What is the value of z in the triangle above?

Question

https://gmatclub.com/forum/download/file.php?id=18380 What is the value of z in the triangle above? (1) x + y = 139 (2) y + z = 108 Triangle.png

Bunuel · Accepted Answer

SOLUTION

https://gmatclub.com/forum/download/file.php?id=18380 
 What is the value of z in the triangle above?

The interior angles of a triangle always add up to 180°. Thus x+y+z=180°.

(1) x+y=139 --> 139+z=180 --> z=41. Sufficient.

(2) y +z= 108. Cannot determine the value of z. Not sufficient.

Answer: A.

SOURH7WK · Answer

St 1: Sufficient: x+y=139, therefore Z= 180-139
St 2: Insufficient: y+z=108, the value of x can be found, but we can not get a definite value of z.

Hence Answer A

fameatop · Answer

z = ?
1) z = 180 - (x+y) = 180 - 139 -->Sufficient
2) y+z = 108 --->z can take different values --->Not Sufficient

Answer A

hamm0 · Answer

Total measure of the sum of a triangle's interior = 180.

1)  x + y + z = 180
139 + z = 180 
z = 41  Sufficient

2) x + y + z = 180
x + 108 = 180
x = 72, but we are not sure of the split between y and z, so this is  Insufficient

Answer:  A

gmatscore800 · Answer

Z===180-(X+y)
 for finding Z we need Sum of X and Y

statement 1: X+Y == given , sufficient 
Statement 2; Y+Z ==given , can not find X+y , insufficient

Hence A

Inten21 · Answer

Sum of a triangle's interior angles= 180.

1) x + y + z = 180
z = 180 - 139 
z = 41.

Hence, A is  sufficient  to find z.

2) y + z= 108
When we solve the equation we could only find x.

x + y + z = 180
x + 108 = 180
x = 72.

Using the info here we can't find the value of z since we don't know how y and z form 108. so this information is  Insufficient

Hence, the answer is A. Only 1 is sufficient.

Hope that helps.

Shower me with Kudos if this helps you understand the problem. :D

andresgalan · Answer

(1) x+y=139

180 - 139 = 41 z=41 sufficient

(2) y +z= 108

180 -108 = 72 x= 72 it doesnt give you the value of z

BrentGMATPrepNow · Answer

Target question :    What is the value of z in the triangle above?  
IMPORTANT: Since angles in a triangle must add to 180 degrees, we can write:  x + y + z = 180

Statement 1 : x + y = 139  
Take:  x + y + z = 180  and replace (x + y) with 139 to get: 139 + z = 180
Solve equation for z to get: z = 41
So, the answer to the target question is  z = 41 
Since we can answer the  target question  with certainty, statement 1 is SUFFICIENT

Statement 2 : y + z = 108  
Take:  x + y + z = 180  and replace (y + z) with 108 to get: x + 108 = 180
Solve equation for x to get: x = 72
Hmmm, we know the value of x, but we have no way to find the value of z. 
So, statement 2 is NOT SUFFICIENT

If you're not convinced, consider the following scenarios that satisfy statement 2: 
 Case a : x = 72, y = 50 and z = 58. In this case, the answer to the target question is  z = 58 
 Case b : x = 72, y = 60 and z = 48. In this case, the answer to the target question is  z = 48 
Since we cannot answer the  target question  with certainty, statement 2 is NOT SUFFICIENT

Answer: A

Cheers,
Brent

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What is the value of z in the triangle above?

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