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Math Expert V
Joined: 02 Sep 2009
Posts: 56256
Each month, a certain manufacturing company's total expenses are equal  [#permalink]

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Difficulty:   35% (medium)

Question Stats: 73% (02:27) correct 27% (02:24) wrong based on 40 sessions

### HideShow timer Statistics Each month, a certain manufacturing company's total expenses are equal to a fixed monthly expense plus a variable expense that is directly proportional to the number of units produced by the company during that month. If the company's total expenses for a month in which it produces 20,000 units are $570,000, and the total expenses for a month in which it produces 25,000 units are$705,000, what is the company's fixed monthly expense?

A. $27,000 B.$30,000

C. $67,500 D.$109,800

E. $135,000 _________________ examPAL Representative P Joined: 07 Dec 2017 Posts: 1074 Re: Each month, a certain manufacturing company's total expenses are equal [#permalink] ### Show Tags Bunuel wrote: Each month, a certain manufacturing company's total expenses are equal to a fixed monthly expense plus a variable expense that is directly proportional to the number of units produced by the company during that month. If the company's total expenses for a month in which it produces 20,000 units are$570,000, and the total expenses for a month in which it produces 25,000 units are $705,000, what is the company's fixed monthly expense? A.$27,000

B. $30,000 C.$67,500

D. $109,800 E.$135,000

We'll break our question into equations to make it easier to understand.
This is a Precise appraoch.

total expense = fixed monthly expense + variable expense --> t = f + ku (where k is a constant - we are told the variable expense in 'proportional to the amount of units)
570,000 = f + 20,000k
705,000 = f + 25,000k

Looking at our equations, it is easy to see that a difference in 5,000 units created another 705,000 - 570,000 = 135,000 dollars of revenue.
So 20,000 units must cost 135,000*4 = 540,000 dollars meaning that, from our first equation, the fixed cost is 570,000 - 540,000 = 30,000

_________________
Senior Manager  G
Joined: 13 Feb 2018
Posts: 411
GMAT 1: 640 Q48 V28 Re: Each month, a certain manufacturing company's total expenses are equal  [#permalink]

We can observe that additional 5000 (25000-20000) items lead to $135 000 ($705000-$570000) increase. So the total variable cost will be: (20000/5000)*135000=540 000 (25000/5000)*135000=675 000 Fixed cost=Total cost - variable cost 570 000-540 000= 30 000 705 000- 675 000 = 30 000 In My Opinion Ans: B Senior SC Moderator V Joined: 22 May 2016 Posts: 3076 Each month, a certain manufacturing company's total expenses are equal [#permalink] ### Show Tags Bunuel wrote: Each month, a certain manufacturing company's total expenses are equal to a fixed monthly expense plus a variable expense that is directly proportional to the number of units produced by the company during that month. If the company's total expenses for a month in which it produces 20,000 units are$570,000, and the total expenses for a month in which it produces 25,000 units are $705,000, what is the company's fixed monthly expense? A.$27,000

B. $30,000 C.$67,500

D. $109,800 E.$135,000

The trap is Answer A. $27 is the cost per unit. That figure is used to calculate variable cost (variable cost total changes because the number of units produced changes) Variable Cost = (Per unit cost) * (# of units) Fixed Cost is a cost that does not change that is incurred with each and every production batch irrespective of number of units. Fixed Cost = (Total Cost - Variable Cost) (1) Total cost of "extra" units? How many [relatively] extra units cost how much total? Fixed cost + 25,000 units =$705,000
Fixed cost + 20,000 units = $570,000 Subtract bottom from top: 5,000 units cost$135,000

(2) Cost per unit:
$$\frac{TotalCost}{No.Of.Units}=\frac{135,000}{5,000}=27$$ per unit

Per unit cost is $27, but$27 per unit is above and beyond some fixed cost that is the same for every production batch. We need that fixed cost.

(3) Fixed cost
Fixed cost = Total cost - (Variable Cost)

Pick one production batch. Doesn't matter which one.

Variable Cost = (# of units) * (cost per unit = $27) Variable Cost of 20,000 units: $$(27 * 20,000) = 540,000$$ Total Cost of 20,000 units:$$570,000$$ Fixed Cost: $$(570,000 - 540,000) = 30,000$$ Answer B _________________ SC Butler has resumed! Get two SC questions to practice, whose links you can find by date, here. Tell me, what is it you plan to do with your one wild and precious life? -- Mary Oliver VP  D Joined: 31 Oct 2013 Posts: 1392 Concentration: Accounting, Finance GPA: 3.68 WE: Analyst (Accounting) Re: Each month, a certain manufacturing company's total expenses are equal [#permalink] ### Show Tags Bunuel wrote: Each month, a certain manufacturing company's total expenses are equal to a fixed monthly expense plus a variable expense that is directly proportional to the number of units produced by the company during that month. If the company's total expenses for a month in which it produces 20,000 units are$570,000, and the total expenses for a month in which it produces 25,000 units are $705,000, what is the company's fixed monthly expense? A.$27,000

B. $30,000 C.$67,500

D. $109,800 E.$135,000

Note:

Fixed cost will not change regardless the number of units produced.

***** If amount changes , that change must be occurred because of Variable cost.

Workings :

For 20000 units total cost is 570000
for 25000 units total cost is 705000

*** For 5000 units cost is increased by 135000.
This 135000 is your variable cost for 5000 units. Note: Fixed cost remains same in all condition.

Variable cost per unit :

135000 / 5000

= 27 / unit.

We know ,

Total cost = Fc + Vc
570000 = Fc + (20000*27)..........(vc = 27 / unit for 20000 units)

570000 - 540000 = Fc

Fc = 30000.

Thus the best answer is B.
Math Expert V
Joined: 02 Aug 2009
Posts: 7764
Re: Each month, a certain manufacturing company's total expenses are equal  [#permalink]

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Bunuel wrote:
Each month, a certain manufacturing company's total expenses are equal to a fixed monthly expense plus a variable expense that is directly proportional to the number of units produced by the company during that month. If the company's total expenses for a month in which it produces 20,000 units are $570,000, and the total expenses for a month in which it produces 25,000 units are$705,000, what is the company's fixed monthly expense?

A. $27,000 B.$30,000

C. $67,500 D.$109,800

E. \$135,000

Since the expense are inclusive of a certain constant amount and variable expense, so the difference in cost will be the difference in cost of variables only..
So cost of 25000-20000=705000-570000=135000
Cost of 5000=135000, so cost of 5000*4 or 20000=135000*4=540000
If the variable cost of 20000 is 540000, the constant cost will be the remaining that is 570000-540000=30000

B
_________________ Re: Each month, a certain manufacturing company's total expenses are equal   [#permalink] 14 Jul 2018, 20:00
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