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A certain manufacturer produces items for which the producti

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A certain manufacturer produces items for which the producti  [#permalink]

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New post 05 Jan 2014, 13:13
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The Official Guide For GMAT® Quantitative Review, 2ND Edition

A certain manufacturer produces items for which the production costs consist of annual fixed costs totaling $130,000 and variable costs averaging $8 per item. If the manufacturer's selling price per item is $15, how many items must the manufacturer produce and sell to earn an annual profit of $150,000 ?

(A) 2,858
(B) 18,667
(C) 21,429
(D) 35,000
(E) 40,000

Problem Solving
Question: 25
Category: Algebra Applied problems
Page: 65
Difficulty: 600


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Re: A certain manufacturer produces items for which the producti  [#permalink]

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New post 05 Jan 2014, 13:13
SOLUTION

A certain manufacturer produces items for which the production costs consist of annual fixed costs totaling $130,000 and variable costs averaging $8 per item. If the manufacturer's selling price per item is $15, how many items must the manufacturer produce and sell to earn an annual profit of $150,000 ?

(A) 2,858
(B) 18,667
(C) 21,429
(D) 35,000
(E) 40,000

Profit = Revenue - Cost.

Let x is the number of items the manufacturer must produce and sell.

Profit = 150,000;
Revenue = 15x;
Cost = 130,000 + 8x.

150,000 = 15x - (130,000 + 8x);
280,000 = 7x;
x = 40,000.

Answer: E.

Similar questions to practice:
marginal-cost-is-the-cost-of-increasing-the-quantity-pr-109332.html
the-expenses-of-a-hostel-are-partly-fixed-and-partly-137287.html
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Re: A certain manufacturer produces items for which the producti  [#permalink]

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New post Updated on: 06 Jan 2014, 02:56
A certain manufacturer produces items for which the production costs consist of annual fixed costs totaling $130,000 and variable costs averaging $8 per item. If the manufacturer's selling price per item is $15, how many items must the manufacturer produce and sell to earn an annual profit of $150,000 ?

(A) 2,858
(B) 18,667
(C) 21,429
(D) 35,000
(E) 40,000

Sol: Let x be the number of items that must be sold to make a annual profit of $150000.
Now Profit= Selling Price - Cost Price

Thus we have 150000= 15x - (130000+8x)-----> 20000= 7x ------> We don't even have to caculate this value because Barring Option A all the other options are automatically ruled out.

Ans is A

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Originally posted by WoundedTiger on 05 Jan 2014, 21:01.
Last edited by WoundedTiger on 06 Jan 2014, 02:56, edited 2 times in total.
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Re: A certain manufacturer produces items for which the producti  [#permalink]

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New post 06 Jan 2014, 02:41
3
A certain manufacturer produces items for which the production costs consist of annual fixed costs totaling $130,000 and variable costs averaging $8 per item. If the manufacturer's selling price per item is $15, how many items must the manufacturer produce and sell to earn an annual profit of $150,000 ?

(A) 2,858
(B) 18,667
(C) 21,429
(D) 35,000
(E) 40,000

Let us say x items were produced
Total cost = 130,000 + 8x
Total Revenue = 15x

For 150,000 Profit Revenue = Cost + 150,000

Profit Revenue = 130,000 + 8x + 150,000 = 15x

7x = 280,000
x = 40,000

Answer E
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Re: A certain manufacturer produces items for which the producti  [#permalink]

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New post 06 Jan 2014, 02:57
WoundedTiger wrote:
A certain manufacturer produces items for which the production costs consist of annual fixed costs totaling $130,000 and variable costs averaging $8 per item. If the manufacturer's selling price per item is $15, how many items must the manufacturer produce and sell to earn an annual profit of $150,000 ?

(A) 2,858
(B) 18,667
(C) 21,429
(D) 35,000
(E) 40,000

Sol: Let x be the number of items that must be sold to make a annual profit of $150000.
Now Profit= Selling Price - Cost Price

Thus we have 150000= 15x - (130000+8x)-----> 20000= 7x ------> We don't even have to caculate this value because Barring Option A all the other options are automatically ruled out.

Ans is A


:x :cry: :oops:


God Help me......I can do better....7x=280000 and x=40000.

Ans E
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Re: A certain manufacturer produces items for which the producti  [#permalink]

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New post 06 Jan 2014, 08:58
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Bunuel wrote:
The Official Guide For GMAT® Quantitative Review, 2ND Edition

A certain manufacturer produces items for which the production costs consist of annual fixed costs totaling $130,000 and variable costs averaging $8 per item. If the manufacturer's selling price per item is $15, how many items must the manufacturer produce and sell to earn an annual profit of $150,000 ?

(A) 2,858
(B) 18,667
(C) 21,429
(D) 35,000
(E) 40,000



Difficulty level : Sub 600.

The difference of Selling and variable cost is : $7.
Now the seller has to make a profit of $150k on top of fixed cost of $130k , so N * 7 = $280k
Now pick up the easiest option to verify, Option E) is the easiest to test and satisfies the equation beautifully. Option E)
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Re: A certain manufacturer produces items for which the producti  [#permalink]

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New post 11 Jun 2014, 13:56
Profit for 1 Item --> 15-8 = 7
(130,000+150,000)/7 = 40,000
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A certain manufacturer produces items for which the producti  [#permalink]

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New post 20 Sep 2017, 10:32
Madelaine88 wrote:
A certain manufacturer produces items for which the production costs consist of annual fixed costs totaling $130,000 and variables costs averaging $8 per item. If the manufacturer’s selling price per item is $15, how many items the manufacturer produce and sell to earn an annual profit of $150,000?

(A) 2,858
(B) 18,667
(C) 21,429
(D) 35,000
(E) 40,000

I eliminated, then backsolved with a shortcut.

Answers A, B, and C have numbers that are absurd. Eliminate them. If GMAT writers require calculations with those numbers in PS, I will risk being wrong over losing too much time for other questions.

Between remaining answers D and E, E looks better: 40,000 is quicker in calculation.

The shortcut: take three zeros off the large numbers. The calculated answer similarly will short by three zeros.

Total revenue = SP * # items
15 * 40 = 600

Total cost = Variable Cost + Fixed Cost

Variable Cost= (cost/item * # items)
Variable Cost = (8 * 40) = 320
Fixed Cost = 130
Total Cost = 320 + 130 = 450

Profit = TR - TC
600 - 450 = 150
That's a match.

Answer E
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