Bunuel wrote:
In the figure above, ABC is a right triangle and BCD is a line. What is the value of x ?
(1) AB = BC
(2) y = z
DS21211
Target question: What is the value of x ? Statement 1: AB = BC If AB = BC, then ∆ABC is an ISOSCELES right triangle, such that y° = z°
We already know that one angle in the triangle is 90°
Since angles in a triangle add to 180°, we can conclude that y° = z° =
45°Since angles on a line add to 180°, we know that: z° + x° = 180°
Substitute to get:
45° + x° = 180°
Solve to get:
x = 135 Since we can answer the
target question with certainty, statement 1 is SUFFICIENT
Statement 2: y = zIn other words, ∆ABC is an ISOSCELES right triangle
Since this is, essentially, the
same information we were given in statement 1, no analysis is necessary.
Since we concluded that statement 1 is SUFFICIENT, we can also conclude that statement 2 is SUFFICIENT,
ASIDE: Whenever two statements provide the exact same information, the correct answer must be either D or E. Answer: D
Cheers,
Brent
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