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In the figure above, lines k1 and k2 are parallel to each

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In the figure above, lines k1 and k2 are parallel to each

by BTGmoderatorLU » Thu Nov 22, 2018 1:42 pm

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Source: Manhattan Prep

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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.
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by Jay@ManhattanReview » Fri Nov 23, 2018 12:04 am
BTGmoderatorLU wrote:Source: Manhattan Prep

Image

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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by deloitte247 » Sat Nov 24, 2018 1:43 pm
We are finding the value of x
angle z are corresponding angles, the same thing goes for y
angle y are corresponding angles
at the intersection of line $$k_1$$ ; $$l_1$$ $$and\ \ m_1$$
$$angles\ \left(x+y+2\right)=180\deg ree\left(angle\ on\ a\ straight\ line\right)$$

statement 1
$$x=3z-y$$
we know that $$x+y+z=180\ and\ x=3z-y$$ $$3z-y+y+z=180$$ $$\frac{4z}{4}=\frac{180}{4}$$ $$z=45$$
but x is still unknown.
Hence statement 1 is INSUFFICIENT

statement 2
$$\left(y-2\right)^2=225$$
square rooting both sides
$$\sqrt{\left(y-2\right)^2}=\sqrt{225}$$ $$y-2=\pm15$$
We cannot determine the value of x with the information provided in statement 2
Hence 2 is INSUFFICIENT.

Combining statement 1 and 2 together
$$z=45\ and\ y-z=\pm15$$
$$y=60\deg ree\ \ OR\ y=30\deg ree$$
$$x+y+z=180\deg ree$$
$$x=180-y-z$$
$$x=180-45-60\ \ OR\ x=180-45-30$$
$$x=75\ \ O\ R\ x=105$$
There are more than one solution
Hence the two statements together are not SUFFICIENT.
$$answer\ is\ option\ E$$
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