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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.

Guys, as my G-day is approaching, I am putting more and more effort in improving my Quant. However, I seem to have troubles with some basic concepts. Below are the 5 questions which I know have simple explanations but are for some reason difficult for me to understand. If you can explain the solutions for any of them, I would greatly appreciate it! Cheers!

Note that the shortest distance between two parallel lines is the perpendicular distance. As the angle keeps decreasing, the length of the line keeps increasing. So if we know that x>y, then PQ < SR. Stmnt 1 Sufficient.

Attachment:

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Since statement 2 doesn't give any information about relative size of x and y, nothing can be said about PQ and SR. Not sufficient.

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.

Re-phrase: Since PS || QR, PQ inversely proportional to angle x, and SR is inversely proportional to angle y. That is we need relationship between Q and R to determine relationship between PQ and SR.

I am the master of my fate. I am the captain of my soul. Please consider giving +1 Kudos if deserved!

DS - If negative answer only, still sufficient. No need to find exact solution. PS - Always look at the answers first CR - Read the question stem first, hunt for conclusion SC - Meaning first, Grammar second RC - Mentally connect paragraphs as you proceed. Short = 2min, Long = 3-4 min

Statement 1 let the distance between the parallel lines be h then sinx=h/PQ & siny=h/RS, we see that PQ*sinx=constant (x in deg) as sinx increases in the domain [0,90] i.e sin60>sin30 we can say that inorder to keep the product constant, if sinx increases then PQ decreases.. for ex if x=30 and y=60 as sin30(=0.5)<sin60(=0.866) so PQ>RS

Thus statement 1 alone is sufficient

Statement 2 If x+y>90 case 1:if both x and y are equal then PQ=RS case 2: if x>y then PQ<RS case 3: if x<y then PQ>RS

So insufficient. Thus the ans is A

Alternatively, if We have two towers of the same height, the farther we are from the tower the lesser we need to raise our head to see the top of the tower. That is ,more is the distance between the top of the tower and our eye lesser is the head raised. I hope it makes sense.

Re: In the figure above, if x and y are each less than 90 and PS [#permalink]

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06 Feb 2015, 02:58

Hi guys,

I went through the task and argued similar we would have argued in a triangle. The side which is opposite the smaller angle is also the smaller side. (in a triangle) But here in a polygon this argumentation doesnt hold.

Because I thought SR is smaller than PQ because angle x is smaller than (180-y).

After reading your explanations I totally get your point, but I dont understand why we can't argue the same way we do with triangles.

I went through the task and argued similar we would have argued in a triangle. The side which is opposite the smaller angle is also the smaller side. (in a triangle) But here in a polygon this argumentation doesnt hold.

Because I thought SR is smaller than PQ because angle x is smaller than (180-y).

After reading your explanations I totally get your point, but I dont understand why we can't argue the same way we do with triangles.

Thanks !

First of all, think, which side of the quadrilateral is the opposite side to any given angle. Look at the diagram, the angle has 2 sides opposite to it (which don't form the angle). You can make one of the opposite sides smaller and the other greater at whim. So there is no defined relation between the angle and the opposite sides.

Note that the shortest distance between two parallel lines is the perpendicular distance. As the angle keeps decreasing, the length of the line keeps increasing.

Above statement I understood

Quote:

So if we know that x>y, then PQ < SR. Stmnt 1 Sufficient.

Above statement i am not able to visualize correctly to identify opposite sides to angles x and y.

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