If x, y, and z are the lengths of the three sides

[BTGModeratorVI]

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

Source: Official Guide
Answer: D

[Brent@GMATPrepNow]

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

Source: Official Guide
Answer: D

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

[deloitte247]

Is y > 4?
For any given triangle, the triangle inequality theorem states that the sum of the lengths of any two sides is greater than the length of the third side.
Statement 1: z = x + 4
Length of traingle:
x = x
y = y
z = z
Following the inequality theorem => x+y > z where z = x + 4
Therefore, x + y > x + 4 (subtract x from both sides)
y > 4
Statement 1 is SUFFICIENT

Statement 2: x=3 and z=7
Following the inequality theorem => x+y > 2 where x=3, and z=7
Therefore, 3+y>7
y > 7-3
y > 4
Statement 2 is SUFFICIENT.

Since each statement alone is SUFFICIENT, then, the correct answer is option D.