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

Question

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

saukrit · Accepted Answer

Here we use the property of triangle that sum of any 2 sides has to be greater than the third side.

Statement 1  Three sides of triangle are x, y, x+4
Since sum of any 2 sides has to be greater than third side, 
 x+y>x+4 
y>4. Hence,   Statement 1 is SUFFICIENT

Statement 2  Sides of triangle are 3, y, 7
 3+y>7 
y>4. Hence   Statement 2 is SUFFICIENT

Hence Answer is D

jinghao · Answer

Condition of triangle;
|x-z|<y<x+z

(1)z=x+4
|x-z|=|x-(x+4)|=4
4<y

(2)x=3, y=7
|x-z|=|3-7|=4
4<y

Answer: D

Posted from my mobile device

BrentGMATPrepNow · Answer

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

RELATED VIDEO 
 https://www.youtube.com/watch?v=sf5GkSd_1nQ

MarmikUpadhyay · Answer

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.

bumpbot · Answer

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

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

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