I tried using numbers to solve this and got B. Is the answer D because we aren’t given any numbers or is it because in one case A can be bigger and in another B can be bigger?

What numbers did you try?

Hint: you can slide ST and UV

I used x=3 and y=2. I thought of them as similar triangles so found the area of the smaller triangle by xy/2 and then second triangle as 4xy/2. And then the bigger triangle as 9xy/2. I got 27 for the bigger triangle so chose B. I don’t understand what you mean by sliding the two sides. Could you explain that more if possible

What is x and y in the triangle?

By sliding I meant that you can position ST and UV anywhere in the triangle, as long as they are parallel. Suppose UV is very close to P (i.e, the area of \Delta RUT is nearly equal to \Delta RPQ) and ST is very close to UV. What do you think the answer would be in that case?

Also,

It’s both - *because* you are given no other information, you can find two cases where in one case A is greater and another where B is greater.

Ohh. I didn’t know we can slide the parallel lines like that. Then in that case the answer would be D. How do we know that we can manipulate the given lines like that?

This is a classic case of “looks can be deceiving”.

What *are* you given? Only that the given lines are parallel. You cannot, for instance, infer *where* the lines are, as there is simply nothing given in the question for you to do so. Remember that geometrical figures are *not* drawn to scale on the GRE.

The key is to consider what information you are given in a question and work using only that. In your case, you made an assumption about the ratio of the side lengths, which caused you to make an incorrect deduction.