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

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inakihernandez
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The cost C, in dollars of producing x units of a certain commodity is [#permalink] New post   Updated on: 24 Apr 2016, 11:36
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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.
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B

Originally posted by inakihernandez on 24 Apr 2016, 10:20.
Last edited by Kurtosis on 24 Apr 2016, 11:36, edited 1 time in total.
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The cost C, in dollars of producing x units of a certain commodity is [#permalink] New post   24 Apr 2016, 10:58
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inakihernandez wrote:
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.


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
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Re: The cost C, in dollars of producing x units of a certain commodity is [#permalink] New post   24 Apr 2016, 21:04
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inakihernandez wrote:
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.


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.
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Re: The cost C, in dollars of producing x units of a certain commodity is [#permalink] New post   24 Apr 2016, 10:47
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Hi inakihernandez,

You should post this question in the DS sub-Forum here:

gmat-data-sufficiency-ds-141/

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Re: The cost C, in dollars of producing x units of a certain commodity is [#permalink] New post   24 Apr 2016, 11:02
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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
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Re: The cost C, in dollars of producing x units of a certain commodity is [#permalink] New post   24 Apr 2016, 11:10
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Vyshak wrote:
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


how did you get this?
a(25*10^4 )
a(50*10^4)
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Re: The cost C, in dollars of producing x units of a certain commodity is [#permalink] New post   24 Apr 2016, 11:13
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paidlukkha wrote:
Vyshak wrote:
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


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


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
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Re: The cost C, in dollars of producing x units of a certain commodity is [#permalink] New post   09 Oct 2016, 04:29
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.
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Re: The cost C, in dollars of producing x units of a certain commodity is [#permalink] New post   20 Sep 2019, 22:51
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inakihernandez wrote:
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.


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
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The cost C, in dollars of producing x units of a certain commodity is [#permalink] New post   Updated on: 20 Apr 2021, 08:48
inakihernandez wrote:
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.


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

Originally posted by Kinshook on 08 Oct 2019, 10:34.
Last edited by Kinshook on 20 Apr 2021, 08:48, edited 1 time in total.
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Re: The cost C, in dollars of producing x units of a certain commodity is [#permalink] New post   02 Dec 2019, 18:22
inakihernandez wrote:
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.


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
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The cost C, in dollars of producing x units of a certain commodity is [#permalink] New post   Updated on: 20 Apr 2021, 02:07
Kinshook wrote:
inakihernandez wrote:
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.


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 + 500b + 25000a
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 + 1000b + 1000000a = 2 (10 + 500b + 250000a)
10 + 1000b + 1000000a = 20 + 1000b + 500000a
10 = 500000a
a = 10/500000
SUFFICIENT

IMO B


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?

Originally posted by gmexamtaker1 on 19 Apr 2021, 12:35.
Last edited by gmexamtaker1 on 20 Apr 2021, 02:07, edited 1 time in total.
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The cost C, in dollars of producing x units of a certain commodity is [#permalink] New post   19 Apr 2021, 17:17
The solution is corrected.

UNSTOPPABLE12 wrote:
Kinshook wrote:
inakihernandez wrote:
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.


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 + 500b + 25000a
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 + 1000b + 1000000a = 2 (10 + 500b + 250000a)
10 + 1000b + 1000000a = 20 + 1000b + 500000a
10 = 500000a
a = 10/500000
SUFFICIENT

IMO B


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?
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Re: The cost C, in dollars of producing x units of a certain commodity is [#permalink] New post   02 Jun 2022, 00:33
Bunuel, GMAT Prep question. Please tag it.
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Re: The cost C, in dollars of producing x units of a certain commodity is [#permalink] New post   02 Jun 2022, 01:07
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.
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Re: The cost C, in dollars of producing x units of a certain commodity is [#permalink] New post   02 Jun 2022, 01:27
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AnkurGMAT20 wrote:
Bunuel, GMAT Prep question. Please tag it.


_____________________
Added the tag. Thank you!
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Re: The cost C, in dollars of producing x units of a certain commodity is [#permalink] New post   11 Jun 2023, 01:58
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Re: The cost C, in dollars of producing x units of a certain commodity is [#permalink]
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