kamalakarthi wrote: Can you please help me on why S1 is not sufficient in the below DS question.

My rational was that according to S1, ABD=60, so ADB must be 90 and we know the length of AD, so we can calculate the lengths of all the sides , SInce BAD must be 30 degrees, DAC also should be 30 degrees and ACD must be 60 degrees so with this, I can calculate DC as well.

From the given information, we know that ABD and ACD are both right triangles. However, since we don't know the angle of B or C, we don't know if they are SYMMETRICAL triangles. Don't just trust your eyes and assume that they are the same! One triangle might be slightly larger or smaller than the other.

Statement (1) tells us that ABD is a 30-60-90 triangle, and thus we can calculate its lengths and area. There is no information given to allow us to infer that DAC is also 30, as you stated. It might be slightly smaller or slightly larger. We don't have sufficient information to find the area of the entire triangle.

Statement (2) likewise only gives us information about triangle ACD, but not ABD. If AC = 12, we can infer that ACD is a 30-60-90, but this won't tell us the area of the whole triangle ABC.

(1) & (2) together: if ABD and ACD are both 30-60-90 triangles with a shared side, they must be identical. Since we know that they are both 30-60-90 triangles and we have a side length for each, we have sufficient information to determine the area of each.

The answer is C.

Trusting your eyes & making assumptions are two of the biggest mistakes you can make on DS geometry problems! Here's an article about why geometry is especially tricky in DS: https://www.manhattanprep.com/gmat/blog ... ncy-wrong/