In the figure below, ∠B

Question

In the figure below,  \angle  B <  \angle  A. Is the area of the triangle ABC greater than 72?

(1) The coordinates of point C are (-8,9)
(2) The coordinates of point B are (-15,0)

Source: TIME Institute, India

GMATinsight · Answer

This question is a replica of an official question which is really good.

Angle B is less than angle A

i.e. AC < BC .   (Side opposite to smallest angle is smallest and side opp. to the largest angle is largest)

Question : Is area greater than 72?

Statement 1 : The coordinates of point C are (-8,9)

i.e. Height of triangle = 9
and Base of triangle is >  2*8  i.e. > 16

For bas = 16
Area = (!/2)16*9 = 72

Since base > 16 theref  Statement 2 : The coordinates of point B are (-15,0)

Base is 15 but no idea about height hence

NOT SUFFICIENT

Answer: Option A

(Poor question formed by TIME as expected because they have very low understanding of GMAT DS. The statements must NEVER contradict which in this case are contradicting)

Ronjith · Answer

How do u know the perpendicular line drawn is a perpendicular bisector, infact it is not since AC  =  BC, the line drawn from vertex to line AB 'll not bisect, so therefore the ans has to be "C"

jkbk1732 · Answer

Ronjith 
You haven't read the explanation properly. It said BC>AC and went on to say that the area > 72.

Let me explain it to you again. Angle A > Angle B. So BC>AC. Consider a perpendicular line from C. Let D be the point where it meets A.

From statement 1 in the question, we know that CD=9, AD=8. Thus area of triangle ACD is 1/2*b*h= 1/2*8*9 = 36. 
Now we know that for triangle BCD, CD=9. Since both triangles share same height. Since BC>AC, BD>AD.(Practically test a few cases).
 Thus, 1/2*BD*CD>1/2*AD*CD
1/2*BD*CD>36

Area of triangle ABC= ACD+ BCD
 = 36 + Something greater than 36
 = Something greater than 72

Let me know if this is clear

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In the figure below, ∠B < ∠A. Is the area of the triangle greater than

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