Author 
Message 
TAGS:

Hide Tags

Math Revolution GMAT Instructor
Joined: 16 Aug 2015
Posts: 8566
GPA: 3.82

In the coordinate plane p≠1, a line L passes through a point (1,p). Wh
[#permalink]
Show Tags
Updated on: 13 Jan 2016, 01:34
Question Stats:
57% (02:29) correct 43% (02:12) wrong based on 101 sessions
HideShow timer Statistics
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.
Official Answer and Stats are available only to registered users. Register/ Login.
_________________
MathRevolution: Finish GMAT Quant Section with 10 minutes to spareThe oneandonly World’s First Variable Approach for DS and IVY Approach for PS with ease, speed and accuracy. "Only $79 for 1 month Online Course""Free Resources30 day online access & Diagnostic Test""Unlimited Access to over 120 free video lessons  try it yourself"
Originally posted by MathRevolution on 10 Jan 2016, 05:30.
Last edited by Bunuel on 13 Jan 2016, 01:34, edited 2 times in total.
Edited the question.



Marshall & McDonough Moderator
Joined: 13 Apr 2015
Posts: 1675
Location: India

Re: In the coordinate plane p≠1, a line L passes through a point (1,p). Wh
[#permalink]
Show Tags
11 Jan 2016, 06:01
P = (1,p)
St1: The line L passes through point (0,1). > y intercept = 1 y = mx + 1 > y  1 = mx Also, m = p1 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



Math Revolution GMAT Instructor
Joined: 16 Aug 2015
Posts: 8566
GPA: 3.82

Re: In the coordinate plane p≠1, a line L passes through a point (1,p). Wh
[#permalink]
Show Tags
12 Jan 2016, 17:32
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) → (p1/10)=(131/p0) → p1=12/p, p^2p12=0. From (p4)(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.
_________________
MathRevolution: Finish GMAT Quant Section with 10 minutes to spareThe oneandonly World’s First Variable Approach for DS and IVY Approach for PS with ease, speed and accuracy. "Only $79 for 1 month Online Course""Free Resources30 day online access & Diagnostic Test""Unlimited Access to over 120 free video lessons  try it yourself"



Director
Joined: 05 Mar 2015
Posts: 958

Re: In the coordinate plane p≠1, a line L passes through a point (1,p). Wh
[#permalink]
Show Tags
11 Oct 2016, 03:16
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 =(y2y2)/(x2x1) (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)=(131)/(p0)(a) slope of (1,p)(p,13)=(13p)/(p1)(b) equate (a) & (b) we get p=3 0r 4>two values>insuff. Ans E



NonHuman User
Joined: 09 Sep 2013
Posts: 14075

Re: In the coordinate plane p≠1, a line L passes through a point (1,p). Wh
[#permalink]
Show Tags
28 Nov 2019, 06:50
Hello from the GMAT Club BumpBot! Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up  doing my job. I think you may find it valuable (esp those replies with Kudos). Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
_________________




Re: In the coordinate plane p≠1, a line L passes through a point (1,p). Wh
[#permalink]
28 Nov 2019, 06:50






