Point D lies on segment AC. Is the area of triangle ABD greater than the area of triangle BDC? (1) DC > AD (2) BC > AB

A. Statement (1) BY ITSELF is sufficient to answer the question, but statement (2) by itself is not. B. Statement (2) BY ITSELF is sufficient to answer the question, but statement (1) by itself is not. C. Statements (1) and (2) TAKEN TOGETHER are sufficient to answer the question, even though NEITHER statement BY ITSELF is sufficient. D. Either statement BY ITSELF is sufficient to answer the question. E. Statements (1) and (2) TAKEN TOGETHER are NOT sufficient to answer the question, meaning that further information would be needed to answer the question.

(A) Remember: In Data Sufficiency questions you can NEVER assume anything is drawn to scale.

The two triangles have the same height drawn from point B.

Statement (1) states that the base of triangle BDC is larger than the base of triangle ABD, so we know that the area of triangle ABD is DEFINITELY NOT greater than that of BDC. Therefore, Statement (1) is sufficient.

Statement (2) is not sufficient; the answer would depend on the exact position of point D, which we are not told and cannot assume from the figure. Imagine moving D along along segment AC. Moving to the left will shrink base AD, while moving to the right will shrink base DC.

Since Statement (1) is sufficient and Statement (2) is insufficient, the correct answer is choice (A). ---------- In this question, the only problem, which I fail to understand is what if we do not take DC and AD as bases of these triangles and take another alternative side as a base? How can we determine this height of the triangle then?

I do not understand why did we take DC and AD as bases of these triangles? what if some other sides were considered as bases then this answer would be incorrect. or will it not be? Please, kindly explain.

I do not understand why did we take DC and AD as bases of these triangles? what if some other sides were considered as bases then this answer would be incorrect. or will it not be? Please, kindly explain.

Area is a property of a triangle. It does not depend on the method you use to calculate it.

In other words, calculating the area of a certain triangle will yield the same result no matter what method you use. So we can pick any method we want.

In this case we choose the height, which is the same for the both triangles. It allows us to compare the areas by comparing the segments AD and DC.

If you pick another sides and heights, then it might be much harder for you to analyze the triangles. But it will only change the fact that you can not analyze the triangles, not the fact that the area of triangle ABD is less than the area of triangle BDC (if to use Statement (1) alone).

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