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In the figure, AB is parallel to EF. What is the value of z?

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In the figure, AB is parallel to EF. What is the value of z?

by Max@Math Revolution » Mon Jul 29, 2019 12:08 am

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[GMAT math practice question]

In the figure, AB is parallel to EF. What is the value of z?

Image

1) x =78
2) y = 70
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Source: — Data Sufficiency |
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by Max@Math Revolution » Tue Jul 30, 2019 10:51 pm

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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.

Since we have 3 variables (x, y and z) and 0 equations, E is most likely to be 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.

Image

Conditions 1) & 2)
We draw lines through C and D, parallel to AB, as shown in the diagram.
Since < a and < ABC=105° are supplementary, a=75°.
< d = 180° - < X - < a = 180° - 78° - 75° = 27°, and < c = < d = 27° as they are alternate interior angles.
Since y = 70°, b = y - c = 70°-27° = 43°
Since < z and < b are alternate interior angles, < z = < b =43°.
Both conditions together are sufficient.

Therefore, C is the answer.
Answer: C
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