuel, very well drawn picture .
difficult problem very easily solved.
thanks a lot.
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12 Oct 2014, 06:19
IN the XY Plane, a certain line L has how many intersections with y=x^2+2 ?
1. Line L doesn't intersect x-axis.
2. The point Q(2,1) lies on line L
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12 Oct 2014, 06:37
1. Line L doesn't intersect x-axis.
Line L is parallel to x axis. But no information on point of intersection with y=x^2+2.
Statement not sufficient.

2. The point Q(2,1) lies on line L
Again statement is not sufficient to determine point of intersection with y=x^2+2.

1+2,
Line L is parallel to x axis and passes through point Q(2,1). Minimum value of y coordinate for y=x^2+2 is 2 when x=0.
As absolute value of x increases, value of y coordinate also increases. Hence Line L has no intersection point with y=x^2+2.

Hence combined statements are sufficient.
Ans= C

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Re: In xy plane, a certain line L1 has how many intersections  [#permalink]

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12 Oct 2014, 07:47
shyam593 wrote:
IN the XY Plane, a certain line L has how many intersections with y=x^2+2 ?
1. Line L doesn't intersect x-axis.
2. The point Q(2,1) lies on line L

Merging similar topics.

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Re: In xy plane, a certain line L1 has how many intersections  [#permalink]

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15 Dec 2015, 19:27
the equation given is a parabola, open upwards, the lowest point is at 0,2.
now, the first statement doesn't tell much, except that it is a parallel line to x-axis, only in the case of parallel to x-axis the line never intersects the x-axis. it might be the case that the line intersects the line at 0, 1, or 2 points. not sufficient.

statement two, says that it intersects at point 1,2. doesn't tell much. might be only 1 point, or more points, depending on the equation of the line.

1+2 says that line L1 is a parallel line, and it doesn't intersect the parabola at all. this one is sufficient to give a definitive answer.
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Re: In xy plane, a certain line L1 has how many intersections  [#permalink]

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09 Apr 2019, 12:33
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Re: In xy plane, a certain line L1 has how many intersections   [#permalink] 09 Apr 2019, 12:33
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