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If on a coordinate plane, point A has the co-ordinates (-3, 4), how far is the point A from point E?
(i) Point E is on the Y- axis four units from the origin.
(ii) If point A were twice as far from point E, it would be the same distance from point E as point C is at co -ordinates (0, -2).
What does second statement imply?
AE(new) = CE
or
AE(new) = AC
I think it's the first one, AE(new) = CE.
Please confirm!
Source: Kaplan
(i) Point E is on the Y- axis four units from the origin.
(ii) If point A were twice as far from point E, it would be the same distance from point E as point C is at co -ordinates (0, -2).
What does second statement imply?
AE(new) = CE
or
AE(new) = AC
I think it's the first one, AE(new) = CE.
Please confirm!
Source: Kaplan
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Where to now? Join ongoing discussions on thousands of quality questions in our Data Sufficiency (DS) Forum
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I would go with C.
Here is my explanation -
Question stem is asking for the distance between A(-3,4) and E(x,y).
Clue 1, it is saying point E is on the Y axis four units from the origin. This means E is having two possible values (0,4) or (0,-4). So the distance between A and E results in two different values. Hence Insufficient.
Clues 2, it is given 2AE = EC.
Again here, A = (-3,4)
E = (x,y)
C = (0,-2)
It is given 2*sqrt((x+3)^2 + (y-4)^2) = sqrt(x^2 + (-2-y)^2) (Applied distance between two points formula)
There are two variables and only one equation. Hence we cannot get the values of x and y.
So this clue is insufficient.
Combine both the clues. It is saying E lies on Y axis and is 4 units away. This means x = 0 and y = +/- 4.
Suppose E = (0,-4), A =(-3,4) C = (0,-2)
AE = sqrt(75)
EC = 2
2AE EC.
Suppose E = (0,4), A =(-3,4) C = (0,-2)
AE = 3
EC = 6 ==> 2AE = EC. (Based on the second clue) SO AE should be 3. Hence sufficient.
Here is my explanation -
Question stem is asking for the distance between A(-3,4) and E(x,y).
Clue 1, it is saying point E is on the Y axis four units from the origin. This means E is having two possible values (0,4) or (0,-4). So the distance between A and E results in two different values. Hence Insufficient.
Clues 2, it is given 2AE = EC.
Again here, A = (-3,4)
E = (x,y)
C = (0,-2)
It is given 2*sqrt((x+3)^2 + (y-4)^2) = sqrt(x^2 + (-2-y)^2) (Applied distance between two points formula)
There are two variables and only one equation. Hence we cannot get the values of x and y.
So this clue is insufficient.
Combine both the clues. It is saying E lies on Y axis and is 4 units away. This means x = 0 and y = +/- 4.
Suppose E = (0,-4), A =(-3,4) C = (0,-2)
AE = sqrt(75)
EC = 2
2AE EC.
Suppose E = (0,4), A =(-3,4) C = (0,-2)
AE = 3
EC = 6 ==> 2AE = EC. (Based on the second clue) SO AE should be 3. Hence sufficient.
Archived Topic
Hi there,
This topic has been closed and archived due to inactivity or violation of community quality standards. No more replies are possible here.
Where to now? Join ongoing discussions on thousands of quality questions in our Data Sufficiency (DS) Forum
Still interested in this question? Check out the "Best Topics" block above for a better discussion on this exact question, as well as several more related questions.
Thank you for understanding, and happy exploring!
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