If in triangle ABC, angle ABC is largest at point D lies GMAT Data Sufficiency

Question: If in triangle ABC, angle ABC is largest at point D lies on the segment AC, is the area of triangle ABD larger than that of triangle DBC?

1. AD < DC
2. AB < BC

1. Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.
2. Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.
3. BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.
4. EACH statement ALONE is sufficient.
5. Statements (1) and (2) TOGETHER are NOT sufficient.

“If in triangle ABC, angle ABC is largest at point D lies on the segment AC, is the area of triangle ABD larger than that of triangle DBC?”- is a topic of the GMAT Quantitative reasoning section of GMAT. This question has been taken from the book "GMAT Quantitative Review". GMAT Quant section consists of a total of 31 questions. GMAT Data Sufficiency questions consist of a problem statement followed by two factual statements. GMAT data sufficiency comprises 15 questions which are two-fifths of the total 31 GMAT quant questions.

Answer:

Approach Solution (1):

Notice that BE is height of the triangle ABC. Now the area of triangle ABD is ½ * height * base = ½ * BE * AD and the area of triangle DBC is ½ * base * height = ½ * BE * DC
So, we can see that the area of triangle ABD will be greater thn the area of triangle DBC if AD is greater than DC.
So, S1 is sufficient
S2 is not sufficient

Correct option: A

Approach Solution (2):

The area of a triangle is 0.5 * base * height. Now we need to compare the areas of ABD and BDC
The area of ABD is 0.5 * AD * h
The area of BDC is 0.5 * CD * h

To compare the area of ABD and BDC, we need to know the relation between AD and CD
So, S1 is sufficient
S2 is not sufficient

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