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Re: In the rectangular coordinate system above, if OP < PQ, is [#permalink]
14 Mar 2012, 15:30
12
This post received KUDOS
Expert's post
5
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Attachment:
Triangle.png [ 15.88 KiB | Viewed 11127 times ]
In the rectangular coordinate system above, if OP < PQ, is the area of region OPQ greater than 48 ?
(1) The coordinates of point P are (6,8). Now, if OP were equal to PQ then the triangle OPQ would be isosceles and OS would be equal to SQ and the area would be: 1/2*base*height=1/2(OS+SQ)*PS=1/2*(6+6)*8=48. Since OP<PQ then OS<SQ and the base OQ is more than 12, which makes the area more than 48. Sufficient.
(2) The coordinates of point Q are (13,0) --> we know the length of the base (OQ=13) but know nothing about the height (PS), which may be 1 or 100, so the area may or may not be more than 48. Not sufficient.
Re: In the rectangular coordinate system above, if OP < PQ, is [#permalink]
30 Mar 2012, 17:51
3
This post received KUDOS
thanks Bunuel. stmt 1 shows us that the smaller triangle is 1/2*6*8 and the other triangle must be larger than the smaller one. adding the two triangles together you get a number larger than 48. _________________
Re: In the rectangular coordinate system above, if OP < PQ, is [#permalink]
09 Jul 2013, 15:37
Bunuel wrote:
In the rectangular coordinate system above, if OP < PQ, is the area of region OPQ greater than 48 ?
(1) The coordinates of point P are (6,8). Now, if OP were equal to PQ then the triangle OPQ would be isosceles and OS would be equal to SQ and the area would be: 1/2*base*height=1/2(OS+SQ)*PS=1/2*(6+6)*8=48. Since OP<PQ then OS<SQ and the base OQ is more than 12, which makes the area more than 48. Sufficient.
(2) The coordinates of point Q are (13,0) --> we know the length of the base (OQ=13) but know nothing about the height (PS), which may be 1 or 100, so the area may or may not be more than 48. Not sufficient.
Answer: A.
Hope it's clear.
Hi Bunuel,
Can thehre be a case when OS= 5.5, SQ=6.5? Then OQ= 12 .... _________________
"Where are my Kudos" ............ Good Question = kudos
Re: In the rectangular coordinate system above, if OP < PQ, is [#permalink]
09 Jul 2013, 15:47
Expert's post
Mountain14 wrote:
Bunuel wrote:
In the rectangular coordinate system above, if OP < PQ, is the area of region OPQ greater than 48 ?
(1) The coordinates of point P are (6,8). Now, if OP were equal to PQ then the triangle OPQ would be isosceles and OS would be equal to SQ and the area would be: 1/2*base*height=1/2(OS+SQ)*PS=1/2*(6+6)*8=48. Since OP<PQ then OS<SQ and the base OQ is more than 12, which makes the area more than 48. Sufficient.
(2) The coordinates of point Q are (13,0) --> we know the length of the base (OQ=13) but know nothing about the height (PS), which may be 1 or 100, so the area may or may not be more than 48. Not sufficient.
Answer: A.
Hope it's clear.
Hi Bunuel,
Can thehre be a case when OS= 5.5, SQ=6.5? Then OQ= 12 ....
No, that's not possible. We know that the coordinates of point P are (6,8). PS is altitude, thus the coordinates of point S are (6,0), so OS=6.
Re: In the rectangular coordinate system above, if OP < PQ, is [#permalink]
09 Jul 2013, 15:51
Bunuel wrote:
Mountain14 wrote:
Bunuel wrote:
In the rectangular coordinate system above, if OP < PQ, is the area of region OPQ greater than 48 ?
(1) The coordinates of point P are (6,8). Now, if OP were equal to PQ then the triangle OPQ would be isosceles and OS would be equal to SQ and the area would be: 1/2*base*height=1/2(OS+SQ)*PS=1/2*(6+6)*8=48. Since OP<PQ then OS<SQ and the base OQ is more than 12, which makes the area more than 48. Sufficient.
(2) The coordinates of point Q are (13,0) --> we know the length of the base (OQ=13) but know nothing about the height (PS), which may be 1 or 100, so the area may or may not be more than 48. Not sufficient.
Answer: A.
Hope it's clear.
Hi Bunuel,
Can thehre be a case when OS= 5.5, SQ=6.5? Then OQ= 12 ....
No, that's not possible. We know that the coordinates of point P are (6,8). PS is altitude, thus the coordinates of point S are (6,0), so OS=6.
Hope it' clear.
Yes Got it!... Thanks _________________
"Where are my Kudos" ............ Good Question = kudos
Re: In the rectangular coordinate system above, if OP < PQ, is [#permalink]
21 Oct 2013, 12:27
Bunuel wrote:
Attachment:
Triangle.png
In the rectangular coordinate system above, if OP < PQ, is the area of region OPQ greater than 48 ?
(1) The coordinates of point P are (6,8). Now, if OP were equal to PQ then the triangle OPQ would be isosceles and OS would be equal to SQ and the area would be: 1/2*base*height=1/2(OS+SQ)*PS=1/2*(6+6)*8=48. Since OP<PQ then OS<SQ and the base OQ is more than 12, which makes the area more than 48. Sufficient.
(2) The coordinates of point Q are (13,0) --> we know the length of the base (OQ=13) but know nothing about the height (PS), which may be 1 or 100, so the area may or may not be more than 48. Not sufficient.
Answer: A.
Hope it's clear.
I didn't understand how are we assuming that OS is equal 6? and how are we concluding t either that OS=QS?Can you pls explain?
Re: In the rectangular coordinate system above, if OP < PQ, is [#permalink]
21 Oct 2013, 21:36
Expert's post
Punyata wrote:
Bunuel wrote:
Attachment:
Triangle.png
In the rectangular coordinate system above, if OP < PQ, is the area of region OPQ greater than 48 ?
(1) The coordinates of point P are (6,8). Now, if OP were equal to PQ then the triangle OPQ would be isosceles and OS would be equal to SQ and the area would be: 1/2*base*height=1/2(OS+SQ)*PS=1/2*(6+6)*8=48. Since OP<PQ then OS<SQ and the base OQ is more than 12, which makes the area more than 48. Sufficient.
(2) The coordinates of point Q are (13,0) --> we know the length of the base (OQ=13) but know nothing about the height (PS), which may be 1 or 100, so the area may or may not be more than 48. Not sufficient.
Answer: A.
Hope it's clear.
I didn't understand how are we assuming that OS is equal 6? and how are we concluding t either that OS=QS?Can you pls explain?
In the rectangular coordinate system above, if OP < PQ, is the area of region OPQ greater than 48 ?
(1) The coordinates of point P are (6,8). Now, if OP were equal to PQ then the triangle OPQ would be isosceles and OS would be equal to SQ and the area would be: 1/2*base*height=1/2(OS+SQ)*PS=1/2*(6+6)*8=48. Since OP<PQ then OS<SQ and the base OQ is more than 12, which makes the area more than 48. Sufficient.
(2) The coordinates of point Q are (13,0) --> we know the length of the base (OQ=13) but know nothing about the height (PS), which may be 1 or 100, so the area may or may not be more than 48. Not sufficient.
In the rectangular coordinate system above, if OP < PQ, is the area of region OPQ greater than 48 ?
(1) The coordinates of point P are (6,8). Now, if OP were equal to PQ then the triangle OPQ would be isosceles and OS would be equal to SQ and the area would be: 1/2*base*height=1/2(OS+SQ)*PS=1/2*(6+6)*8=48. Since OP<PQ then OS<SQ and the base OQ is more than 12, which makes the area more than 48. Sufficient.
(2) The coordinates of point Q are (13,0) --> we know the length of the base (OQ=13) but know nothing about the height (PS), which may be 1 or 100, so the area may or may not be more than 48. Not sufficient.
Answer: A.
Hope it's clear.
This is not correct because we are not given that OPQ is a right triangle, thus you cannot write OP^2 + PQ^2 = OQ^2.
Re: In the rectangular coordinate system above, if OP < PQ, is [#permalink]
15 Apr 2014, 11:32
Hi Bunuel,
In the above diagram,what if we consider the triangle to be inscribed in a rectangle and prove angle p to be a right angle, in that case, statement 1 and 2 might be sufficient to answer the question if the area of the triangle is greater than 48 right??
gmatclubot
Re: In the rectangular coordinate system above, if OP < PQ, is
[#permalink]
15 Apr 2014, 11:32
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