If x, y, and z are lengths of three sides of a triangle, is x < 3?

VERITAS PREP OFFICIAL SOLUTION:

Question Type: Yes/No. This question asks: “Is x < 3?”

Given information in the question stem or diagram: x, y, and z are the lengths of three sides of a triangle. Note: Even before going to the statements you should recognize that the third side rule of triangles will almost certainly come into play: The third side (i.e., any side) of a triangle is always between the sum and the difference of the other two sides.

Statement 1: z = y + 3 OR z – y = 3. This statement does not give you the value of any of the sides and does not allow you to determine the actual value of side x. However, using the third side rule you know that x must be greater than the difference between z and y, which is given as 3 in this statement. Therefore x must be greater than 3 and you can answer this question with a definitive “no” from this information. The information is sufficient so the correct answer is either A and D. Note: People tend to underleverage this piece of information because it does not lock down a value for x (which is not necessary) and because people have forgotten the third side rule.

Statement 2: y = 3 and z = 6. This gives very similar information to statement 1 and also allows you to apply the third side rule. Since the explicit values are given you can see that x must be greater than the difference between x and y (which is again 3). Statement 2 is also sufficient and the answer is thus D. Note: The answer could never be C on this question. While this is not a common construct (and thus not mentioned in the lesson portion of this book), it is one that you will see occasionally. The first piece of information (z = y + 3) is automatically known from the second, so putting them together could never help you! It is either answer A, B, D, or E whenever one statement is known from the other, so C should be eliminated automatically here.

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