If perpendicular lines m and n intersect at (0,b) in teh standard (x,y) coordinate plane, what is the value of b?
(1) The slope of line m is -1/2.
(2) The point (-1,0) is on line n.
OA is C
Would like to see experts' approaches here. Thanks.
Perpendicular lines m and n...
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Last edited by mjpinvestor on Sun Jul 13, 2014 6:25 am, edited 1 time in total.
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I need one clarification, can you please check st2. How can it be (-0,0). Is it a typo error?mjpinvestor wrote:If perpendicular lines m and n intersect at (0,b) in teh standard (x,y) coordinate plane, what is the value of b?
(1) The slope of line m is -1/2.
(2) The point (-0,0) is on line n.
OA is C
Would like to see experts' approaches here. Thanks.
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The problem should read as follows:
The slopes of perpendicular lines are NEGATIVE RECIPROCALS.
Since the slope of line m = -1/2, the slope of line n = 2.
Thus:
The equation for line m is y = (-1/2)x + b.
The equation for line n is y = 2x + b.
No way to determine the value of b.
INSUFFICIENT.
Statement 2:
Since an infinite number lines of lines pass through (-1,0), there is no way to determine the value of b.
INSUFFICIENT.
Statements combined:
Substituting (-1, 0) into y = 2x + b, we get:
0 = 2(-1) + b
b = 2.
SUFFICIENT.
The correct answer is C.
Statement 1:If perpendicular lines m and n intersect at (0,b) in the standard (x,y) plane, what is the value of b?
(1) The slope of the line m is -1/2
(2) The point (-1,0) is on the line n
The slopes of perpendicular lines are NEGATIVE RECIPROCALS.
Since the slope of line m = -1/2, the slope of line n = 2.
Thus:
The equation for line m is y = (-1/2)x + b.
The equation for line n is y = 2x + b.
No way to determine the value of b.
INSUFFICIENT.
Statement 2:
Since an infinite number lines of lines pass through (-1,0), there is no way to determine the value of b.
INSUFFICIENT.
Statements combined:
Substituting (-1, 0) into y = 2x + b, we get:
0 = 2(-1) + b
b = 2.
SUFFICIENT.
The correct answer is C.
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To answer the question we need to have equation of line m or line nIf perpendicular lines m and n intersect at (0,b) in the standard (x,y) coordinate plane, what is the value of b?
(1) The slope of line m is -1/2.
(2) The point (-1,0) is on line n.
Statement 1)The slope of line m is -1/2.
This only gives us that the slope of line n as 2 [Product of slopes of perpendicular lines = -1]
However since the equation of any line is unknown therefore we can't substitute the point in the equation to obtain the value of b
Statement 2)The point (-1,0) is on line n
There are infinite lines passing through the given point therefore INSUFFICIENT
Combining the two statements
line n has slope 2, therefore the equation becomes
y = 2x + c {where c is y-intercept}
Also, Line n passes through point (-1,0)
0 = 2*(-1)+c ===> c=2
Equation of line n, y = 2x + 2
Now since (o,b) lies on this line therefore it will satisfy the equation
b = 2*0 + 2
i.e. b=2
SUFFICIENT
Answer: Option C
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Typo, corrected (-1,0)phanikpk wrote:I need one clarification, can you please check st2. How can it be (-0,0). Is it a typo error?mjpinvestor wrote:If perpendicular lines m and n intersect at (0,b) in teh standard (x,y) coordinate plane, what is the value of b?
(1) The slope of line m is -1/2.
(2) The point (-0,0) is on line n.
OA is C
Would like to see experts' approaches here. Thanks.
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Given: Perpendicular lines m and n intersect at (0,b)mjpinvestor wrote:If perpendicular lines m and n intersect at (0,b) in teh standard (x,y) coordinate plane, what is the value of b?
(1) The slope of line m is -1/2.
(2) The point (-1,0) is on line n.
OA is C
Target question: What is the value of b?
Statement 1: The slope of the line m is -1/2
Since line n is PERPENDICULAR to line m, we know that line n has slope 2
However, we can raise and lower the two lines so that the value of b is different.
To see what I mean, here are two possible cases:
As you can see, with each case, we get a different value of b.
Since we cannot answer the target question with certainty, statement 1 is NOT SUFFICIENT
Statement 2: The point (-1,0) is on the line n
So, we know that the lines are perpendicular AND line n goes through the point (-1, 0)
However, since we don't know the SLOPES of the two lines, the value of b can change.
To see what I mean, here are two possible cases:
As you can see, with each case, we get a different value of b.
Since we cannot answer the target question with certainty, statement 2 is NOT SUFFICIENT
Statements 1 and 2 combined
Statement 1 tells us that line m has slope -1/2 and line n has slope 2
Statement 2 tells us that line n passes through (-1,0)
These two pieces of information, LOCK line n into just ONE POSSIBLE line
In fact, this also means the y-intercept (0, b) is also LOCKED in.
We get:
This also means that line m is also LOCKED in.
Since both lines are now locked in, there is only one possible value of b.
Are we going to bother to actually find the value of b?
No, that would be a waste of valuable time. We need only recognize that there is ONLY ONE possible pair of lines that satisfy the two statements, which means we COULD find the value of b
Since we COULD answer the target question with certainty, the combined statements are SUFFICIENT
Answer: C
Cheers,
Brent