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05 Sep 2010, 12:50
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A
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In the figure above, if x and y are each less than 90 and PS||QR, is the length of segment PQ less than the length of segment SR ?
(1) x > y
(2) x + y > 90
Attachment:
Figure.PNG [ 5.28 KiB | Viewed 72733 times ]
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02 Jan 2012, 16:01
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Hi there. I'm happy to help with this. 
So, the lines PS & RQ are parallel, angles X & Y are each less than 90 degrees.
Statement #1 tells us angle X is greater than angle Y. In the diagram, I showed an exaggerated example of this ---- if Y is a much smaller angle, it follows a less steep diagonal, which travels a longer distance between the two lines, as shown in the diagram. Therefore, if (angle X) > (angle Y), then segment RS is longer than segment PQ. Statement #1 is sufficient.
(Notice that this logic depends on both angles staying less than 90 degrees. If X had a value greater than 90 degrees, it would start making a longer, less steep, line segment on the left side.)
Statement #2 says only that the sum (x + y) is greater than 90. The trouble with that is: it doesn't give us any way to distinguish x vs. y --- either one could be much bigger than the other, or they both could be equal. No way to distinguish x vs. y ==> no way to distinguish RS vs. PQ. Insufficient.
Correct answer = A
Does that make sense? Let me know if you have any questions on that.
Mike
So, the lines PS & RQ are parallel, angles X & Y are each less than 90 degrees.
Statement #1 tells us angle X is greater than angle Y. In the diagram, I showed an exaggerated example of this ---- if Y is a much smaller angle, it follows a less steep diagonal, which travels a longer distance between the two lines, as shown in the diagram. Therefore, if (angle X) > (angle Y), then segment RS is longer than segment PQ. Statement #1 is sufficient.
(Notice that this logic depends on both angles staying less than 90 degrees. If X had a value greater than 90 degrees, it would start making a longer, less steep, line segment on the left side.)
Statement #2 says only that the sum (x + y) is greater than 90. The trouble with that is: it doesn't give us any way to distinguish x vs. y --- either one could be much bigger than the other, or they both could be equal. No way to distinguish x vs. y ==> no way to distinguish RS vs. PQ. Insufficient.
Correct answer = A
Does that make sense? Let me know if you have any questions on that.
Mike
Attachments
parallel lines, unequal angles.PNG [ 7.81 KiB | Viewed 71662 times ]
05 Sep 2010, 13:15
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In the figure above, if x and y are each less than 90 and PS||QR, is the length of segment PQ less than the length of segment SR ?
(1) x>y --> if the angles x and y were equal then the length of segment PQ would be equal to the length of segment SR (as PS||QR). Now, as x>y it means that point R is to the left of the position it would be if x and y were equal (previous case), or in other words, we should drag point R to the left to the position of R2 to make angle y less than x, thus making the length of segment SR bigger than the length of segment PQ. So as x>y than SR>PQ. Sufficient.
(2) x+y>90 --> clearly insufficient: if \(x=y=60\) then the length of segment PQ would be equal to the length of segment SR but if \(x=60\) and \(y=45\) then the length of segment PQ would be less than the length of segment SR. Not sufficient.
Answer: A.
Attachment:
untitled.PNG [ 38.85 KiB | Viewed 73925 times ]
