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In the rectangular coordinate system above, if OQ >= PQ, is
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Updated on: 27 Sep 2013, 09:44
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In the rectangular coordinate system above, if OQ >= PQ, is the area of region OPQ less than 30? (1) The coordinates of point P are (6,0). (2) The coordinates of point Q are (3,8)
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Originally posted by PrateekDua on 27 Sep 2013, 09:15.
Last edited by Bunuel on 27 Sep 2013, 09:44, edited 1 time in total.
Renamed the topic and edited the question.



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In the rectangular coordinate system above, if OQ >= PQ, is
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27 Sep 2013, 09:57
In the rectangular coordinate system above, if OQ >= PQ, is the area of region OPQ less than 30?(1) The coordinates of point P are (6,0). We know the length of the base (OP=6) but know nothing about the height (QS), which may be 1 or 100, so the area may or may not be less than 30. Not sufficient. (2) The coordinates of point Q are (3,8). Now, if OQ were equal to PQ then the triangle OPQ would be isosceles and OS would be equal to SP and the area would be: \(\frac{1}{2}*base*height=\frac{1}{2}(OS+SP)*QS=\frac{1}{2}*(3+3)*8=24\). Since \(OQ\geq{PQ}\) then \(OS\geq{SP}\) and the base OP is less than or equal to 6, which makes the area less than or equal 24. Sufficient. Answer: B. Similar question to practice: intherectangularcoordinatesystemaboveifoppqis129092.htmlHope it's clear. Attachment:
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Re: In the rectangular coordinate system above, if OQ >= PQ, is
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27 Sep 2013, 10:07
PrateekDua wrote: Attachment: Untitled.jpg In the rectangular coordinate system above, if OQ >= PQ, is the area of region OPQ less than 30? (1) The coordinates of point P are (6,0) (2) The coordinates of point Q are (3,8) I'm happy to help. Statement #1: The coordinates of point P are (6,0)The base = 6, but the height could be anything, so the area could be anything. This statement, alone and by itself, is not sufficient. Statement #2: The coordinates of point Q are (3,8)This is tricky. Segment OQ has some length  we could find this length from the Pythagorean theorem (3^2 + 8^2, then take a square root), but the exact number is not important. The requirement OQ >= PQ allows for two cases  let's look at them: Case #1: Suppose OQ = PQ  then this would be an isosceles triangle, and when PQ came down 8 vertical units from point Q, it would have to go over three horizontal units to (6, 0)  base = 6, height = 8, area = 12 Case #2: Suppose OQ > PQ  then PQ would have to be steeper, and come down the 8 vertical units while going fewer than 3 horizontal units to the right. This would make the base less than 6, so the area would be less than 12. Either way, we have a definitive answer to the prompt. This statement, alone and by itself, is sufficient. Answer = (B)Does this make sense? Mike
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Re: In the rectangular coordinate system above, if OQ >= PQ, is
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27 Sep 2013, 23:47
Thanks Bunuel and Mike, the explanation you provided was way easier than the one I read.
Kudos to both of you!



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Re: In the rectangular coordinate system above, if OQ >= PQ, is
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19 Jun 2015, 18:43
I guess , the coordinates of point O is (0,0) should be given in the stem, unless otherwise could be stated



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Re: In the rectangular coordinate system above, if OQ >= PQ, is
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20 Jun 2015, 06:48
mikemcgarry wrote: PrateekDua wrote: Attachment: Untitled.jpg In the rectangular coordinate system above, if OQ >= PQ, is the area of region OPQ less than 30? (1) The coordinates of point P are (6,0) (2) The coordinates of point Q are (3,8) I'm happy to help. Statement #1: The coordinates of point P are (6,0)The base = 6, but the height could be anything, so the area could be anything. This statement, alone and by itself, is not sufficient. Statement #2: The coordinates of point Q are (3,8)This is tricky. Segment OQ has some length  we could find this length from the Pythagorean theorem (3^2 + 8^2, then take a square root), but the exact number is not important. The requirement OQ >= PQ allows for two cases  let's look at them: Case #1: Suppose OQ = PQ  then this would be an isosceles triangle, and when PQ came down 8 vertical units from point Q, it would have to go over three horizontal units to (6, 0)  base = 6, height = 8, area = 12 Case #2: Suppose OQ > PQ  then PQ would have to be steeper, and come down the 8 vertical units while going fewer than 3 horizontal units to the right. This would make the base less than 6, so the area would be less than 12. Either way, we have a definitive answer to the prompt. This statement, alone and by itself, is sufficient. Answer = (B)Does this make sense? Mike Hi Mike , I could not understand ur explanation for statement B. Are we assuming here points O and P are fixed , and we moving point Q in order to consider scenario of OQ>PQ ?? and how can be assume point P to be fixed ?? O is fixed since it is origin
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In the rectangular coordinate system above, if OQ >= PQ, is
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20 Jun 2015, 08:21
adityadon wrote: mikemcgarry wrote: PrateekDua wrote: Attachment: Untitled.jpg In the rectangular coordinate system above, if OQ >= PQ, is the area of region OPQ less than 30? (1) The coordinates of point P are (6,0) (2) The coordinates of point Q are (3,8) I'm happy to help. Statement #1: The coordinates of point P are (6,0)The base = 6, but the height could be anything, so the area could be anything. This statement, alone and by itself, is not sufficient. Statement #2: The coordinates of point Q are (3,8)This is tricky. Segment OQ has some length  we could find this length from the Pythagorean theorem (3^2 + 8^2, then take a square root), but the exact number is not important. The requirement OQ >= PQ allows for two cases  let's look at them: Case #1: Suppose OQ = PQ  then this would be an isosceles triangle, and when PQ came down 8 vertical units from point Q, it would have to go over three horizontal units to (6, 0)  base = 6, height = 8, area = 12 Case #2: Suppose OQ > PQ  then PQ would have to be steeper, and come down the 8 vertical units while going fewer than 3 horizontal units to the right. This would make the base less than 6, so the area would be less than 12. Either way, we have a definitive answer to the prompt. This statement, alone and by itself, is sufficient. Answer = (B)Does this make sense? Mike Hi Mike , I could not understand ur explanation for statement B. Are we assuming here points O and P are fixed , and we moving point Q in order to consider scenario of OQ>PQ ?? and how can be assume point P to be fixed ?? O is fixed since it is origin Hi Adityadon, Statement 2: The coordinates of point Q are (3,8)i.e. X coordinate of Q is 3 and Ycoordinate is 8 i.e. OQ= \(\sqrt{8^2 + 3^2} = \sqrt{73}\) BUT Since, OQ >= PQ i.e. PQ <\(\sqrt{73}\) But in Triangle PQS since QS=8 therefore PS<3i.e. OP = OS + PS = 3 + ( <3) i.e. OP <6 i.e. Area of Triangle OPQ = (1/2)*OP*QS = (1/2)*( <6)*(8) i.e. Area of Triangle OPQ < 24 Which answers the Questions with Certainty Hence, SUFFICIENT
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Re: In the rectangular coordinate system above, if OQ >= PQ, is
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22 Jun 2015, 10:18
Thanks Mike and Bunuel



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Re: In the rectangular coordinate system above, if OQ >= PQ, is
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18 Aug 2018, 22:42
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