What is the value of z in the figure above?

Question

https://gmatclub.com/forum/download/file.php?id=54102 What is the value of z in the figure above? (1) x = 50 (2) y = 35 DS27860.02 2020-04-28_1905.png

BrentGMATPrepNow · Accepted Answer

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)° https://i.imgur.com/oVQkLOJ.png 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 https://www.youtube.com/watch?v=MyG1K3ee69w

Kinshook · Answer

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

Rebaz · Answer

Z is equal to the sum of x+y.

Hence, both statements are together sufficient (C)

MathRevolution · Answer

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.

itspCv2 · Answer

LOL

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

CrackverbalGMAT · 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)

GMATinsight · Answer

Answer: Option C

Video solution by  GMATinsight

https://www.youtube.com/watch?v=PLySLLpjEV0

bumpbot · Answer

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What is the value of z in the figure above?

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What is the value of z in the figure above?

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