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GMAT Club Forum DS Question - Right Triangle on a Plane

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GMAT Club Forum DS Question - Right Triangle on a Plane

by 800_or_bust » Tue May 24, 2016 6:03 pm
I have an issue with this question. The credited answer is given as (B), but I believe the correct answer should be (E). Can anybody explain why (B) is correct? Update: See Post #3. I think the correct answer is actually (C). Also note there were no drawings accompanying this, so conceivably any configuration of Triangle ABC should be valid.

PROBLEM M04-12

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

(1) AB=6

(2) The product of the non-hypotenuse sides is equal to 24.
Last edited by 800_or_bust on Tue May 24, 2016 6:29 pm, edited 1 time in total.
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by 800_or_bust » Tue May 24, 2016 6:21 pm
800_or_bust wrote:I have an issue with this question. The credited answer is given as (B), but I believe the correct answer should be (E). Can anybody explain why (B) is correct?

PROBLEM M04-12

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

(1) AB=6

(2) The product of the non-hypotenuse sides is equal to 24.
Here's an illustration. In both cases, BD is the height of the triangle. In case one, the height is measured from leg BC. And in case two, the height is measured from hypotenuse AC. Note in case one AB is a hypotenuse and in case two AB is a leg.

Image
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by 800_or_bust » Tue May 24, 2016 6:26 pm
I suppose technically you could make the case for (C), i.e. together the two statements are sufficient, because I think (II) would imply AB must be a leg if its length were 6. I don't think there are any possible combinations of legs such that the product of those legs would be 24, and the corresponding hypotenuse is 6. That just doesn't seem plausible. Obviously the hypotenuse cannot be 6, if the legs are 6 and 4. And no other integer values would work. But even something like 5.xxx and 4.xxxx couldn't possibly work, because the sum of their squares would be much greater than 36.

So it may be (C), but definitely not (B) IMO.
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by 800_or_bust » Wed May 25, 2016 12:38 pm
800_or_bust wrote:I have an issue with this question. The credited answer is given as (B), but I believe the correct answer should be (E). Can anybody explain why (B) is correct? Update: See Post #3. I think the correct answer is actually (C). Also note there were no drawings accompanying this, so conceivably any configuration of Triangle ABC should be valid.

PROBLEM M04-12

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

(1) AB=6

(2) The product of the non-hypotenuse sides is equal to 24.
So I guess an altitude technically is a line segment from one vertex to any base such that the angle formed between the segments is a 90-degree angle. I have no idea whether "height" and "altitude" are synonymous in this sense. The question specified "a height" - not sure if that implies altitude or not? Would a GMAT question require us to know the formal definition of a term like "altitude"? It seems like the GMAT is pretty good about defining terms of art, or at least providing accompanying diagrams that illustrate the concept.
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by Matt@VeritasPrep » Thu May 26, 2016 2:58 pm
AFAIK height and altitude are synonymous, and since your triangle isn't obtuse, all three altitudes are WITHIN the triangle by convention. (Much) more here.

This is a pretty typical GMATClub question: sloppily written, overly technical, and on the borderline of the scope of the GMAT.
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