In an xy-coordinate plane, a line is defined by y = kx + 1. If (4, b), (a, 4), and (a, b
+1) are three points on the line, where a and b are unknown, then k = ?
(A) 1/2
(B) 1
(C) 1(1/2) Mixed number
(D) 2
(E) 2(1/2) Mixed number
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Hi Sanjeev,
I think that this question has a typo in it. Two of the three points on the line are defined as (a,4) and (a,b+1), but since the x-coordinate is the same, then you either don't have a line or you don't have 2 different coordinates. If you can double-check and update this question, then I'll be happy to help you solve it.
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I think that this question has a typo in it. Two of the three points on the line are defined as (a,4) and (a,b+1), but since the x-coordinate is the same, then you either don't have a line or you don't have 2 different coordinates. If you can double-check and update this question, then I'll be happy to help you solve it.
GMAT assassins aren't born, they're made,
Rich
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Hi there,[email protected] wrote:Hi Sanjeev,
I think that this question has a typo in it. Two of the three points on the line are defined as (a,4) and (a,b+1), but since the x-coordinate is the same, then you either don't have a line or you don't have 2 different coordinates. If you can double-check and update this question, then I'll be happy to help you solve it.
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Rich
Check page 186, Question:77 of the VERITAS PREP Geometry Guide. The question is so written ! Don't know whether they made the typo themselves.
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Hi Sanjeev,
I don't own that book, but I can still offer a suggestion. Check the wording in the explanation; it's unlikely that a typo would show up in both spots. If that doesn't work, then post in the Veritas Forum (on this site); someone from that company should be able to address the issue.
GMAT assassins aren't born, they're made,
Rich
I don't own that book, but I can still offer a suggestion. Check the wording in the explanation; it's unlikely that a typo would show up in both spots. If that doesn't work, then post in the Veritas Forum (on this site); someone from that company should be able to address the issue.
GMAT assassins aren't born, they're made,
Rich
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answer is A
PUT the 3 inputs of x and y in line
and get
b = 4k+1 ...(1)
4 = ak+1 ...(2)
b+1 = ak+1 ...(3)
now compare (2) & (3)
and get
b+1 = 4
so b= 3
put the value of b in (1)
3 = 4k+1
2=4k
k = 1/2
PUT the 3 inputs of x and y in line
and get
b = 4k+1 ...(1)
4 = ak+1 ...(2)
b+1 = ak+1 ...(3)
now compare (2) & (3)
and get
b+1 = 4
so b= 3
put the value of b in (1)
3 = 4k+1
2=4k
k = 1/2
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(a, 4) and (a, b+1) must represent the SAME point on the line.Sanjeev k Sexena wrote:In an xy-coordinate plane, a line is defined by y = kx + 1. If (4, b), (a, 4), and (a, b
+1) are three points on the line, where a and b are unknown, then k = ?
(A) 1/2
(B) 1
(C) 1(1/2) Mixed number
(D) 2
(E) 2(1/2) Mixed number
Thus, the y-value in each case must be the same:
4 = b+1
b=3.
Since b=3, (4,b) = (4,3).
Since the equation of the line is y = kx + 1, the y-intercept = (0,1).
Since both (4,3) and (0,1) are on the line, the slope = (3-1)/(4-0) = 2/4 = 1/2.
The correct answer is A.
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there is another way to prove it
b+1-b/a-4 = 4-b/a-4
b=3
Since b=3, (4,b) = (4,3)
(3-1)/(4-0) = 2/4 = 1/2.
b+1-b/a-4 = 4-b/a-4
b=3
Since b=3, (4,b) = (4,3)
(3-1)/(4-0) = 2/4 = 1/2.
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There's a HUGE CLUE in the fact that (a, 4) and (a, b+1) are both on the same line. Notice that the x-coordinates are the same. If the x-coordinates are the same, then there are two possible scenarios:Sanjeev k Sexena wrote:In an xy-coordinate plane, a line is defined by y = kx + 1. If (4, b), (a, 4), and (a, b
+1) are three points on the line, where a and b are unknown, then k = ?
(A) 1/2
(B) 1
(C) 1(1/2) Mixed number
(D) 2
(E) 2(1/2) Mixed number
scenario #1: The points (a, 4) and (a, b+1) are DIFFERENT points, in which case the line is vertical (with undefined slope)
scenario #2: The points (a, 4) and (a, b+1) define the SAME point
IMPORTANT: If a line is defined by y = kx + 1, then k represents the slope. So, the question is really asking us to find the slope of the line.
In scenario #1, the slope would be undefined. Since none of the answer choices are undefined, we can rule out scenario #1, which means (a, 4) and (a, b+1) define the SAME point. So, we can be certain that b+1 = 4, which means b = 3
Now that we know that b = 3, we can use the fact that the point (4,b) is on the line.
This means that the point (4,3) is on the line y = kx + 1.
When we plug x=4 and y=3 into the equation, we get 3 = (k)(4) + 1
Solve to get k = 1/2
Answer: A
Cheers,
Brent