Data Sufficiency

AbeNeedsAnswers wrote: ↑

Fri Jun 05, 2020 6:13 pm

OG2021DS296.png

What is the value of z in the figure above?

1. x = 50
2. y = 35

C

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: Here’s a video with tips on rephrasing the target question: https://www.gmatprepnow.com/module/gmat- ... cy?id=1100

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