BTGModeratorVI wrote: ↑Mon Sep 07, 2020 6:56 am
If x, y, and z are the lengths of the three sides of a triangle, is y > 4?
(1) z = x + 4
(2) x = 3 and z = 7
Answer:
D
Source: Official guide
IMPORTANT RULE: If two sides of a triangle have lengths A and B, then . . .
DIFFERENCE between A and B < length of third side < SUM of A and B
Given: x, y, and z are the lengths of the three sides of a triangle
Target question: Is y > 4?
Statement 1: z = x + 4
This means that x and x+4 are the lengths of two sides of the triangle.
When we apply the
rule above, we can see that: (x + 4) - x < length of third side (aka y) < (x + 4) + x
Simplify: 4 < y < 2x + 4
At this point we can see that the answer to the target question is
YES, y IS greater than 4
Since we can answer the
target question with certainty, statement 1 is SUFFICIENT
Statement 2: x = 3 and z = 7
When we apply the
rule above, we can see that:7 - 3 < length of third side (aka y) < 7 + 3
Simplify: 4 < y < 10
The answer to the target question is
YES, y IS greater than 4
Since we can answer the
target question with certainty, statement 2 is SUFFICIENT
Answer: D
Cheers,
Brent
