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

GMAT Insight,

you mentioned (y-z)^2 = 225 => y-z = 15, I guess this is not correct, it should be y -z = 15 or y-z = -15

therefore after combining st 1 and st2 ,we will have two answers, So final answer is E.

You are right. Correction Done. Thank you!

MANHATTAN GMAT OFFICIAL SOLUTION:

Redraw the diagram and label as much as possible. Using the rules about a transversal (line m) intersecting parallel lines (in this case, two sets of parallel lines), we can label at least two more angles y° and z°:


We have labeled three angles that form a straight line at the intersection of k1, l1, and m, so x + y + z = 180. Since x = 180 – (y + z), the rephrased question is “What is the value of x or the value of (y + z)?"

(1) INSUFFICIENT: Substitute x = 3z – y into x + y + z = 180 and simplify:
(3z – y) + y + z = 180
4z = 180
z = 45
This provides neither the value of x nor the value of (y + z).

(2) INSUFFICIENT: Simplify the expression.
(y – z)^2 = 225
(y – z) = –15 or 15, so |y – z| = 15.
This provides neither the value of x nor the value of (y + z).

(1) & (2) INSUFFICIENT: There are two solutions as indicated by the absolute value in (2):
y – z = 15: OR y – z = –15:
y = 15 + z OR y = –15 + z
y = 15 + 45 OR y = –15 + 45
y = 60 OR y = 30
y + z = 60 + 45 = 105 OR y + z = 30 + 45 = 75

The correct answer is E, because even with both statements, we cannot tell whether x = y + z = 75 or 105.

The key to solving the question is to get all the possibble alternatives
statement 1
(1) x = 3z – y
x +y+z= 180
=>z= 45
This doesn't provide us with any info on the value of X
Hence INsuff

(2) (y – z)^2 = 225
=> y-z = 15/
=>y-z=-15
Clearly insuff
Even if we combine both of them sinnce we are going to get different values of y from B
we wil get different values of X
Hence IMO E

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