The cost C, in dollars of producing x units of a certain commodity is

Question

The cost C, in dollars of producing x units of a certain commodity is given by the formula C(x) = 10.000 + bx + ax^2 where a, and b are constants. What is the value of a?

(1) The cost of producing 500 units is $15.833.

(2) The cost of producing 1,000 units is twice the cost of producing 500 units.

chetan2u · Accepted Answer

Hi 
the equation has got two constants a and b..
 lets see the statements

(1) The cost of producing 500 units is $15.833. 
we have two constants a and b, and one equation
Insuff

(2) The cost of producing 1,000 units is twice the cost of producing 500 units 
here when you make two quation and equate them you will realize you can find answer..
 C(1000) = 10.000 + b*1000 + a1000^2  ..
 C(500) = 10.000 + b*500 + a500^2  ..

now  C(1000) = 2* C(500) ..
so  10.000 + b*1000 + a1000^2 = 2( 10.000 + b*500 + a500^2 ) ..
 10.000 + b*1000 + a1000^2 = 20.000 + b*1000 + 2*a*500^2 
b will get cancelled and you can find value of a..
Suff

Hope it helps

KarishmaB · Answer

Let me point out here that this is a (C) trap question. The first statement will give an equation in a and b. So we know that we cannot find the value of a. When we look at the second statement, we see another equation in a and b which is not a multiple of the first equation and suddenly, it seems that we will be able to solve both equations simultaneously and get the answer. So (C) seems to be correct. But that is just too easy. Beware of the (C) trap. This should make you think - can I solve the question using a single statement alone. Make the equation of statement 2 since it gives you some convoluted relative data. When you do, you see that b gets canceled and in fact, you can get the value of a. Note that you cannot find the value of b from the second statement alone but the question doesn't ask for the value of b. We only need the value of a and hence second statement is sufficient alone.

EMPOWERgmatRichC · Answer

Hi inakihernandez, You should post this question in the DS sub-Forum here: gmat-data-sufficiency-ds-141/ GMAT assassins aren't born, they're made, Rich

Kurtosis · Answer

C(x) = 10.000 + bx + ax^2
a = ?

St1: C(500) = 10 + 500b + a(25*10^4 ) = 15.833
We have 2 unknowns and hence value of 'a' cannot be determined without knowing the value of 'b'
Not Sufficient

St2: C(1000) = 2*C(500)
10 + 1000b + a(10^6) = 20 + 1000b + a(50*10^4)
a(10^6 - 5*10^5) = 10
Sufficient to determine the value of 'a'

Answer: B

paidlukkha · Answer

how did you get this?
 a(25*10^4 ) 
 a(50*10^4)

Kurtosis · Answer

Hi,

I have skipped some multiplication steps in my explanation.

x = 5*10^2 --> x^2 = 25*10^4

2*C(500) --> 2(10 + 500b + 25*10^4) --> 20 + 1000b + 2*25*10^4

keats · Answer

The correct statement 1 is
(1) The cost of producing 500 units of this commodity is $15833

It is NOT 15.833 although that won't affect the OA.

Kinshook · Answer

Given: The cost C, in dollars of producing x units of a certain commodity is given by the formula C(x) = 10.000 + bx + ax^2 where a, and b are constants.

Asked: What is the value of a?

(1) The cost of producing 500 units is $15.833.
C(x) = 10.000 + bx + ax^2
x = 500
C(x) = $15.833 = 10 + 500b + 250000a
Since there are 2 unknowns
NOT SUFFICIENT

(2) The cost of producing 1,000 units is twice the cost of producing 500 units.
10 + 1000b + 1000000a = 2(10 + 500b + 250000a)
1000000a = 10 + 500000a
500000a = 10
 a = \frac{1}{50000} 
SUFFICIENT

IMO B

Kinshook · Answer

Given: The cost C, in dollars of producing x units of a certain commodity is given by the formula C(x) = 10.000 + bx + ax^2 where a, and b are constants.

Asked: What is the value of a?

(1) The cost of producing 500 units is $15.833.
15.833 = 10,000 + 500b + 250000a
Since b is unknown, a can not be found out
NOT SUFFICIENT

(2) The cost of producing 1,000 units is twice the cost of producing 500 units.
10,000 + 1000b + 1000000a = 2 (10,000 + 500b + 250000a) 
10,000 + 1000b + 1000000a = 20,000 + 1000b + 500,000a
10,000 = 500000a
a = 10,000/500,000
SUFFICIENT

IMO B

dabaobao · Answer

1) 1 equation and 2 unknowns => Not sufficient

2) 10 + 1000b + a(1000)^2 = 2 (10 + 500b + a(500)^2)
b cancels out. We can find a. => Sufficient

ANSWER: B

gmexamtaker1 · Answer

Hello  Kinshook ,
Could you please explain why are you writing 10 and 25000 instead of 10,000 and 250,000 in "15.833 = 10 + 500b + 25000a" ? Is it for a strategic reason or a typo?

Kinshook · Answer

The solution is corrected.

AnkurGMAT20 · Answer

Bunuel , GMAT Prep question. Please tag it.

GmatPoint · Answer

Given, C(x) = 10.000 + bx + ax^2....(x)

Now from statement 1, we know C(500) = $ 15.833
From statement 2, C(1000) = 2 x C(500)

Since there are two variables, we cannot get the value of a and b from only one of the statements.

Thus, let's consider the case of using both the statements:

Putting the value of statement 1 in the given equation(x):

C(500) = 10.000 + b(500) + a(500)^2 = $ 15.833......(i)

Using statement 2 with equation (i),

C(1000) = 2 x (10.000 + b(500) + a(500)^2) = 20.000 + b(1000) + a(1000)(500)
C(1000) = 20.000 + b(1000) + a(1000)(500)....(ii)

Also, by using the given equation(x):

C(1000) = 10.000 + b(1000) + a(1000)^2 .....(iii)

Subtracting (ii) and (iii) will give the value of a, and we can find the value of b by putting a in any of the equations.

Bunuel · Answer

_____________________
Added the tag. Thank you!

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The cost C, in dollars of producing x units of a certain commodity is

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