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Re: If distinct points A , B , C , and D form a right triangle [#permalink]

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01 Apr 2011, 20:46

I think that the answer should be C. Am I right ?

seekmba wrote:

Why is S1 insufficient? As given in the question, ABC is a right triangle with a height BD, which means B is the right angle and AC is the hypotenuse. Then AB has to be equal to BC and if AB = 6 then BC = 6 too and gives the product of AB and BC.

If distinct points A , B , C , and 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.

Statement (1) ALONE is sufficient, but Statement (2) ALONE is not sufficient Statement (2) ALONE is sufficient, but Statement (1) ALONE is not sufficient BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient EACH statement ALONE is sufficient Statements (1) and (2) TOGETHER are NOT sufficient

Explanation:

Statement (1) by itself is insufficient. is unknown.

Statement (2) by itself is sufficient. is the hypotenuse. We know that is the right angle because height can be drawn only from the right angle vertex. The four points are distinct and, consequently, can't be congruent with any of the legs. Now that we know what angle is the right angle, the product is of and (non-hypotenuse sides) is given in S2

Re: If distinct points A , B , C , and D form a right triangle [#permalink]

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01 Apr 2011, 23:55

Hello pesfunk knowing the geometry of rt angled triang is different from knowing the area. The Ds question is more simply- do you know the area of the rt angled trig ABC? S1 is insuff S2 is suff. If you paraphrase it tells you the 1/2 of base *height is known. Hence area is known

Unless you confuse the question with what is the geometry of the triangle - you are good . C is overanalysis.

Re: If distinct points A , B , C , and D form a right triangle [#permalink]

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02 Apr 2011, 00:01

Oh yes...Answer B is indeed correct. I didn't understand the question correctly in the first place and thus chose C.

gmat1220 wrote:

Hello pesfunk knowing the geometry of rt angled triang is different from knowing the area. The Ds question is more simply- do you know the area of the rt angled trig ABC? S1 is insuff S2 is suff. If you paraphrase it tells you the 1/2 of base *height is known. Hence area is known

Unless you confuse the question with what is the geometry of the triangle - you are good . C is overanalysis.

Re: If distinct points A , B , C , and D form a right triangle [#permalink]

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02 Apr 2011, 07:42

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.

Attachments

ABC_RightAngleTriangle.PNG [ 7.17 KiB | Viewed 1682 times ]

1. AB is given, but we dont know anything abt area or BC..so cant answer the question hence options A and D are gone

2. so taking the right angled triangle, we know that the other product of non-hypotenuse sides is equal to twice the area and that is what the question is asking us. hence this gives the answer...so option B is the answer _________________

Regards, Harsha

Note: Give me kudos if my approach is right , else help me understand where i am missing.. I want to bell the GMAT Cat

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.

I assumed that D should be a distinct pt. However, if the triangle is right-angled at A then the altitude BD can be drawn outside the triangular region ABC such that the BD will be parallel to AB or AC. In this case, the value of AB*BC will be 6*sqrt(52), which is different from the ans that we get if we assume that the triangle is right angled at B.

Please let me know if it I'm missing something.

BD can never be parallel to AB since they intersect at the common point B. Also, BD (height) can never be parallel to AC as it has to be perpendicular to AC to qualify as height.