GRE Sample Test 4 Quantitative Reasoning 2

The perimeter of ABC is 40 and the length of BC is 12, and you want to compare the length of AB with 14. In an isosceles triangle, there are two sides with equal length, but you don’t know whether side BC is one of those sides or not. If side BC is the unequal side, there are two unknown sides plus 12, and they have a sum of 40, the perimeter. The two remaining sides have a sum of 28, so each is 14. That would mean that AB and AC would have length 14. Then the answer would be (C). If BC is one of the equal sides, however, there are two sides with length 12 and a third unknown side, and the sum is 40. Because 12 + 12 is 24, the third side has length 16. AB could be one of the sides of length 12 or the side of length 16. There are three possible lengths for side AB—16, 14, and 12—so the answer is (D).