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Re: If distinct points A , B , C , and D form a right triangle [#permalink]
26 Jul 2012, 10:00

fluke wrote:

144144 wrote:

Fluke - my friend,

Isnt the 2nd statement exactly what they are asking in the question?

am i missing something here?

I believe you are correct!!! 2nd statement is telling us exactly what the question had asked.

Stem says: ABC is a right angled triangle. My only concern here is that the question stem doesn't explicitly say that the triangle ABC is a right angled triangle, right angled at B. I am assuming that the triangle is right angled at B.

Now, Point D is located somewhere in the co-ordinate such that BD becomes the height.

Attached image is showing 3 of the possible scenarios where D can be located. D can superimpose A i.e. D and A can be the two points at the same co-ordinate, D and B can be the two points at the same co-ordinate or D can somewhere be on the line segment AC, which is the hypotenuse.

Now, we need to find out AB*BC. Note: we don't need to know AB and BC individually. So far we get "AB*BC", we are good.

St1: AB=6; We don't know anything about BC and thus AB*BC can't be found. Not Sufficient. St2: The product of the non-hypotenuse sides is equal to 24. From the stem, we know AB and BC are the non-hypotenuse sides. Thus, the statement 2 is telling us exactly what we wanted to know. Sufficient.

Turns out that extra information about the BD was given just to provide some extraneous information and confuse the test takers. We could have done without that. Well!! I feel that there is some loop hole in this question and I don't consider it to be one of my favorites.

You are missing out on a very important word mentioned in the question - DISTINCT. The question states that A,B, C and D are distinct points. Hence the only valid figure here is the second one as D cannot superimpose any other point.

Did not find it tough though. One normally tends to imagine that the the right triangle has the non-hypotenuse sides parallel to either the X and Y axis. This problem becomes much easier when we imagine the right triangle with the hypotenuse parallel to the X-axis. That helps plot the point D easily.

B it is.
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Did not find it tough though. One normally tends to imagine that the the right triangle has the non-hypotenuse sides parallel to either the X and Y axis. This problem becomes much easier when we imagine the right triangle with the hypotenuse parallel to the X-axis. That helps plot the point D easily.

B it is.

when you will be drawing a perpendicular from B to the side AC (i.e. drawing BD), two more right-angled triangles would be created, thus creating ambiguity. Check my previous posts for the ambiguity in the question I am referring to.

The answer cannot be B. Actually, the question is ambiguous. If we have triangle ABC as the right-angled triangle, it means that B = 90. Now we have two more triangles here, ADB and BDC and both these triangles are right-angled triangles (since D is the height of the triangle ABC and in Maths, height = perpendicular drawn from one vertex to the opposite side). If we say "non-hypotenuse sides", we have to be very clear as to which triangles non-hypotenuse sides we are referring to. As we can see from above, there would be 6 non-hypotenuse sides in this figure (because there are 3 right angled triangles). So the answer cannot be B.

Hope this helps!

I figured the ambiguity as the height in Maths need not be parallel to any axis. As long as it is perpendicular to the sides, it can be considered at the height. In fact for that matter in a right-triangle (ABC), one on the non-hypotenuse sides can be considered the height. Why do we need a height BD then.

That said, the question does not state anywhere that the triangle ABC is the only right triangle formed between the points A,B,C and D. For that matter, the second statement just gives a rephrased version of the question asked.

B is the point of the right angle and hence AB times BC is effectively product of the non-hype sides of the triangle ABC.

But I get your point regarding the non-hypo sides. Overall this is a non-standard question which might not appear in the GMAT.
_________________

My attempt to capture my B-School Journey in a Blog : tranquilnomadgmat.blogspot.com

BELOW IS REVISED VERSION OF THIS QUESTION WITH A SOLUTION:

A, B, C, and D are distinct points on a plane. If triangle ABC is a right angled and BD is a height of this triangle, what is the value of AB times BC ?

Since all points are distinct and BD is a height then B must be a right angle and AC must be a hypotenuse (so BD is a height from right angle B to the hypotenuse AC). Question thus asks about the product of non-hypotenuse sides AB and BC.

(1) AB = 6. Clearly insufficient. (2) The product of the non-hypotenuse sides is equal to 24 --> directly gives us the value of AB*BC. Sufficient.

Unless we know where D is, we cannot really determine the solution. BD was mentioned as 'a height'. But, not as 'the only height'.. So,answer should be 'E'
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Unless we know where D is, we cannot really determine the solution. BD was mentioned as 'a height'. But, not as 'the only height'.. So,answer should be 'E'

Since BD is given to be the height, this would mean that triangle ABC is right angled at B. This is because only the right angled vertex can have a height that is not a side of a triangle. Thus D helps us in identifying the 3 vertices of the triangle.

=> AB^2 + BC^2 = AC^2 and hence AB and BC are the non-hypotenuse sides and we need to find AB*BC

clearly B. In a traiangle there are 3 vertexes and we can draw max 3 heights.

Now the twist in the question is about two points: 1) it is a right angle traingle. So that means we have two heights with us .the one problem states 'BD' does not coincide with these two heights.Question is how come?check the second point.

2)questionstem says A,B,C and D are distinct points.What do we infer from here: a)that BD is the height on the hypotenuse.it cant coincide with other two heights cause the question will contradict itself. b)secondly,the triangle is right angles at B.

After you have found the above two statements you can easily see choice B is sufficient.

ABC does form a right angled triangle. but then again BD can be the height (i.e.) perpendicular drawn from B on the hypotenuse AC. i think this could be the reason D is given.

Distinct points A, B, C, D form a right triangle ABC with a height BD. What is the value of AB times BC?

1. AB=6 2. The product of the non-hypotenuse sides is equal to 24

I think we can understand this question in a manner .. that ABC is a triangle. B is right angle (Based on notation) in right angle triangle right angle is always written in center.

Now point D can traverse from b to c at any location on line AB. as BD will be a part of perpendicular AB. so taking option 1 AB =6

we have AB^2 + BC^2=AC^2 ====> 6^2=AC^2 - BC^2 ====> 36= (AC+BC)(AB-BC) which does not gives us a unique solution. as 36 has 1*36/2*18/3*12/4*9/6*6 as factors. So one is insufficient.

Statement 2 directly tells us AB * BC = 24 which is asked. So B is the right answer

Distinct points A, B, C, D form a right triangle ABC with a height BD. What is the value of AB times BC?

1. AB=6 2. The product of the non-hypotenuse sides is equal to 24

I think we can understand this question in a manner .. that ABC is a triangle. B is right angle (Based on notation) in right angle triangle right angle is always written in center.

Now point D can traverse from b to c at any location on line AB. as BD will be a part of perpendicular AB. so taking option 1 AB =6

we have AB^2 + BC^2=AC^2 ====> 6^2=AC^2 - BC^2 ====> 36= (AC+BC)(AB-BC) which does not gives us a unique solution. as 36 has 1*36/2*18/3*12/4*9/6*6 as factors. So one is insufficient.

Statement 2 directly tells us AB * BC = 24 which is asked. So B is the right answer

Kudos if you understand ..

i understood what you said except for the fact that D can traverse from b to c at any location on line AB. if it does that, it won't be the height as mentioned in the question. otherwise, i follow your answer. thnks...