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In the rectangular coordinate system above, if OB < BC then is the are [#permalink]
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09 Feb 2015, 02:34
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In the rectangular coordinate system above, if OB < BC then is the area of the triangle ABC lesser than 12 square units? (1) Point A lies above the line y = 5 (2) The midpoint of B and C is (6, 0)
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In the rectangular coordinate system above, if OB < BC then is the are [#permalink]
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09 Feb 2015, 11:40
Hi TARGET730, In DS questions, you have to be careful about any pictures that you're given  as a general rule, you CANNOT trust any pictures in DS questions. From the drawing, it "looks like" the base of the triangle is bigger than the height of the triangle, but we DO NOT KNOW that for sure. It might be that the base and the height are equal; it might also be that the height is bigger than the base. As such, we can only use the math "facts" that we're given to try to answer this question. We're told that the length of OB is less than the length of BC. We're asked if the area of the triangle is less than 12. This is a YES/NO question. Fact 1: Point A lies above the line Y = 5. This tells us that the height of the triangle is > 5, but it dos not tell us anything about the base. IF.... Height = 6 Base = 6 Area = (1/2)(6)(6) = 18 and the answer to the question is NO. IF..... Height = 6 Base = 1 Area = (1/2)(1)(6) = 3 and the answer to the question is YES. Fact 1 is INSUFFICIENT Fact 2: The midpoint of B and C is (6,0) This Fact limits the possible base of the triangle, since OB < BC, the range for the base is....4 < base < 12, but tells us nothing about the height. The examples that we used in Fact 1 (above) would fit here. Fact 2 is INSUFFICIENT Combined, we could have... Base = 6 Height = 6 Area = (1/2)(6)(6) = 18 and the answer to the question is NO. Base = 4.1 Height = 5.1 Area = (1/2)(4.1)(5.1) = just above 10 and the answer to the question is YES. Combined, INSUFFICIENT Final Answer: GMAT assassins aren't born, they're made, Rich
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Re: In the rectangular coordinate system above, if OB < BC then is the are [#permalink]
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09 Feb 2015, 20:52
TARGET730 wrote: Attachment: download.png In the rectangular coordinate system above, if OB < BC then is the area of the triangle ABC lesser than 12 square units? (1) Point A lies above the line y = 5 (2) The midpoint of B and C is (6, 0) hi target 730, ans E.. FOR THIS QUESTION.. but just a point that each statement does convey a pertinant point.. 1) statement 1 tells us that height is 5 or >5.. insufficient since the Q asks <12, we will take the lowest value of 2) statement 2 tells us the width, here it gives the lowest value for width to be 4... insufficient.. combined if we take the lowest value for area..1/2*5*4=10 ao area >10 so not sufficient however if the coord were (8,0).. the lowest value of base would be 16/3.. so lowest area = 1/2*5*16/3 >12 so ans would be combined sufficient.. my point we have to read the values very minutely..
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Re: In the rectangular coordinate system above, if OB < BC then is the are [#permalink]
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11 Feb 2015, 04:49
chetan2u wrote: TARGET730 wrote: Attachment: download.png In the rectangular coordinate system above, if OB < BC then is the area of the triangle ABC lesser than 12 square units? (1) Point A lies above the line y = 5 (2) The midpoint of B and C is (6, 0) hi target 730, ans E.. FOR THIS QUESTION.. but just a point that each statement does convey a pertinant point.. 1) statement 1 tells us that height is 5 or >5.. insufficient since the Q asks <12, we will take the lowest value of 2) statement 2 tells us the width, here it gives the lowest value for width to be 4... insufficient.. combined if we take the lowest value for area..1/2*5*4=10 ao area >10 so not sufficient however if the coord were (8,0).. the lowest value of base would be 16/3.. so lowest area = 1/2*5*16/3 >12 so ans would be combined sufficient.. my point we have to read the values very minutely.. hi chetan2u, I have a question in the second statement As (6,0) [lets call it as X] is the midpoint of BC ,so BX=XC=BC/2 and you have taken the lowest value for width to be 4 so BX=XC=4/2=2according to this B([62],0) and C([6+2],0)which means B(4,0) and C(8,0)this gives OB=BC=4but in the stem it is given that OB<BC.



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Re: In the rectangular coordinate system above, if OB < BC then is the are [#permalink]
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13 Feb 2015, 03:15
Hi all, To calculate the area of the triangle we need base and the height here That is we got to check ½ (BC)(height)<12? 1). Statement 1 is insufficient. This talks only about height. This says height is greater than or equal to 5. 2). Statement 2 is insufficient. This talks only about base which is BC. This says base length can be 6 or 8. B(3.0) and C(9,0) B(2,0) and C(10,0) Together sufficient, Height minimum we can take is 5 and base minimum can be 6. Then the area is 15. Always the area going to be greater than 12. Together sufficient. So the answer is C.
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Re: In the rectangular coordinate system above, if OB < BC then is the are [#permalink]
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16 Feb 2015, 02:35
CrackVerbalGMAT, I think the answer is E. What if B is (3.9, 0) and C is (8.1,0) ? In this case BC = 4.2, which is greater than OB. Area will be 10.5 which is less than 12
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Re: In the rectangular coordinate system above, if OB < BC then is the are [#permalink]
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16 Feb 2015, 17:54
CrackVerbalGMAT wrote: Hi all, To calculate the area of the triangle we need base and the height here That is we got to check ½ (BC)(height)<12? 1). Statement 1 is insufficient. This talks only about height. This says height is greater than or equal to 5. 2). Statement 2 is insufficient. This talks only about base which is BC. This says base length can be 6 or 8. B(3.0) and C(9,0) B(2,0) and C(10,0) Together sufficient, Height minimum we can take is 5 and base minimum can be 6. Then the area is 15. Always the area going to be greater than 12. Together sufficient. So the answer is C. Hi CrackVerbalGMAT, The prompt never states that the coordinates are integers and there are more possible values for the base of the triangle in Fact 2 than the 6 and 8 that you noted. If you try minimizing the base and the height of the triangle, you'll get the correct answer. GMAT assassins aren't born, they're made, Rich
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Re: In the rectangular coordinate system above, if OB < BC then is the are [#permalink]
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16 Feb 2015, 17:58
vinyasgupta wrote: hi chetan2u, I have a question in the second statement As (6,0) [lets call it as X] is the midpoint of BC ,so BX=XC=BC/2 and you have taken the lowest value for width to be 4 so BX=XC=4/2=2according to this B([62],0) and C([6+2],0)which means B(4,0) and C(8,0)this gives OB=BC=4but in the stem it is given that OB<BC. hi vinay... you are right that OB<BC.... however i have taken it as OB = BC because that is the value slightly above max value it can take and if it still does not satisfy the equation at slightly higher value than its max value, it will not satisfy at any other value.. also it is easier and faster to work with integer than x.9999 and other value as y.0001....
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