Author 
Message 
TAGS:

Hide Tags

Math Expert
Joined: 02 Sep 2009
Posts: 59124

A candle company determines that, for a certain specialty candle, the
[#permalink]
Show Tags
03 Jul 2016, 10:47
Question Stats:
71% (01:52) correct 29% (01:55) wrong based on 834 sessions
HideShow timer Statistics
A candle company determines that, for a certain specialty candle, the supply function is \(p = m_1*x + b_1\) and the demand function is \(p = m_2*x + b_2\), where p is the price of each candle, x is the number of candles supplied or demanded, and \(m_1\), \(m_2\), \(b_1\), and \(b_2\) are constants. At what value of x do the graphs of the supply function and demand function intersect? (1) \(m_1 = m_2 = 0.005\) (2) \(b_2 – b_1 = 6\)
Official Answer and Stats are available only to registered users. Register/ Login.
_________________




Verbal Forum Moderator
Status: Greatness begins beyond your comfort zone
Joined: 08 Dec 2013
Posts: 2431
Location: India
Concentration: General Management, Strategy
GPA: 3.2
WE: Information Technology (Consulting)

Re: A candle company determines that, for a certain specialty candle, the
[#permalink]
Show Tags
03 Jul 2016, 20:45
Bunuel wrote: A candle company determines that, for a certain specialty candle, the supply function is \(p = m_1*x + b_1\) and the demand function is \(p = m_2*x + b_2\), where p is the price of each candle, x is the number of candles supplied or demanded, and \(m_1\), \(m_2\), \(b_1\), and \(b_2\) are constants. At what value of x do the graphs of the supply function and demand function intersect?
(1) \(m_1 = m_2 = 0.005\) (2) \(b_2 – b_1 = 6\) supply function is \(p = m_1*x + b_1\) demand function is \(p = m_2*x + b_2\) At the point of intersection , the lines will have same value of p . Therefore , we can set the equations equal to each other . \(m_1*x + b_1 = m_2*x + b_2\) (1) \(m_1 = m_2 = 0.005\) Not sufficient as we have no information about \(b_1\) and \(b_2\) (2) \(b_2 – b_1 = 6\) Not sufficient as we have no information about \(m_1\) and \(m_2\) Combining 1 and 2 ,we get Sufficient Answer C
_________________
When everything seems to be going against you, remember that the airplane takes off against the wind, not with it.  Henry Ford The Moment You Think About Giving Up, Think Of The Reason Why You Held On So Long




Senior Manager
Joined: 02 Mar 2012
Posts: 269

Re: A candle company determines that, for a certain specialty candle, the
[#permalink]
Show Tags
03 Jul 2016, 23:16
C for me .
equation you get is:
x(m1m2)=b2b1
1+2 is needed for value of x



Senior Manager
Status: Gathering chakra
Joined: 05 Feb 2018
Posts: 440

Re: A candle company determines that, for a certain specialty candle, the
[#permalink]
Show Tags
21 May 2019, 12:09
Value Question: What is x when the two equations (lines) are set to be equal (intersect)?
(1) \(m_1 = m_2 = 0.005\) We have the slopes of the two lines, but no information about the yintercepts. Insufficient.
(2) \(b_2 – b_1 = 6\) We have the yintercepts of the two lines, but no information about the slopes. Insufficient.
(3) We have 1 variable and 1 equation, we can find x. Sufficient. line 1 = 0.005x + b1 line 2 = 0.005x + b1 + 6  set equal and remove b1 constant 0.005x = 0.005x + 6 0.01x = 6 x = 600



Intern
Joined: 25 Oct 2015
Posts: 3
WE: Analyst (Computer Software)

Re: A candle company determines that, for a certain specialty candle, the
[#permalink]
Show Tags
06 Jul 2016, 11:41
(1) \(m_1 = m_2 = 0.005\) Not sufficient as we have no information about \(b_1\) and \(b_2\)
(2) \(b_2 – b_1 = 6\) Not sufficient as we have no information about \(m_1\) and \(m_2\) Combining , Sufficient
Answer C



Manager
Joined: 17 Nov 2014
Posts: 50
Location: India

Re: A candle company determines that, for a certain specialty candle, the
[#permalink]
Show Tags
10 Jul 2016, 16:41
supply function p=m1∗x+b1p=m1∗x+b1 demand function p=m2∗x+b2p=m2∗x+b2
At the point of intersection , the lines will have same value of p . Therefore , we can set the equations equal to each other . m1∗x+b1=m2∗x+b2m1∗x+b1=m2∗x+b2 ( 4 varaibles i.e \(m1, m2, b1,b2)\)
Statement 1 : m1=−m2=0.005m1=−m2=0.005 Not sufficient as we have no information about b1 and b2
Statement 2: \(b2–b1\)=6b2–b1=6 Not sufficient as we have no information about m1 and m2
Combining 1 and 2 ,we get the value of \(X\) Sufficient Answer C



Manager
Joined: 27 Aug 2016
Posts: 87
Location: India
GPA: 3
WE: Engineering (Energy and Utilities)

Re: A candle company determines that, for a certain specialty candle, the
[#permalink]
Show Tags
02 Nov 2016, 07:25
My approach: at the pt. of intersection we will have values of p & x equal, further solving m1x+ b1=m2x+ b2, which implies (m1m2)x=b2b1, to get value of x we need both a & b and subsequently value of y through reverse substitutions. Can there be a conceptual / qualitative approach as well...or i am right in this approach?



Manager
Joined: 10 Sep 2014
Posts: 76
Location: Bangladesh
GPA: 3.5
WE: Project Management (Manufacturing)

A candle company determines that, for a certain specialty candle, the
[#permalink]
Show Tags
14 Apr 2018, 06:21
@Bunuel,@Veritasprepkarishma, I know where 2 lines intersect, the value of P should be same but could you please how value of P could be same or not for this problem? Thanks.



Manager
Joined: 24 Sep 2018
Posts: 137

A candle company determines that, for a certain specialty candle, the
[#permalink]
Show Tags
03 Oct 2018, 12:02
sadikabid27 wrote: @Bunuel,@Veritasprepkarishma, I know where 2 lines intersect, the value of P should be same but could you please how value of P could be same or not for this problem? Thanks. Dear sadikabid27, The equation given here is the equation of a line \(y = mx+c\) For any 2 lines to intersect the x and y coordinates need to be the same, otherwise they would not interest. So as the statement mentions : Quote: At what value of x do the graphs of the supply function and demand function intersect? Which means value of x is same for both the equations, all we need to do is put the value of y as same, P in this case. I hope this helps.
_________________
Please award kudos, If this post helped you in someway.



Director
Joined: 19 Oct 2013
Posts: 511
Location: Kuwait
GPA: 3.2
WE: Engineering (Real Estate)

Re: A candle company determines that, for a certain specialty candle, the
[#permalink]
Show Tags
18 Oct 2018, 08:58
Bunuel wrote: A candle company determines that, for a certain specialty candle, the supply function is \(p = m_1*x + b_1\) and the demand function is \(p = m_2*x + b_2\), where p is the price of each candle, x is the number of candles supplied or demanded, and \(m_1\), \(m_2\), \(b_1\), and \(b_2\) are constants. At what value of x do the graphs of the supply function and demand function intersect?
(1) \(m_1 = m_2 = 0.005\) (2) \(b_2 – b_1 = 6\) They will intersect when they are equal. \(m_1*x + b_1 = m_2*x + b_2\) this can be rewritten as \(m_1*x  m_2 *x = b_2  b_1\) From statement 1) we have only one side of the equation the \(m_1 and the m_2\) value. Insufficient From statement 2) we have only one side of the equation the \(b_2  b_1\). Insufficient. Combined we know both sides and as a result can find x. Sufficient. C



Manager
Joined: 04 Jun 2017
Posts: 108
Location: India
Concentration: Strategy, Operations
GPA: 3.82

A candle company determines that, for a certain specialty candle, the
[#permalink]
Show Tags
23 Jun 2019, 06:13
At the point of intersection , the lines will have same value of p . m1∗x+b1=m2∗x+b2
(1) m1=−m2=0.005 Not sufficient as we have no information about b1b1 and b2b2 (2) b2–b1=6b2–b1=6 Not sufficient as we have no information about m1m1 and m2m2 Answer C




A candle company determines that, for a certain specialty candle, the
[#permalink]
23 Jun 2019, 06:13






