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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

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

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Given: x, y and z are lengths of triangle.
Is y > 4?
In a triangle |z - x| < y < z + x.


Statement 1:
z = x + 4
=> z - x = 4
=> |z - x| = 4 < y
Therefore, y > 4.
Statement 1 is Sufficient.

Statement 2:
x = 3 and z = 7
=> z - x = 7 - 3 = 4
=> |z - x| = 4 < y
Therefore, y > 4.
Statement 2 is also Sufficient.

So, correct answer is option D.
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Hello from the GMAT Club BumpBot!

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