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11 Jan 2015, 12:21
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C
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
15%
(low)
Question Stats:
83% (01:18) correct
17%
(01:30)
wrong
based on 106
sessions
History
Date
Time
Result
Not Attempted Yet
Attachment:
2015-01-11_2320.png [ 5.15 KiB | Viewed 2921 times ]
(1) BX bisects angle ABY and BZ bisects angle YBC.
(2) The measure of angle YBZ is 60 degrees.
Kudos for a correct solution.
11 Jan 2015, 23:48
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Answer : C
Statement (1) States that Angle ABX = Angle XBY (say p) and Angle YBZ = Angle ZBC (say q)
This is insufficient to determine the value of Angle ABX
Statement (2) States that Angle YBZ = 60 degrees
Clearly this information is insufficient to determine the value of Angle ABX
Combining both: 2p + 2q = 180
p + q = 90
or, 60 + q = 90
or, q = 30
Statement (1) States that Angle ABX = Angle XBY (say p) and Angle YBZ = Angle ZBC (say q)
This is insufficient to determine the value of Angle ABX
Statement (2) States that Angle YBZ = 60 degrees
Clearly this information is insufficient to determine the value of Angle ABX
Combining both: 2p + 2q = 180
p + q = 90
or, 60 + q = 90
or, q = 30
19 Jan 2015, 03:32
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Bunuel
OFFICIAL SOLUTION:
It’s important to recognize that because these four angles lie along a straight line, they add up to 180 degrees.
Although it’s lovely to know that BX bisects (which means cuts exactly in half) the two angles on the left side and that BZ bisects the two angles on the right side, without the measure of at least one of the angles, you have no way of knowing the measurements of any of the angles. So statement (1) isn’t sufficient, and the answer has to be B, C, or E.
Statement (2) gives you only one of the angle measures, which by itself doesn’t clarify the measure of ∠ABX any better than statement (1) does. Statement (2) isn’t sufficient.
But remember that we said all we needed for statement (1) was a value for at least one of the angles. Well, statement (2) provides that value. Taken together, the two statements allow you to solve for the measure of ∠ABX. You can stop right there.
Correct answer: C.
You don’t actually have to figure out the measurement of the angle, but because we’re so thorough, we go through the calculations for you anyway. This step is unnecessary on test day. Knowing that BZ bisects ∠YBC and that ∠YBZ measures 60 degrees allows you to deduce that ∠ZBC is also 60 degrees. Additionally, you’ve now accounted for 120 of the total 180 degrees allotted for the four angles, leaving 60 degrees to play with. Finally, because BX bisects angle ABY, two equal angles remain. Two equal angles that together equal 60 degrees must equal 30 degrees each, because 60⁄2 = 30.
