MGMAT EXAM PROBLEM

[guest]

If AD is 6, and ADC is a right angle, what is the area of triangular region ABC?

(1) Angle ABD = 60°

(2) AC = 12



Can you please explain the answer here? Why wouldn't either answer be sufficient? According the the explanation, you can only determine the portion of the base to which each statement refers. However, I thought the rule for a perpendicular line drawn from an angle is that it bisects the base (if so, wouldnt you be able to solve this with either statement). If I've interpreted the rule incorrectly, can you please tell me when (and how to determine if) the base is bisected by a perpendicular line.

thanks

[Harish Dorai]

The perpendicular line bisect only in the case of Equilateral triangle and Isosceles triangle. From the 2 statements it is not clear. Hence both statements are not sufficient to determine the Base side which is BC.

If in the question, if the triangle were an Isosceles triangle, Statement (2) would have been sufficient. We know AD and AC and from that we can determine DC using Pythagoras theorem, which in turn would help us find BC.

Hope it helps.

[Guest]

Thanks, but Im still uncertain. I agree that a perpendicular line bisects the base in an equilateral and an isosceles triangle. But in this case, you can prove that this is an isoceles triange (correct me if im wrong here).

My Logic: Since the perpendicular line creates two 90 degree angles, then the opposing sides must me equal (if angles are equal, their opposing sides must be equal). Therefore, AB = AC --> Isosceles Triangle.

what am I missing?

[Harish Dorai]

Here the situation is different. The 90 degrees are formed in 2 different triangles ADC and ADB. Your theorem is right with in a single triangle. If you take just take a single Triangle XYZ, in which if Angle X = Angle Y, then its opposite sides are equal. That is YZ = XZ.

You can see it by drawing an obtuse triangle, which has one of the angles greater than 90 degrees (see the attached image). Clearly from the figure you can see how the perpendicular forms two right angles and the difference in the lengths of the opposite sides.

Hope it helps.

[shaji]

The correct answer is C. The area of the triangle ABC is 3*(sqrt(108)+6/Tan60).

If AD is 6, and ADC is a right angle, what is the area of triangular region ABC?

(1) Angle ABD = 60°

(2) AC = 12



Can you please explain the answer here? Why wouldn't either answer be sufficient? According the the explanation, you can only determine the portion of the base to which each statement refers. However, I thought the rule for a perpendicular line drawn from an angle is that it bisects the base (if so, wouldnt you be able to solve this with either statement). If I've interpreted the rule incorrectly, can you please tell me when (and how to determine if) the base is bisected by a perpendicular line.

thanks

[Harish Dorai]

Technically you are correct. But I doubt whether GMAT tests knowledge of Trigonometry. A question for instructors???

[shaji]

GMAT like other similar tests do not and can not consider the technique used to get at an answer. All that matters is the correct answer in the alloted time or earlier the merrier!!!.

One of the key management appltitude is to arrive at the correct answer in the shortest possible time.

No doubt, you can arrive at the correct even without using 'trignometry'.

Technically you are correct. But I doubt whether GMAT tests knowledge of Trigonometry. A question for instructors???

[StaceyKoprince]

You don't need trig to solve anything (though you can use it if you want, of course!). Correct answer is C and you can figure that out either with or without trig.

Harish - nice explanations on the plain altitude vs. bisector rules.

[Matt]

The question is from the Manhattan GMAT free CAT exam, and it shows a picture of an isosceles triangle along with the question, though it is never explicitly stated. Right away, I was thinking "okay, am I to assume given that this diagram is here, that the question is telling me this is an isosceles right triangle, or is this a trap for me to make that assumption without any proper grounds for it."

I haven't put in my answer yet, but if the test maker is hoping I make that assumption on the false premise that it just looks like an isosceles triangle, then knowing the properties of one side isn't good enough because the other is not necessarily the same.

If I am right in being skeptical that the diagram alone is not enough for me to conclude the triangle is isosceles, then I need information on both sides of the triangle if I am to solve the problem properly.

For the record, statement (1) only helps to solve the left side, and statement (2) only helps to solve the right side. Either piece of information is sufficient if we KNOW that we're dealing with an isosceles triangle. It turns out that it is, (I did the math with both, and no trig was needed fyi). Since I don't think we know that from the problem itself, I would lean towards the answer being (C), both statements necessary, but I can certainly understand why (D) would tempt many people, myself included.

[JonathanSchneider]

In general, on PS you can assume drawings are to scale unless they say otherwise.
On DS, however, you should assume that the drawings are not to scale. Occasionally you can use info in the problem to re-draw the drawing to scale on your own page - this can help to visualize the answer. But be careful about making any assumptions on DS.

[frigorificos]

Hi

The answer is C

With statement 1 - use TAN 60 = 6/BD = SQRT 3

to get BD = 6/sqrt 3

from the 2nd statement use pythagoras thrm - to get DE as sqrt 108

BE = BD plus DC =

we know the base and height so calc the area

ans C

[JonathanSchneider]

This looks right. Just remember that you don't actually need trigonometry to solve this. (See Stacey's post above.)

[william.h.shu]

Maybe this is a dumb question, but why do we assume that angle ADB is a right angle? And why therefore do we assume that triangle ABD is a right triangle? There is no indication that angle ADB is a right angle, there is only an indication that angle ADC is right.

[tomslawsky]

1) identifies ABD as a 30,60, 90 triangle and the stem says that the height is 6, therefore the base is 6(sqrt 3). The area of ABC can be determined.
http://www2.krellinst.org/UCES/archive/ ... ode20.html

2) Using pathagerian theorum, you can find DC, and then the area of ACD.

Answer is C: add results from 1 and 2.