If lines y=mx+b and x=y+bm intersect at a degrees angle (where a<90), what is the value of angle a?
(1) m=2
(2) m=b
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what is the value of angle a?
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Hi Himu,
This is a complicated-looking graphing question. As a category, you're likely to see just 1-2 graphing questions and they're normally not this complex.
It asks what is the measure of angle A (the smaller angle that forms when the two lines intersect). Since it's graphing, I would make sure that the lines were in slope-intercept format:
y = mx + b
y = x - mb
Since we're interested in the angle that forms, we need to focus on the SLOPE of the two lines (the y-intercept would only determine where each line crosses the y-axis).
Fact 1 tells us that m = 2, so our lines would be....
y = 2x + b
y = x - 2b
No matter what values you choose for b (and then for x and y), the two lines would have consistent slopes (so they'd always be at the same respective angles, just on different parts of the graph). Try drawing some example pictures and you'll see). This means that the lines will intersect in the exact same way every time and that angle A will always be the same.
Fact 1 is SUFFICIENT.
Fact 2 tells us that m = b, so they could both be 2, 3, 4, 5, etc.
This changes the slope of the first line (depending on the slope), while the slope of the second line stays the same. So, the angle between the two lines would change. If you draw two example pictures, then you see. Angle A changes, so Fact 2 is INSUFFICIENT.
Final Answer: A (1 only is Sufficient)
GMAT assassins aren't born, they're made,
Rich
This is a complicated-looking graphing question. As a category, you're likely to see just 1-2 graphing questions and they're normally not this complex.
It asks what is the measure of angle A (the smaller angle that forms when the two lines intersect). Since it's graphing, I would make sure that the lines were in slope-intercept format:
y = mx + b
y = x - mb
Since we're interested in the angle that forms, we need to focus on the SLOPE of the two lines (the y-intercept would only determine where each line crosses the y-axis).
Fact 1 tells us that m = 2, so our lines would be....
y = 2x + b
y = x - 2b
No matter what values you choose for b (and then for x and y), the two lines would have consistent slopes (so they'd always be at the same respective angles, just on different parts of the graph). Try drawing some example pictures and you'll see). This means that the lines will intersect in the exact same way every time and that angle A will always be the same.
Fact 1 is SUFFICIENT.
Fact 2 tells us that m = b, so they could both be 2, 3, 4, 5, etc.
This changes the slope of the first line (depending on the slope), while the slope of the second line stays the same. So, the angle between the two lines would change. If you draw two example pictures, then you see. Angle A changes, so Fact 2 is INSUFFICIENT.
Final Answer: A (1 only is Sufficient)
GMAT assassins aren't born, they're made,
Rich
