What is the value of z in the figure above?

Target question: What is the value of z in the figure above?
This is a great candidate for rephrasing the target question.

Since angles on a line add to 180°, we can conclude that the missing angle in the triangle = (180 - z)°


Now let's focus on the triangle.
Since angles in a triangle add to 180°, we can write: x° + y° + (180 - z)° = 180°
Simplify: x + y + 180 - z = 180
Subtract 180 from both sides of the equation to get: x + y - z = 0
Add z to both sides of the equation to get: x + y = z (this relationship is known as the exterior angle theorem: https://www.onlinemathlearning.com/exte ... eorem.html)
Since z = x + y, we can rephrase the target question as follows

REPHRASED target question: What is the value of x + y?

Aside: the video below has tips on rephrasing the target question

Statement 1: x = 50
Since we don't have any information about the value of y, there is no way to answer the REPHRASED target question with certainty
Statement 1 is NOT SUFFICIENT

Statement 2: y = 35
Since we don't have any information about the value of x, there is no way to answer the REPHRASED target question with certainty
Statement 2 is NOT SUFFICIENT

Statements 1 and 2 combined
Statement 1 tells us that x = 50
Statement 2 tells us that y = 35
So, x + y = 50 + 35 = 85
Since we can answer the REPHRASED target question with certainty, the combined statements are SUFFICIENT

Answer: C

Cheers,
Brent

RELATED VIDEO

What is the value of z in the figure above?
z = x + y

(1) x = 50
Since y is unknown
NOT SUFFICIENT

(2) y = 35
Since x is unknown
NOT SUFFICIENT

(1) + (2)
(1) x = 50
(2) y = 35
z = x + y = 50 + 35 = 85
SUFFICIENT

IMO C

Z is equal to the sum of x+y.

Hence, both statements are together sufficient (C)

Forget conventional ways of solving math questions. For DS problems, the VA (Variable Approach) method is the quickest and easiest way to find the answer without actually solving the problem. Remember that equal numbers of variables and independent equations ensure a solution.
Visit https://www.mathrevolution.com/gmat/lesson for details.

The first step of the VA (Variable Approach) method is to modify the original condition and the question. We then recheck the question. We should simplify conditions if necessary.

An exterior angle of a triangle is a sum of non-adjacent interior angles of the triangle.
Thus we have z = x + y.

Since we have 3 variables (x, y and z) and 1 equation, C is most likely the answer. So, we should consider conditions 1) & 2) together first. After comparing the number of variables and the number of equations, we can save time by considering conditions 1) & 2) together first.

Conditions 1) & 2)

Since x = 50 and y = 35, we have z = x + y = 85.
Since both conditions together yield a unique solution, they are sufficient.

Therefore, C is the answer.

Normally, in problems which require 2 equations, such as those in which the original conditions include 2 variables, or 3 variables and 1 equation, or 4 variables and 2 equations, each of conditions 1) and 2) provide an additional equation. In these problems, the two key possibilities are that C is the answer (with probability 70%), and E is the answer (with probability 25%). Thus, there is only a 5% chance that A, B, or D is the answer. This occurs in common mistake types 3 and 4. Since C (both conditions together are sufficient) is the most likely answer, we save time by first checking whether conditions 1) and 2) are sufficient, when taken together. Obviously, there may be cases in which the answer is A, B, D, or E, but if conditions 1) and 2) are NOT sufficient when taken together, the answer must be E.

LOL Make it easy:

Some high school math: Exterior angle = sum of interior opposite angles
-->Z=x+y;
Therefore C is answer

Solution:

A new og 2021 question

We know that the external angle is obtained as a sum of two opposite internal angles in a triangle.

=> z = x + y

St(1):- x = 50

We do not know the value of y to figure out the value of z. (Insufficient)

St(2) :- y = 35

We do not know the value of x to figure out the value of z. (Insufficient)

Combining both we have

x=50 and y =35
Thus z = x + y
= 50 + 35 (Sufficient) Option (c)


Hope this helps
Devmitra Sen (GMAT Quant Expert)

Answer: Option C

Video solution by GMATinsight



Get TOPICWISE: Concept Videos | Practice Qns 100+ | Official Qns 50+ | 100% Video solution CLICK HERE.
Two MUST join YouTube channels : GMATinsight (1000+ FREE Videos) and GMATclub

Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
_________________