Does anyone have input on a efficient way to solve this problem. I used my judgement on angles/sides to get my answer...was hoping there was a better way to see this.
Appreciate the help.
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- Guest
GMAT PREP1 - #7
Hey Guys,
Does anyone have input on a efficient way to solve this problem. I used my judgement on angles/sides to get my answer...was hoping there was a better way to see this.
Appreciate the help.
Does anyone have input on a efficient way to solve this problem. I used my judgement on angles/sides to get my answer...was hoping there was a better way to see this.
Appreciate the help.
- Harish Dorai
Note: Please have a paper and pencil handy to draw the figures for analyzing this question.
This problem can be easily solved using Pythagoras theorem.
Given PS and QR are parallel. Draw a perpendicular line from point Q to segment PS and call the point of intersection in PS as X. Similarly draw a perpendicular line from point R to segment PS and call it Y. Now this forms 2 Right Triangles - Triangle PXQ and SYR. PQ is the hypotenuse of PXQ and SR is the hypotenuse of SYR.
As per Pythagoras theorm
PQ^2 = PX^2 + XQ^2
RS^2 = SY^2 + YR^2
XQ and YR are both equal and they represent the distance between the parallel lines PS and QR. So in order to determine whether PQ or RS is bigger than each other, we need to find out which among PX and SY are bigger. If PX > SY then PQ will be greater than RS (From the above equation), if not it will be RS > PQ.
Now let us analyze the diagram and see how the measurement of angle x and angle y alters the length of the segments PX and SY.
Condition 1) If both angle x and angle y are equal then the segment PX and SY will be equal.
Condition 2) If angle x is less than y then the segment PX will be greater than SY.
Condition 3) If angle x is greater than angle y then the segment PX will be less than SY.
So with all of the above analysis we can rephrase the above Data sufficiency question as - Which one among angle x or angle y is greater? (This is typical of geometry questions. We have to use the figures and apply all the known principles to rephrase the question to a simpler one).
Now the given statements are easy to comprehend.
Statement (1) Very straight one and it says angle x is greater than angle y. So as per our rephrased DS question, this is SUFFICIENT.
Statement (2) x + y > 90. However this doesn't give us a hint on which one is greater - x or y? So NOT SUFFICIENT.
The answer is (A).
Hope this helps.
This problem can be easily solved using Pythagoras theorem.
Given PS and QR are parallel. Draw a perpendicular line from point Q to segment PS and call the point of intersection in PS as X. Similarly draw a perpendicular line from point R to segment PS and call it Y. Now this forms 2 Right Triangles - Triangle PXQ and SYR. PQ is the hypotenuse of PXQ and SR is the hypotenuse of SYR.
As per Pythagoras theorm
PQ^2 = PX^2 + XQ^2
RS^2 = SY^2 + YR^2
XQ and YR are both equal and they represent the distance between the parallel lines PS and QR. So in order to determine whether PQ or RS is bigger than each other, we need to find out which among PX and SY are bigger. If PX > SY then PQ will be greater than RS (From the above equation), if not it will be RS > PQ.
Now let us analyze the diagram and see how the measurement of angle x and angle y alters the length of the segments PX and SY.
Condition 1) If both angle x and angle y are equal then the segment PX and SY will be equal.
Condition 2) If angle x is less than y then the segment PX will be greater than SY.
Condition 3) If angle x is greater than angle y then the segment PX will be less than SY.
So with all of the above analysis we can rephrase the above Data sufficiency question as - Which one among angle x or angle y is greater? (This is typical of geometry questions. We have to use the figures and apply all the known principles to rephrase the question to a simpler one).
Now the given statements are easy to comprehend.
Statement (1) Very straight one and it says angle x is greater than angle y. So as per our rephrased DS question, this is SUFFICIENT.
Statement (2) x + y > 90. However this doesn't give us a hint on which one is greater - x or y? So NOT SUFFICIENT.
The answer is (A).
Hope this helps.
- RonPurewal
- Students
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- Joined: Tue Aug 14, 2007 8:23 am
Harish's solution is correct. Make sure that you take note of the following:
(1) The only thing that really matters here is which angle is bigger. As usual, the GMAT is throwing at you something that looks complicated, but in fact is a stand-in for something very simple.
(2) There is absolutely nothing wrong with using your judgment, along with several sketches, to establish the same facts that Harish has established with the Pythagorean theorem. If you simply draw a number of angles between the parallel lines, with the angles getting smaller and smaller, you'll notice that the segments are getting longer and longer. Pattern recognition is a wonderful way to solve problems like this.
(1) The only thing that really matters here is which angle is bigger. As usual, the GMAT is throwing at you something that looks complicated, but in fact is a stand-in for something very simple.
(2) There is absolutely nothing wrong with using your judgment, along with several sketches, to establish the same facts that Harish has established with the Pythagorean theorem. If you simply draw a number of angles between the parallel lines, with the angles getting smaller and smaller, you'll notice that the segments are getting longer and longer. Pattern recognition is a wonderful way to solve problems like this.
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