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Data Sufficiency: Coordinate Geometry

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Data Sufficiency: Coordinate Geometry

by nishant1309 » Wed Mar 09, 2011 12:07 pm
1. (a,b) divides the line segment XY in what ratio. The coordinates are as follows X (+1,-4) and Y (+1,14)



1. a = +1



2. b = +1

2. (a,b) divides the line segment XY in what ratio. The coordinates are as follows X (+1,-4) and Y (+2,14)



1. a = +1.5



2. b = +5.0

Please explain in terms of section formula. Why in these cases answers behave differently?
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by Geva@EconomistGMAT » Wed Mar 09, 2011 12:48 pm
nishant1309 wrote:1. (a,b) divides the line segment XY in what ratio. The coordinates are as follows X (+1,-4) and Y (+1,14)



1. a = +1



2. b = +1

2. (a,b) divides the line segment XY in what ratio. The coordinates are as follows X (+1,-4) and Y (+2,14)



1. a = +1.5



2. b = +5.0

Please explain in terms of section formula. Why in these cases answers behave differently?
I think we might need more clarification on this. !) are these data sufficiency questions? 2) What do you mean, the answers behave differently?
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by Night reader » Wed Mar 09, 2011 3:58 pm
:) hi , just condensed the text for space economy. In your first DS question, x-coordinates of XY line segment is the same i.e. 1. Here we could select choice B BUT we still need x-coordinate as the one may not be 1 to answer this question and solve for the ratio it's (14-1)/(4+1) OR 13/5. Select choice C.

In your second DS question, x-coordinates are different +1 and +2, hence we need both statements to check actually if the point (a;b) after combining statements 1 and 2 is on the line segment XY; for this we have to derive XY line equation --> slope=(14+4)/(2-1)=18, y=18x+b {y=ax+b, a-slope, b-y intercept), at X(+1;-4) -4=18*1+b, b=-22 --> y=18x-22, Now we check point (a,b) OR (+1.5,+5.0) by plug into y=18x-22 --> 5=18*1.5 - 22 and reveal that indeed our point is on the line segment XY. As long as this point is in the line segment geometrically we can find out the distance between divided new line segments and answer this question with solving for the ratio of point (a,b) to divide XY. Hence select choice C. BUT don't solve for the ratio - only select Combined st(1&2) is sufficient.
nishant1309 wrote:1. (a,b) divides the line segment XY in what ratio. The coordinates are as follows X (+1,-4) and Y (+1,14)

1. a = +1
2. b = +1

2. (a,b) divides the line segment XY in what ratio. The coordinates are as follows X (+1,-4) and Y (+2,14)

1. a = +1.5
2. b = +5.0

Please explain in terms of section formula. Why in these cases answers behave differently?
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by nishant1309 » Wed Mar 09, 2011 9:40 pm
Night reader wrote::) hi , just condensed the text for space economy. In your first DS question, x-coordinates of XY line segment is the same i.e. 1. Here we could select choice B BUT we still need x-coordinate as the one may not be 1 to answer this question and solve for the ratio it's (14-1)/(4+1) OR 13/5. Select choice C.

In your second DS question, x-coordinates are different +1 and +2, hence we need both statements to check actually if the point (a;b) after combining statements 1 and 2 is on the line segment XY; for this we have to derive XY line equation --> slope=(14+4)/(2-1)=18, y=18x+b {y=ax+b, a-slope, b-y intercept), at X(+1;-4) -4=18*1+b, b=-22 --> y=18x-22, Now we check point (a,b) OR (+1.5,+5.0) by plug into y=18x-22 --> 5=18*1.5 - 22 and reveal that indeed our point is on the line segment XY. As long as this point is in the line segment geometrically we can find out the distance between divided new line segments and answer this question with solving for the ratio of point (a,b) to divide XY. Hence select choice C. BUT don't solve for the ratio - only select Combined st(1&2) is sufficient.
nishant1309 wrote:1. (a,b) divides the line segment XY in what ratio. The coordinates are as follows X (+1,-4) and Y (+1,14)

1. a = +1
2. b = +1

2. (a,b) divides the line segment XY in what ratio. The coordinates are as follows X (+1,-4) and Y (+2,14)

1. a = +1.5
2. b = +5.0

Please explain in terms of section formula. Why in these cases answers behave differently?
@Night Rider: Many Thanks! From your explanation, the key learning point is to ensure whether the point lies on the line before actually solving for ratio. Thanks again!
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by ankur.agrawal » Thu Mar 10, 2011 6:22 am
U really dissected this question very well.

Thanks for the detailed explanation.
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by nishant1309 » Thu Mar 10, 2011 7:03 am
nishant1309 wrote:
Night reader wrote::) hi , just condensed the text for space economy. In your first DS question, x-coordinates of XY line segment is the same i.e. 1. Here we could select choice B BUT we still need x-coordinate as the one may not be 1 to answer this question and solve for the ratio it's (14-1)/(4+1) OR 13/5. Select choice C.

In your second DS question, x-coordinates are different +1 and +2, hence we need both statements to check actually if the point (a;b) after combining statements 1 and 2 is on the line segment XY; for this we have to derive XY line equation --> slope=(14+4)/(2-1)=18, y=18x+b {y=ax+b, a-slope, b-y intercept), at X(+1;-4) -4=18*1+b, b=-22 --> y=18x-22, Now we check point (a,b) OR (+1.5,+5.0) by plug into y=18x-22 --> 5=18*1.5 - 22 and reveal that indeed our point is on the line segment XY. As long as this point is in the line segment geometrically we can find out the distance between divided new line segments and answer this question with solving for the ratio of point (a,b) to divide XY. Hence select choice C. BUT don't solve for the ratio - only select Combined st(1&2) is sufficient.
nishant1309 wrote:1. (a,b) divides the line segment XY in what ratio. The coordinates are as follows X (+1,-4) and Y (+1,14)

1. a = +1
2. b = +1

2. (a,b) divides the line segment XY in what ratio. The coordinates are as follows X (+1,-4) and Y (+2,14)

1. a = +1.5
2. b = +5.0

Please explain in terms of section formula. Why in these cases answers behave differently?
@Night Rider: Many Thanks! From your explanation, the key learning point is to ensure whether the point lies on the line before actually solving for ratio. Thanks again!
@Night Rider: I chose B for 1st and D for 2nd because question states "(a,b) divides the line segment XY....". So i thought its not imperative to check whether (a,b) lies on XY because it is already given. OA is not known because it is a memory based question from one of the CATs.
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