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In the coordinate plane p≠1, a line L passes through a point (1,p). Wh

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In the coordinate plane p≠1, a line L passes through a point (1,p). Wh  [#permalink]

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New post Updated on: 13 Jan 2016, 02:34
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In the coordinate plane p≠1, a line L passes through a point (1,p). What is the slope of the line L?

(1) The line L passes through point (0,1).
(2) The line L passes through point (p,13).



*A solution is going to be uploaded in two days.

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Originally posted by MathRevolution on 10 Jan 2016, 06:30.
Last edited by Bunuel on 13 Jan 2016, 02:34, edited 2 times in total.
Edited the question.
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Re: In the coordinate plane p≠1, a line L passes through a point (1,p). Wh  [#permalink]

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New post 11 Jan 2016, 07:01
P = (1,p)

St1: The line L passes through point (0,1). --> y intercept = 1
y = mx + 1 --> y - 1 = mx
Also, m = p-1
Value of m is not known
St1 is not sufficient

St2: The line L passes through point (p,13). --> Q = (p,13)
m = (p - 13)/(1 - p)
Value of m is not known
St2 is not sufficient

Combining St1 and St2:
(p - 1) = (p - 13)/ (1 - p)
(p - 1)^2 = 13 - p
p^2 + 1 - 2p = 13 - p
p^2 - p - 12 = 0
p = 4 or -3

If p = 4, m = p - 1 = 3
If p = -3, m = p - 1 = -4

Thus we do not have a unique value for m.

Answer: E
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Re: In the coordinate plane p≠1, a line L passes through a point (1,p). Wh  [#permalink]

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New post 12 Jan 2016, 18:32
Forget conventional ways of solving math questions. In DS, Variable approach is the easiest and quickest way to find the answer without actually solving the problem. Remember equal number of variables and independent equations ensures a solution.

In the coordinate plane p≠1, a line L passes through a point (1,p). What is the slope of the line L?
1) The line L passes through point (0,1).
2) The line L passes through point (p,13).

In the original condition, there are 3 variables(1,p),(x1,y1), which should match with the number of equations. So you need 3 equations. For 1) 1 equation, for 2) 1 equation, which is likely to make E the answer. When 1) & 2), (1,p),(0,1),(p,13) → (p-1/1-0)=(13-1/p-0) → p-1=12/p, p^2-p-12=0. From (p-4)(p+3)=0, p=-3,4. Then the slope is 3,-4, which means there are 2 answers. So it is not unique and not sufficient. Therefore, the answer is E.


 For cases where we need 3 more equations, such as original conditions with “3 variables”, or “4 variables and 1 equation”, or “5 variables and 2 equations”, we have 1 equation each in both 1) and 2). Therefore, there is 80% chance that E is the answer (especially about 90% of 2 by 2 questions where there are more than 3 variables), while C has 15% chance. These two are the majority. In case of common mistake type 3,4, the answer may be from A, B or D but there is only 5% chance. Since E is most likely to be the answer using 1) and 2) separately according to DS definition (It saves us time). Obviously there may be cases where the answer is A, B, C or D.
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Re: In the coordinate plane p≠1, a line L passes through a point (1,p). Wh  [#permalink]

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New post 11 Oct 2016, 04:16
MathRevolution wrote:
In the coordinate plane p≠1, a line L passes through a point (1,p). What is the slope of the line L?

(1) The line L passes through point (0,1).
(2) The line L passes through point (p,13).



*A solution is going to be uploaded in two days.

points to keep remember while solving this question is for two points P1(x1,y1) and P2(x2,y2) slope(m) is defined as =(y2-y2)/(x2-x1)

(1) we have two coordinates (0,1) and (1,p)
with variation in value p our slope changes............insuff
(2) again we have two cordinates (1,p) &(p,13) with variable p thus slope changes accordingly with p........insuff

combining we have 3 coordinates with variable p of same line.
so lets us take slope of any 2 pairs of coordinate and equate them
slope of (0,1) (p,13)=(13-1)/(p-0)-------(a)
slope of (1,p)(p,13)=(13-p)/(p-1)--------(b)
equate (a) & (b)
we get p=-3 0r 4----------->two values------->insuff.

Ans E
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Re: In the coordinate plane p≠1, a line L passes through a point (1,p). Wh  [#permalink]

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