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# A clothing manufacturer has determined that she can sell 100

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Director
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A clothing manufacturer has determined that she can sell 100 [#permalink]  30 Jun 2008, 22:33
A clothing manufacturer has determined that she can sell 100 suits a week at a selling price of $200 each. For each rise of$4 in the selling price she will sell two less suits each week. If she sells the suits for x dollars each, how many dollars a week will she receive from sales of the suits?
(A) {(x)(x)} / 2
(B) 200 - (x / 2)
(C) 50x + {(x)(x) / 4}
(D) 150x - {(x)(x) / 4}
(E) 200x - {(x)(x) / 4}

OA and explanation to follow later.
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Re: Clothing Jumbled Up [#permalink]  30 Jun 2008, 22:55
100 suits for $200 each if the price is say x=200+4n they can sell 100-n suits [ wrong calculation deleted ...] _________________ Kudos (+1) if you find this post helpful. Last edited by code19 on 01 Jul 2008, 03:02, edited 1 time in total. Current Student Joined: 12 Jun 2008 Posts: 287 Schools: INSEAD Class of July '10 Followers: 6 Kudos [?]: 40 [0], given: 0 Re: Clothing Jumbled Up [#permalink] 01 Jul 2008, 01:20 code19 wrote: if the price is say x=200+4n they can sell 100-n suits It says "For each rise of$4 in the selling price she will sell two less suits each week", so I guess that they would sell 100-2n suits...

This would lead with the same reasoning that you had to 100 - 2*(x/4-50) = 200x - x^2/2

And that's not an answer choice... I don't get it.

I arrived to the same results another way:

if f(x) is the number of suits they can sell at price x per week, we have f(200) = 100 and f(204) = 98

The equation of f(x), which is a straight line, would be f(x) = 200 - x/2

The amount of dollars they will receive per week is x*f(x), that is 200x - x^2/2

Why is it not an answer choice ??
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Re: Clothing Jumbled Up [#permalink]  01 Jul 2008, 03:01
code19 wrote:
(D)

100 suits for $200 each if the price is say x=200+4n they can sell 100-n suits so the return is (100-n) (200+4n) however we need to find the solution in terms of x 200+4n = x n= x/4 - 50 if we put n in the equation (100-n) (200+4n) (for total earning) the total return is 150x - {(x)(x) / 4} Oh yes.. Thanks for the correction So i will do the same calculations with (100-2n) so the return is (100-2n) (200+4n) = 8(50-n)(50+n) = 8 (2500 - (n)(n)) however we need to find the solution in terms of x 200+4n = x n= (x - 200)/4 if we put n in the equation 8 (2500 - (n)(n)) (for total earning) = 8 (2500 - (x-200)(x-200)/16) = 200x-(x)(x)/2 The same.. _________________ Kudos (+1) if you find this post helpful. Intern Joined: 15 Jun 2008 Posts: 17 Location: Kiev, Ukraine Schools: INSEAD Followers: 0 Kudos [?]: 2 [0], given: 0 Re: Clothing Jumbled Up [#permalink] 01 Jul 2008, 04:11 I also got the answer of (200x-1/2x^2). Could anybody clarify this issue pls? Thanks Director Joined: 26 Mar 2008 Posts: 652 Schools: Duke 2012 Followers: 14 Kudos [?]: 118 [0], given: 16 Re: Clothing Jumbled Up [#permalink] 01 Jul 2008, 05:28 I got 200x-(x^2/4) For each increase in price of$4 (x-200/4), you have two less suits ->
#suits=100-2*{(x-200)/4}
Double check - $4 increase in price =$204, $204-200=one$4 increment->2 less suits.

So, you have #suits*price=x*[100-{2*(x-200)/4]
=x*[100-{(2x-400)/4}]
=x*[(400-2x+400)/4]
=(400x-2*x^2+400x)/4
=(800x-2*x^2)/4
=200x-(x^2/4)

Sorry for all the parentheses
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Re: Clothing Jumbled Up [#permalink]  01 Jul 2008, 05:38
highhopes wrote:
=(800x-2*x^2)/4
=200x-(x^2/4)

Your error is right at the end (the rest is perfectly true): 2*x^2/4 = x^2/2
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Re: Clothing Jumbled Up [#permalink]  01 Jul 2008, 07:15
abhijit_sen wrote:
OA is E.

Then (E) should be 200x - {(x)(x) / 2} and not 200x - {(x)(x) / 4}
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Re: Clothing Jumbled Up [#permalink]  01 Jul 2008, 07:46
Oski wrote:
abhijit_sen wrote:
OA is E.

Then (E) should be 200x - {(x)(x) / 2} and not 200x - {(x)(x) / 4}

I agree this is what I got from old official Full length test. I to initially doubted my calculation but wanted to confirm my findings.
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Re: Clothing Jumbled Up [#permalink]  02 Jul 2008, 12:38
abhijit_sen wrote:
A clothing manufacturer has determined that she can sell 100 suits a week at a selling price of $200 each. For each rise of$4 in the selling price she will sell two less suits each week. If she sells the suits for x dollars each, how many dollars a week will she receive from sales of the suits?
(A) {(x)(x)} / 2
(B) 200 - (x / 2)
(C) 50x + {(x)(x) / 4}
(D) 150x - {(x)(x) / 4}
(E) 200x - {(x)(x) / 4}

OA and explanation to follow later.

If the answer truly is E, could someone explain what I am doing wrong here. I used actual numbers to find an answer since there are variables in the answer choices.

Initial scenario: 100 suits @ $200 / suit =$20,000 in revenue

Price change: lets say she increased the price by $20 to$220 (x = 220)---> this an increase of $4 -- 5 times. So for every increase of$4 (which is 5), 2 less suits are sold -->
5 * 2 = 10 less suits sold (for a total of 90 suits)

New revenue calculation: 90 suits @ $220 / suit =$19,800 in revenue

Now, lets plus in x (220) for the answer choices to see which answer gives $19,800 as the result: A) (220*220)/2 =$24,200 --> INCORRECT
B) 200-(220/2) = $90 --> INCORRECT C) 50(220) + {(220*220)/4} = 23,100 --> INCORRECT D) 150(220) - {(220*220)/4} = 20,900 --> INCORRECT E) 200*220 - {(220*220)/4} = 31,900 --> INCORRECT None of these yield$19,800 ???
I agree with abhijit_sen that E should be 200x - {(x)(x) / 2} ---> which yields \$19,800 as the result
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Re: Clothing Jumbled Up   [#permalink] 02 Jul 2008, 12:38
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