A candle company determines that, for a certain specialty candle, the

(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

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

My approach:
at the pt. of intersection we will have values of p & x equal, further solving
m1x+ b1=m2x+ b2, which implies (m1-m2)x=b2-b1, 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?

@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 :
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.

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

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 y-intercepts. Insufficient.

(2) \(b_2 – b_1 = 6\)
We have the y-intercepts 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

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 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) \(m_1 = -m_2 = 0.005\)

No information on \(b_2 or b_1\). INSUFFICIENT.

(2) \(b_2 – b_1 = 6\)

No information on \(m_2 or m_1\). INSUFFICIENT.

(1&2) Combining both statements, we can formulate one equation with one variable. SUFFICIENT.

Answer is C.

At the intersection point, the price of the candle P will be equal. i.e.,

\( m_1*x + b_1=m_2*x + b_2\)

\(=m_1*x - m_2*x= b_2-b_1\)

\(=x(m_1 - m_2)= b_2-b_1\)

(1) Gives the value \(m_1 & \ m_2\), only; Insufficient.

(2) Gives the value \(b_2 & \ b_1\), only; Insufficient.

Considering both: Sufficient.

The answer is C.

Solution:

Question Stem Analysis:

We need to determine the value of x where the graphs of p = m_1 * x + b_1 and p = m_2 * x + b_2 intersect. To determine that x-value, we can subtract the second equation form the first and obtain:

0 = (m_1 - m_2)x + (b_1 - b_2)

b_2 - b_1 = (m_1 - m_2)x

x = (b_2 - b_1) / (m_1 - m_2)

As we can see, if we can determine each individual values of b_1, b_2, m_1, and m_2, or if we can determine the values of (b_2 - b_1) and (m_1 - m_2), then we can determine the value of x.

Statement One Alone:

We see that m_1 = 0.005 and m_2 = -0.005. This means m_1 - m_2 = 0.01. However, without knowing the values of b_1 and b_2, we can’t determine the x-value where the graphs of the two functions intersect. Statement one alone is not sufficient.

Statement Two Alone:

We see that b_2 - b_1 = 6. However, without knowing the values of m_1 and m_2, we can’t determine the x-value where the graphs of the two functions intersect. Statement two alone is not sufficient.

Statements One and Two Together:

With the two statements, we have:

x = (b_2 - b_1)/(m_1 - m_2) = 6/0.01 = 600

Both statements together are sufficient.

Answer: C

The entire question is based on the logic-

If 2 lines interesect, their x and y coordinates will be the same at the point of intersection. 
Rest, it tests your skill at Data Sufficiency. 

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The entire question is based on the logic-

If 2 lines interesect, their x and y coordinates will be the same at the point of intersection. 
Rest, it tests your skill at Data Sufficiency.