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

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.

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?

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.

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

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

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'.

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.