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E
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
75%
(hard)
Question Stats:
44% (02:11) correct
56%
(02:05)
wrong
based on 57
sessions
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In the x-y plane, the straight lines L1 and L2 cut the x-axis at point A and point C respectively. If B is the point of intersection of L1 and L2, Is the slope of AB positive?
(1) The angle which the line BC makes with the positive direction of x-axis is greater than 60 degrees and less than 90 degrees.
(2) Angle CBA = 40 degree.
(1) The angle which the line BC makes with the positive direction of x-axis is greater than 60 degrees and less than 90 degrees.
(2) Angle CBA = 40 degree.
07 Feb 2022, 08:46
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Bunuel
Breaking Down the Info:
Both B and A are on L1, so the slope of AB is the slope of L1. Thus we can rephrase the question as "what is the slope of L1?"
Similarly, both B and C are on L2, so BC is part of L2.
Statement 1 Alone:
This tells us BC (hence L2) has a positive slope and is as small as \(\sqrt{3}\) while as big as infinite, since the angle is between 60 and 90. However, this tells us nothing about L1, so statement 1 alone is insufficient.
Statement 2 Alone:
This does tell us the relation between the slopes of L1 and L2, but we don't know the slope of either line to begin with. Thus statement 2 alone is insufficient.
Both Statements Combined:
BC makes an angle of 60~90 with the positive x-axis. Comparing with the positive x-axis, AB could be within the 20~50 angle, which would give a positive L1 slope, or AB could be within the 100~130 angle range, which would give us a negative L1 slope. Then we cannot confirm whether L1 (AB) has a positive slope. Combined it is still insufficient.
Answer: E
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