BTGmoderatorLU wrote:Source: Manhattan Prep
In the figure above, lines k1 and k2 are parallel to each other, lines l1 and l2 are parallel to each other, and line m passes through the intersection points of k1 with l1 and k2 with l2. What is the value of x?
1) x = 3z - y
2) (y - z)^2 = 225
The OA is
E.
In the triangle enclosed by angles x, y and z, we have angles: (180 - x), y, and (180 - z).
Thus, the sum of all the three angles of the triangle = (180 - x) + y + (180 - z) = 180
=> x + y + z = 180.
Question: What's the value of x?
Let's take each statement one by one.
1) x = 3z - y
Plugging-in the value of x in x + y + z = 180, we get (3z - y) + y + z = 180 => z = 45º
Can't get the value of x. Insufficient.
2) (y - z)^2 = 225
=> y - z = 15 or y - z = -15
Even with the help of x + y + z = 180, we can't get x. Insufficient.
(1) and (2)
Case 1: y - z = 15
=> At z = 45, we have y - z = 15 => y = 60; thus, x + y + z = 180 => x + 60 + 45 = 180 => x = 75
Case 2: y - z = -15
=> At z = 45, we have y - z = -15 => y = 30; thus, x + y + z = 180 => x + 30 + 45 = 180 => x = 105
No unique value of x. Insufficient.
The correct answer:
E
Hope this helps!
-Jay
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