A certain manufacturer produces items for which the producti

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

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

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)

Profit for 1 Item --> 15-8 = 7
(130,000+150,000)/7 = 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

Letting n = the number of items that must be sold, we can create the equation:

15n - (8n + 130,000) = 150,000

15n - 8n - 130.000 = 150,000

7n = 280,000

n = 40,000

Answer: E

This is how I did in 45 seconds.

What is the profit he is making by selling one unit? 7$. Cool

Let's recover the initial cost of 130,000. That's around 20k units.

Let's make a profit of 150,000. That's around 20k too.

Answer E.

Note: If you understood what I did then you can just see that you need to make 130,000+150,000=280,000/7=40,000

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