BTGModeratorVI wrote: ↑

Sun Sep 27, 2020 7:12 am

The lengths of two sides of a certain triangle are 3 and 9. What is the length of the 3rd side of the triangle?

1) The perimeter of the triangle is 20
2) The length of the 3rd side of the triangle is a multiple of 4

Answer: D
Source: Math Revolution

Target question: What is the length of the 3rd side of the triangle?

Given: The other two sides have lengths 3 and 9

Statement 1: The perimeter of the triangle is 20
Let x = the length of the third side
If the perimeter is 20, we can write: 3 + 9 + x = 20
Solve to get: x = 8
So, the answer to the target question is 8
Since we can answer the target question with certainty, statement 1 is SUFFICIENT

Statement 2: The length of the 3rd side of the triangle is a multiple of 4

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

Let x = the length of the third side
So, we can write: 9 - 3 < x < 9 + 3
Simplify: 6 < x < 12
Since 8 is the only multiple of 4 between 6 and 12, we can conclude that x = 8
Since we can answer the target question with certainty, statement 2 is SUFFICIENT

Answer: D