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In the xyplane, a triangle ABC consists of 3 points A(0,0), B(6,0), [#permalink]
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02 May 2016, 22:21
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In the xyplane, a triangle ABC consists of 3 points A(0,0), B(6,0), and C(0,12). If a point (x,y) is in the triangle ABC, what is the probability that y is smaller than x? A. 1/2 B. 1/3 C. 1/4 D. 2/3 E. 3/4 * A solution will be posted in two days.
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Re: In the xyplane, a triangle ABC consists of 3 points A(0,0), B(6,0), [#permalink]
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02 May 2016, 23:09
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we have 2 equations 2x + y = 12 and x = y for the point C so x = 4 and y = 4 We know that for any point in the triangle OCB, Y<X
so area of OCB is 1/2 x 6 x 4 = 12 Area of OAB is 1/2 x 12x 6 =36
so the probibility is 12/36 = 1/3



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Re: In the xyplane, a triangle ABC consists of 3 points A(0,0), B(6,0), [#permalink]
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07 May 2016, 07:15
The probability of y<x is same as the area of △OBC/the area of △OBA. Since the lower base=OB=6, we get a/12. Also, if we substitute this into 2x+y=12, we get 2a+12. From this we get a=4. Then, we obtain a/12=4/12=1/3. Hence, the correct answer is B.
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Re: In the xyplane, a triangle ABC consists of 3 points A(0,0), B(6,0), [#permalink]
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20 Jul 2016, 01:22
MathRevolution wrote: In the xyplane, a triangle ABC consists of 3 points A(0,0), B(6,0), and C(0,12). If a point (x,y) is in the triangle ABC, what is the probability that y is smaller than x?
A. 1/2 B. 1/3 C. 1/4 D. 2/3 E. 3/4
* A solution will be posted in two days. Quote: Sir, This attachment that you have in the problem. Is that information GIVEN or you have derived that drawing based on the information provided in the following question: In the xyplane, a triangle ABC consists of 3 points A(0,0), B(6,0), and C(0,12). If a point (x,y) is in the triangle ABC, what is the probability that y is smaller than x?
Thanks, Yosita



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Re: In the xyplane, a triangle ABC consists of 3 points A(0,0), B(6,0), [#permalink]
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13 Jan 2017, 05:19
Y would be smaller than x, if the point lies within triangle OBC, i.e., between the lines OB and OC of the given diagram. C is the intersection AB and OC. To find the coordinates of C we need to solve the equation of AB and OC. The equation for AB: \(y=ax+b\). Slope of AB is 2, y intersection is 6. \(∴y=2x+6=>y+2x=6(i)\) The equation for OC: \(y=x(ii)\) Solving equations (i) and (ii) we get x and y coordinates of point C, x = 4 and y = 4 So, the area of triangle OCB is 4 = 12 and the Area of triangle OAB is 36. ∴ The probability is \(\frac{12}{36}=\frac{1}{3}\)
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Re: In the xyplane, a triangle ABC consists of 3 points A(0,0), B(6,0), [#permalink]
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25 Aug 2017, 09:32
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2 methods are posted Normal way and shortcut in these questions hope you will like the approach.
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In the xyplane, a triangle ABC consists of 3 points A(0,0), B(6,0), [#permalink]
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26 Aug 2017, 19:57
MathRevolution wrote: The probability of y<x is same as the area of △OBC/the area of △OBA. Since the lower base=OB=6, we get a/12. Also, if we substitute this into 2x+y=12, we get 2a+12. From this we get a=4. Then, we obtain a/12=4/12=1/3. Hence, the correct answer is B. It is given y should be less than x , Would this solution account for the integer values where y=x ??



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Re: In the xyplane, a triangle ABC consists of 3 points A(0,0), B(6,0), [#permalink]
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26 Aug 2017, 22:23
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Siddhuftr wrote: MathRevolution wrote: The probability of y<x is same as the area of △OBC/the area of △OBA. Since the lower base=OB=6, we get a/12. Also, if we substitute this into 2x+y=12, we get 2a+12. From this we get a=4. Then, we obtain a/12=4/12=1/3. Hence, the correct answer is B. It is given y should be less than x , Would this solution account for the integer values where y=x ?? Hello siddhuftr From the triangle x and y can take non integer values as well , no where it is mentioned about integer values. You have to consider all points in that area. Hope its clear. Sent from my iPhone using GMAT Club Forum mobile app
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Re: In the xyplane, a triangle ABC consists of 3 points A(0,0), B(6,0), [#permalink]
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21 Sep 2017, 00:43
Hi, attached is how I approached it, and got 1/2 instead of 1/3. General approach seems to be correct, but I am thinking that the area of smaller triangle shoul be 18, not 12, because the question asks for situation where Y (= height) is less than X (=base), so I drew a triangle (shaded area), where base = 6, height =6. Where am I wrong with this?? Please enlighten me!! BunuelThank you so much in advance!
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In the xyplane, a triangle ABC consists of 3 points A(0,0), B(6,0), [#permalink]
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21 Sep 2017, 01:38
HappyQuakka wrote: Hi, attached is how I approached it, and got 1/2 instead of 1/3. General approach seems to be correct, but I am thinking that the area of smaller triangle shoul be 18, not 12, because the question asks for situation where Y (= height) is less than X (=base), so I drew a triangle (shaded area), where base = 6, height =6. Where am I wrong with this?? Please enlighten me!! BunuelThank you so much in advance! Your x,y coordinate of point F are wrong. I dont know how you got 6,6 => can you explain how you got 6,6?? and the correct coordinate will be 4,4
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In the xyplane, a triangle ABC consists of 3 points A(0,0), B(6,0),
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