Author 
Message 
TAGS:

Hide Tags

Manager
Joined: 21 Sep 2010
Posts: 248

The equation of line k is y=mx+b, where m and b are constant
[#permalink]
Show Tags
29 Apr 2014, 12:21
Question Stats:
36% (01:10) correct 64% (01:08) wrong based on 209 sessions
HideShow timer Statistics
The equation of line k is y=mx+b, where m and b are constants. What is the value of m? 1) (b,2b) belongs to k. 2) (2,2) belongs to k. Had a difficult time understanding the explanation. Anyone want to take a stab?
Official Answer and Stats are available only to registered users. Register/ Login.
_________________
"Only by going too far, can one find out how far one can go."
T.S. Elliot




Veritas Prep GMAT Instructor
Joined: 16 Oct 2010
Posts: 8406
Location: Pune, India

Re: The equation of line k is y=mx+b, where m and b are constant
[#permalink]
Show Tags
29 Apr 2014, 22:06
TwoThrones wrote: The equation of line k is y=mx+b, where m and b are constants. What is the value of m?
1) (b,2b) belongs to k. 2) (2,2) belongs to k.
Had a difficult time understanding the explanation. Anyone want to take a stab? Stmnt 1: If by statement 1 you mean that the point (b, 2b) lies on the line k, you can plug in the point in the equation of the line y=mx+b to get 2b = m*b + b. 2b = b(m + 1) b = mb (m1)b = 0 Either m is 1 or b = 0 or both. In case we prove that b is not 0, then m must be 1. If b is 0, m could be anything including 1. Not sufficient. Stmnt 2: If line passes through (2, 2), we get 2 = m*2 + b We have 2 unknowns and only one equation. Not enough to get the value of m. Using both together, we have 2m + b = 2 .... (I) such that either b is 0 or m is 1 or both. If b is 0, put b = 0 in (I) which gives us m = 1 If b is not 0, m must be 1. So in any case, m is always 1. Answer (C)
_________________
Karishma Veritas Prep GMAT Instructor
Learn more about how Veritas Prep can help you achieve a great GMAT score by checking out their GMAT Prep Options >
GMAT selfstudy has never been more personalized or more fun. Try ORION Free!




Director
Joined: 25 Apr 2012
Posts: 692
Location: India
GPA: 3.21
WE: Business Development (Other)

Re: The equation of line k is y=mx+b, where m and b are constant
[#permalink]
Show Tags
29 Apr 2014, 22:05
TwoThrones wrote: The equation of line k is y=mx+b, where m and b are constants. What is the value of m?
1) (b,2b) belongs to k. 2) (2,2) belongs to k.
Had a difficult time understanding the explanation. Anyone want to take a stab? I will give it a try St1 says (b,2b) belong to k so, we have 2b=mb+b or b=mb or (m1)*b=0 >This implies either m=1 or b=0. St1 is not sufficient. So A and D ruled out St 2: 2=2m+b or \(m= (2b)/2\) or m =1(b/2).. But we don't know anything about b. So not sufficient. Option B ruled out Combining we get that b=0 then m=1. Alternatively if m=1 then b=0. Therefore ans is C
_________________
“If you can't fly then run, if you can't run then walk, if you can't walk then crawl, but whatever you do you have to keep moving forward.”



Intern
Joined: 25 Jan 2014
Posts: 44
Concentration: Strategy, International Business
GMAT 1: 600 Q44 V29 GMAT 2: 710 Q48 V38
GPA: 3.35
WE: Analyst (Computer Software)

Re: The equation of line k is y=mx+b, where m and b are constant
[#permalink]
Show Tags
15 May 2014, 07:08
Can anybody explain why m cant be 0 ?



Intern
Joined: 25 Jan 2014
Posts: 44
Concentration: Strategy, International Business
GMAT 1: 600 Q44 V29 GMAT 2: 710 Q48 V38
GPA: 3.35
WE: Analyst (Computer Software)

Re: The equation of line k is y=mx+b, where m and b are constant
[#permalink]
Show Tags
15 May 2014, 07:11
Also when 2b = mb + b, why can i not cancel b to get m+1 = 2 and m =1?



Math Expert
Joined: 02 Sep 2009
Posts: 50042

Re: The equation of line k is y=mx+b, where m and b are constant
[#permalink]
Show Tags
15 May 2014, 07:23
gaurav1418z wrote: The equation of line k is y=mx+b, where m and b are constants. What is the value of m?
1) (b,2b) belongs to k. 2) (2,2) belongs to k.
Can anybody explain why m cant be 0 ? From (1): m = 1 or b = 0 or both. From (2): 2m + b = 2. If m is not 1, then b must be 0. But if b = 0, then from 2m + b = 2, we get that m = 1. So, in any case, m = 1. Hope it's clear.
_________________
New to the Math Forum? Please read this: Ultimate GMAT Quantitative Megathread  All You Need for Quant  PLEASE READ AND FOLLOW: 12 Rules for Posting!!! Resources: GMAT Math Book  Triangles  Polygons  Coordinate Geometry  Factorials  Circles  Number Theory  Remainders; 8. Overlapping Sets  PDF of Math Book; 10. Remainders  GMAT Prep Software Analysis  SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS)  Tricky questions from previous years.
Collection of Questions: PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.
What are GMAT Club Tests? Extrahard Quant Tests with Brilliant Analytics



Math Expert
Joined: 02 Sep 2009
Posts: 50042

Re: The equation of line k is y=mx+b, where m and b are constant
[#permalink]
Show Tags
15 May 2014, 07:26



Intern
Joined: 25 Jan 2014
Posts: 44
Concentration: Strategy, International Business
GMAT 1: 600 Q44 V29 GMAT 2: 710 Q48 V38
GPA: 3.35
WE: Analyst (Computer Software)

Re: The equation of line k is y=mx+b, where m and b are constant
[#permalink]
Show Tags
15 May 2014, 23:56
Thank you Bunuel, much appreciated



Math Revolution GMAT Instructor
Joined: 16 Aug 2015
Posts: 6398
GPA: 3.82

Re: The equation of line k is y=mx+b, where m and b are constant
[#permalink]
Show Tags
21 Nov 2015, 09:50
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. The equation of line k is y=mx+b, where m and b are constants. What is the value of m? 1) (b,2b) belongs to k. 2) (2,2) belongs to k. In the original condition, we need to know the gradient and the yintercept, so we need 2 equations There are 2 equations given by the 2 conditions, so there is high chance (C) will be our answer. Looking at the conditions together, from 2b=mb+b, b=mb, b(m1)=0, we get b=0 or m=1, and from 2=2m+b, if b=0, m=1. This is sufficient, and the answer becomes (C). For cases where we need 2 more equation, such as original conditions with “2 variables”, or “3 variables and 1 equation”, or “4 variables and 2 equations”, we have 1 equation each in both 1) and 2). Therefore, there is 70% chance that C is the answer, while E has 25% 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 C 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, D or E.
_________________
MathRevolution: Finish GMAT Quant Section with 10 minutes to spare The oneandonly World’s First Variable Approach for DS and IVY Approach for PS with ease, speed and accuracy. "Only $99 for 3 month Online Course" "Free Resources30 day online access & Diagnostic Test" "Unlimited Access to over 120 free video lessons  try it yourself"



NonHuman User
Joined: 09 Sep 2013
Posts: 8533

Re: The equation of line k is y=mx+b, where m and b are constant
[#permalink]
Show Tags
25 Sep 2018, 05:51
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.
_________________
GMAT Books  GMAT Club Tests  Best Prices on GMAT Courses  GMAT Mobile App  Math Resources  Verbal Resources




Re: The equation of line k is y=mx+b, where m and b are constant &nbs
[#permalink]
25 Sep 2018, 05:51






