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13 May 2017, 02:28
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E
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
55%
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Question Stats:
53% (01:38) correct
47%
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At how many points do the two graphs named as "First Graph" and "Second Graph" intersect?
1) The Equation of the first graph is x^2 + y^2 = 4
2) The second graph has equation y = ax^2 + 4 where a is a constant
Source: https://www.GMATinsight.com
1) The Equation of the first graph is x^2 + y^2 = 4
2) The second graph has equation y = ax^2 + 4 where a is a constant
Source: https://www.GMATinsight.com
14 May 2017, 04:10
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Each statement independently is insufficient because the equations for both the graphs are needed to find the point of intersection
From Statement 1 we get the first graph represents a circle with centre (0,0) and a radius of 2 (y intercept of (2,0))
From Statement 2 we get the second graph is a parabola with a y intercept of (4,0) however the value of "a" in y = ax^2 + 4 is unknown
The constant "a" has 2 implications:-
1) The larger the absolute value of a, the steeper (or thinner) the parabola
2) If "a" is positive, the parabola upward facing, if negative, the parabola downward facing
Accordingly the 2 graphs could have no intersections or 2 points. Hence IMO E
Please do correct me if i missed something!
From Statement 1 we get the first graph represents a circle with centre (0,0) and a radius of 2 (y intercept of (2,0))
From Statement 2 we get the second graph is a parabola with a y intercept of (4,0) however the value of "a" in y = ax^2 + 4 is unknown
The constant "a" has 2 implications:-
1) The larger the absolute value of a, the steeper (or thinner) the parabola
2) If "a" is positive, the parabola upward facing, if negative, the parabola downward facing
Accordingly the 2 graphs could have no intersections or 2 points. Hence IMO E
Please do correct me if i missed something!
15 May 2017, 05:17
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Tan2017
Each statement independently is insufficient because the equations for both the graphs are needed to find the point of intersection
From Statement 1 we get the first graph represents a circle with centre (0,0) and a radius of 2 (y intercept of (2,0))
From Statement 2 we get the second graph is a parabola with a y intercept of (4,0) however the value of "a" in y = ax^2 + 4 is unknown
The constant "a" has 2 implications:-
1) The larger the absolute value of a, the steeper (or thinner) the parabola
2) If "a" is positive, the parabola upward facing, if negative, the parabola downward facing
Accordingly the 2 graphs could have no intersections or 2 points. Hence IMO E
Please do correct me if i missed something!
From Statement 1 we get the first graph represents a circle with centre (0,0) and a radius of 2 (y intercept of (2,0))
From Statement 2 we get the second graph is a parabola with a y intercept of (4,0) however the value of "a" in y = ax^2 + 4 is unknown
The constant "a" has 2 implications:-
1) The larger the absolute value of a, the steeper (or thinner) the parabola
2) If "a" is positive, the parabola upward facing, if negative, the parabola downward facing
Accordingly the 2 graphs could have no intersections or 2 points. Hence IMO E
Please do correct me if i missed something!
As per the given information in two statements, we can deduce that
first graph is a circle with radius 2 and centre at origin
Second graph is a parabola with 4 as y intercept how we don't know if parabola is open upwards (if a>0) of open downwards (if a <0)
Also, if graph is open upwards then the two graphs will have NO point of intersection but in case the parabola is open downwards then the two graphs may intersect at number of points ranging from 0 to 4
Hence all possibilities are open and Number of points of intersection may range from 0 to 4 even after combining the two statements hence
Answer: Option E
