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assume one of the non hyp sides is AB = x. then the other side AC = 24/x because the product of the two sides 24.

using these two sides - the hypotenuse BC = sqrt(x^2 + [24/x]^2) We are required to find AB times BC which IMO is AB*BC x*sqrt(x^2 + [24/x]^2)

But we don't know the value of x. A gives the value of x. So IMO the ans should be D - we need both choices to answer the question. I am not sure how B could be right.

Even if AB times BC means AB/BC we still can't do without taking both choices into consideration because then we would have to calculate x/sqrt(x^2 + [24/x]^2)

If you draw the triangle you will see that AB and BC are the 2 short sides of the right triangle. You are asked for AB*BC, but stmt 1 doesn't say anything about BC. Stmt 2 instead gives you exactly the answer (you can read it as AB*BC=24). That's why the answer is B!

I am missing something. Can someone tell me how a triangle can have 4 distinct points, A,B,C,D? Can someone please sketch the question so that I can see the triangle visually?

Good question. At first I drew an isosceles right triangle with height BD. Almost went with answer D. Then when I read (2) I thought wait could there be two different length sides?

I have found on the GMAT some times thinking creatively can be bad. For example, if you draw the picture you see 3 triangles: ABC ABD BDC

However, the question only mentions one triangle ABC. You must limit yourself to this limited concept.

Similar to which is the assumption questions on Critical Reasoning, about a subject that you know well.

If you draw a diagram try thinking about this in two different colors, or draw using 2 different line types.

Dear TallJTinChina, if you are referring to the picture with 3 triangles please read explanation first. there is stated that only FIRST option is possible in accordance to the q-n. Regards, VT

If distinct points A , B , C , and D form a right triangle [#permalink]
30 Aug 2010, 10:10

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

Does the height "BD" specifically mean BD has to be within the triangle? Could BD just "happen" to be the same length as the height of the right triangle?

For example, if the height of ABC was 4 units, could you not draw D 4 units away from B, in effect saying BD = the height, but it just isn't specifically diagramming it? _________________

a-insuffecient b-it's mentioned that abc is right triangle and bd is perpendicular.that means bd can be base or on height.the product of non hypo is given so its difficult to get the result.

Re: If distinct points A , B , C , and D form a right triangle [#permalink]
01 Apr 2011, 10:31

this question is rly unclear to me... is it possible they give the whole answer in statement 2?! is it GMAT style? am i missing something? _________________