Big Book/ Test 3, Sec 6, Q 10

GRE Quant Problem Solving
1

Hi,
Can someone please help me solve this one? The correct answer is D but I would like to know the theory behind it.

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Thanks in advance!

2

We can associate the sides of a triangle to their corresponding angles. So, side RS is associated with angle y, side RT is associated with angle z, and side ST is associated with angle x. Thus, instead of comparing RT with RS, you can just compare z with y. Notice that x=z, so we are really comparing x to y. What do we know? That we have an isosceles triangle, and so x+x+y=180. This leads us to conclude that 2x+y=180. Now you can choose numbers. Suppose that x=50, then y=80. In this case Quantity B is greater. Now suppose that x=70, so y=40, and in this case Quantity A is greater. Thus, the correct answer must be D.