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# A, B, C, and D are distinct points on a plane. If triangle A

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Director
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A, B, C, and D are distinct points on a plane. If triangle A [#permalink]

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10 Oct 2007, 22:17
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75% (hard)

Question Stats:

55% (01:00) correct 45% (01:53) wrong based on 97 sessions

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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.

OPEN DISCUSSION OF THIS QUESTION IS HERE: a-b-c-and-d-are-distinct-points-on-a-plane-if-triangle-a-129328.html
[Reveal] Spoiler: OA

Last edited by Bunuel on 04 Jul 2014, 05:50, edited 1 time in total.
Renamed the topic, edited the question and added the OA.
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Re: A, B, C, and D are distinct points on a plane. If triangle A [#permalink]

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10 Oct 2007, 22:24
isn't it B,

it already tells that 'The product of the non-hypotenuse sides is equal to 24'

Ans: B
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Re: A, B, C, and D are distinct points on a plane. If triangle A [#permalink]

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10 Oct 2007, 22:37
Ferihere wrote:
isn't it B,

it already tells that 'The product of the non-hypotenuse sides is equal to 24'

Ans: B

AO is B,

I am just thinking that,

AB and AC could be the non-hypotenuse sides and BC the hypotenuse.

The stem says BD is the height, so if point D coincides with A, then it is still height. (there is no info limiting this possibility)

Please explain where I am wrong in my reasoning. Thank you.
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Re: A, B, C, and D are distinct points on a plane. If triangle A [#permalink]

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11 Oct 2007, 00:37
IrinaOK wrote:
Ferihere wrote:
isn't it B,

it already tells that 'The product of the non-hypotenuse sides is equal to 24'

Ans: B

AO is B...

I am just thinking why cant it be that,

AB and AC are the non-hypotenuse sides and BC is the hypotenuse.

The stem says BD is the height, so if point D coincides with A, then it is still height. (there is no info limiting this possibility)

Please explain where I am wrong in my reasoning. Thank you.

I agree with your reasoning that the OA is wrong.

Perhaps the question was supposed to come with a diagram that shows which corner has the right angle. If we know D does not coincide with A, then B is correct. If we know that D does coincide with A, then C would be correct.
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Re: A, B, C, and D are distinct points on a plane. If triangle A [#permalink]

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11 Oct 2007, 02:59
IrinaOK wrote:
Right triangle ABC has a height BD. What is the value of AB times BC?

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

DS

I think, from the stem above, only traingle that can be drawn is TRAINGLE 1 below. furthermore stem says BD is the height. if it coincides with AB then stem should not mention the point D. so it doesnt coincide.

any ideas?
Attachments

traingles.JPG [ 11.21 KiB | Viewed 1358 times ]

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Re: A, B, C, and D are distinct points on a plane. If triangle A [#permalink]

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11 Oct 2007, 08:35
Ravshonbek:

In your diagram angle B is the right angle, what if the right angle in the triangle is A or C?
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Re: A, B, C, and D are distinct points on a plane. If triangle A [#permalink]

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11 Oct 2007, 08:43
Hyperstorm wrote:
Ravshonbek:

In your diagram angle B is the right angle, what if the right angle in the triangle is A or C?

Hi Hyperstorm,

good question. did not think about that.

Right triangle ABC has a height BD. What is the value of AB times BC?

it can be C or A.
then try to make BD height from ABC whose right angle is not B.
i could not figure out anythign from that. i am sure there should be smth else if you bring that up here.

I understand that BD can coincide with one of the hypotenuses. then why the stem mentions the POINT D. instead it can say BA or BC or other.
To me the stem is fine. but let's wait until Tino makes move.
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Re: A, B, C, and D are distinct points on a plane. If triangle A [#permalink]

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11 Oct 2007, 08:52
IrinaOK wrote:
Ferihere wrote:
isn't it B,

it already tells that 'The product of the non-hypotenuse sides is equal to 24'

Ans: B

AO is B,

I am just thinking that,

AB and AC could be the non-hypotenuse sides and BC the hypotenuse.

The stem says BD is the height, so if point D coincides with A, then it is still height. (there is no info limiting this possibility)

Please explain where I am wrong in my reasoning. Thank you.

You would be right if the question would not classify a point B, in other words question does not says any hypotenuse, it states that it is BD. If height lies on one of the sides of triangle than there would be 4 points ABCD and BD would be some portion of triangle's side, which is not height actually.

If you have any question feel free to ask...
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Re: A, B, C, and D are distinct points on a plane. If triangle A [#permalink]

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11 Oct 2007, 13:55
Ferihere, Ravshonbek, thank you for your explanations.

Please kindly have a look at the picture below. I used Ravshonbeks drawing.

If it is first triangle the asnwer is B, if it is second triangle the asnwer is C, just as Jing wrote above.

It is second triangle, if point D coincides with point A (stem gives no info that would limit this posssibility). Thus, BA is the same as BD and both are heights of the triangle.

I used the definition of height from OG11th, p. 130-131.

Can it be that in GMAT, annotation of right triangle already indicates what letter represents the right angle?

for example:

ABC--------> B must be the right angle
ACB--------> C must be the right angle

Attachments

traingles_editted.jpg [ 8.66 KiB | Viewed 1330 times ]

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Re: A, B, C, and D are distinct points on a plane. If triangle A [#permalink]

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11 Oct 2007, 22:42
IrinaOK wrote:
Right triangle ABC has a height BD. What is the value of AB times BC?

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

DS

B cannot be OA. only C can be the OA.

Scenerio: ABC is a right angle triangle so any angle could be right angle and any side can be Hypoteneous (H), base (B) and perpendicular (P). but we do not know.

Since BD is a highet of the triangle, it is perpendicuar to the hypoteneous.

1: St 1 tells us nothing. AB could be H or B or P. .......
2: st 2 also doesnot tell the measures clearly. because we do not know which one is B, P, and H.

From 1 and 2, we can say that AB is not H, which should be grater than 6. AB is either B or P and BC is what AB is not.

So AB x BC should equal to 24.
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Re: A, B, C, and D are distinct points on a plane. If triangle A [#permalink]

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11 Oct 2007, 22:52
IrinaOK wrote:
Ferihere, Ravshonbek, thank you for your explanations.

Please kindly have a look at the picture below. I used Ravshonbeks drawing.

If it is first triangle the asnwer is B, if it is second triangle the asnwer is C, just as Jing wrote above.

It is second triangle, if point D coincides with point A (stem gives no info that would limit this posssibility). Thus, BA is the same as BD and both are heights of the triangle.

I used the definition of height from OG11th, p. 130-131.

Can it be that in GMAT, annotation of right triangle already indicates what letter represents the right angle?

for example:

ABC--------> B must be the right angle
ACB--------> C must be the right angle

I go with B on this one. The first triangle would be the most possible case. The second triangle requires an assumption that point A is also point D, and the GMAT doesn't gives leeways for these assumptions. However, that part about the annotation of a right triangle given by the OG is new stuff to me.
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Re: A, B, C, and D are distinct points on a plane. If triangle A [#permalink]

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11 Oct 2007, 22:56
1
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ywilfred wrote:
IrinaOK wrote:
Ferihere, Ravshonbek, thank you for your explanations.

Please kindly have a look at the picture below. I used Ravshonbeks drawing.

If it is first triangle the asnwer is B, if it is second triangle the asnwer is C, just as Jing wrote above.

It is second triangle, if point D coincides with point A (stem gives no info that would limit this posssibility). Thus, BA is the same as BD and both are heights of the triangle.

I used the definition of height from OG11th, p. 130-131.

Can it be that in GMAT, annotation of right triangle already indicates what letter represents the right angle?

for example:

ABC--------> B must be the right angle
ACB--------> C must be the right angle

I go with B on this one. The first triangle would be the most possible case. The second triangle requires an assumption that point A is also point D, and the GMAT doesn't gives leeways for these assumptions. However, that part about the annotation of a right triangle given by the OG is new stuff to me.

for the sake of clarity, it was just a question...
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Re: A, B, C, and D are distinct points on a plane. If triangle A [#permalink]

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11 Oct 2007, 23:09
Fistail wrote:
IrinaOK wrote:
Right triangle ABC has a height BD. What is the value of AB times BC?

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

DS

B cannot be OA. only C can be the OA.

Scenerio: ABC is a right angle triangle so any angle could be right angle and any side can be Hypoteneous (H), base (B) and perpendicular (P). but we do not know.

Since BD is a highet of the triangle, it is perpendicuar to the hypoteneous.

1: St 1 tells us nothing. AB could be H or B or P. .......
2: st 2 also doesnot tell the measures clearly. because we do not know which one is B, P, and H.

From 1 and 2, we can say that AB is not H, which should be grater than 6. AB is either B or P and BC is what AB is not.

So AB x BC should equal to 24.

I agree I came across this question and had the same problem.
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Re: A, B, C, and D are distinct points on a plane. If triangle A [#permalink]

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Re: A, B, C, and D are distinct points on a plane. If triangle A [#permalink]

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04 Jul 2014, 05:52
Expert's post
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 ?

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.

OPEN DISCUSSION OF THIS QUESTION IS HERE: a-b-c-and-d-are-distinct-points-on-a-plane-if-triangle-a-129328.html
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Re: A, B, C, and D are distinct points on a plane. If triangle A   [#permalink] 04 Jul 2014, 05:52
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