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C
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
45%
(medium)
Question Stats:
61% (01:38) correct
39%
(01:42)
wrong
based on 271
sessions
History
Date
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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
(1) Line L1 does not intersect the X- Axis
(2) The point Q (2,1) lies on line L1
03 Oct 2012, 04:20
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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: 
Parabola.png [ 10.82 KiB | Viewed 16383 times ]
Not sufficient.
(2) The point Q (2,1) lies on line L1. Again, we can have 0, 1, or 2 intersection points: 
Parabola2.png [ 10.18 KiB | Viewed 16347 times ]
Not sufficient.
(1)+(2) Line L1 is parallel to x-axis and passes through the point (2, 1): 
Parabola3.png [ 10.83 KiB | Viewed 16318 times ]
As we can see the line does not intersect the parabola. Sufficient.
Answer: C.
Hope it's clear.
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 16383 times ]
(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 16347 times ]
(1)+(2) Line L1 is parallel to x-axis and passes through the point (2, 1):
Attachment:
Parabola3.png [ 10.83 KiB | Viewed 16318 times ]
Answer: C.
Hope it's clear.
General Discussion
Updated on: 03 Oct 2012, 06:26
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.
Last edited by BrushMyQuant on 03 Oct 2012, 06:26, edited 1 time in total.
Kudos
Bookmarks
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.
So, answer will be C
Hope it helps!
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.
So, answer will be C
Hope it helps!
