(1) Angle ABD = 60°
(2) AC = 12
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 one ALONE is sufficient.
EACH statement ALONE is sufficient.
Statements (1) and (2) TOGETHER are NOT sufficient
Well thats the question i encountered . At the outset i am sorry for posting an old question that has been discussed a million times but i searched the posts and could never really see anyone raising this particular doubt that i have .
1) says that angle ABD is 60 . hence it is a 30-60-90 triangle . now from which we can see that AB is 12 (1:root 3:2) and AD is 6 root 3 and BD is 6 . Now i realise that BD is not equal to DC and cannot be assumed to be so.
But here's the strategy i used and i cannot disprove it myself.So i need your help.
AB is side a equals 12. And AD is 6 root 3. From this can be seen that AD equals root3/2 *AB or Root 3/2 a .
We know that any perpendicular line drawn from the vertex to the opposite side is a altitude( though not a perpendicular bisector).
Altitude is root3/2 times side in this triangle .
But we know that in an equilateral triangle only altitude is root3/2 times side or conversely when altitude is root 3/2 times side it is an equilateral triangle .
The triangle under consideration is an equilateral triangle whose area is root3/4 a^2 .Hence sufficient.
Same reasoning applies for statement 2.
Ans choice D.
Fire those guns away profs:P (Btw while reviewing i figured the only is wrongly qualifying altitude instead of equilateral triangle-thats for the crazy people like me trying to implement SC rules to posts :P )