ACME’s manufacturing costs for sets of horseshoes

Question

ACME’s manufacturing costs for sets of horseshoes include a $11,450 initial outlay, and $19.75 per set. They can sell the sets $52.50. If profit is revenue from sales minus manufacturing costs, and the company produces & sells 987 sets of horseshoes, what was their profit?
(A) $20,874.25
(B) $30,943.25
(C) $41,308.50
(D) $51,817.50
(E) $53,624.25

Unless you're Johannes Kepler or Will Hunting, you probably would not be able to do that exact calculation in your head, and of course you get no calculator on the GMAT. With estimation, though, this is a remarkably simple question. For more on the power of estimation on the GMAT, as well as an elegant solution to this question, see:
https://magoosh.com/gmat/2012/the-power- ... mat-quant/

Experts, what wisdom and specific tips would you like to share about estimation on the GMAT Quantitative section?

Mike :-)

Narenn · Answer

its A

since options are not so close we can solve this by uniting calculation and guessing

total sales will be bit lower than 52500

from that initial outlay will get deducted 11500 so we left with 41000

variable cost say 20 X 1000 = 20000 will be deducted so finally we left with 21000

since we have considered the price greater than it actually is, the correct answer will certainly not cross the threshold of 21000.

@Mike Sir
Thanks for sharing the link.

Regards,

Abhijit

PareshGmat · Answer

The OA in this problem have a great variation; so we can use approximation

19.75 \approx {20}

52.50 \approx {50}

987 \approx {1000}

Total Cost Price = 11450 + 20*1000 \approx{31000}

Total Sell Price  = 1000*50 \approx {50000}

Profit \approx {20000}

Answer = A

BrentGMATPrepNow · Answer

Here's a slight twist:

It COSTS $19.75 per set, and each set is SOLD for $52.50
So, the company makes approximately $33 per set ($52.50 - $19.75 ≈ $33)

The company sold 987 sets. 
So, the profit ≈ ($33)(1000) ≈$33,000

Keep in mind, that there's also the initial outlay of $11,450

So, the TOTAL PROFIT ≈$33,000 - $11,450
≈ $21,500

The best (closest) answer is A

Cheers,
Brent

fskilnik · Answer

The alternative choices ARE far apart (except the last two ones), therefore we are allowed to use (always carefully!) approximations (to be reconsidered ONLY if we come close to $50,000) !!

? = {\rm{revenue}} - {\rm{costs}}\,\,\,\,\,\,\left( {{\rm{987}}\,\,{\rm{sets}}} \right)

{\rm{revenue}} = 987\,\,sets\,\,\left( {{{\$ 52{1 \over 2}} \over {1\,\,{\rm{set}}}}} \right)\,\,\,\, \cong \,\,\,\$ 990 \cdot 52

{\rm{costs}}\,\,\,{\rm{ = }}\,\,\,{\rm{11450 + }}987\,\,sets\,\,\left( {{{\$ 19{3 \over 4}} \over {1\,\,{\rm{set}}}}} \right)\,\,\,\, \cong \,\,\,\$ \left( {11450 + 990 \cdot 20} \right)

? \cong \,10 \cdot 99 \cdot \left( {52 - 20} \right) - 11450 \cong 10 \cdot 100 \cdot 32 - 11450 \cong 21000\,\,\left( \$ \right)

This solution follows the notations and rationale taught in the GMATH method.

Regards, 
fskilnik.

ScottTargetTestPrep · Answer

The profit is:

987(52.50) -

987(52.50) - 11,450 - 987(19.75)

987(52.50 - 19.75) - 11,450

987(32.75) - 11,450

At this point, we will approximate 987 as 1,000 and 32.75 as 32. So the approximate total profit is:

1,000(32) - 11,450

32,000 - 11,450

20,550

We see that this is closest to 20,874.25 in choice A.

Alternate Solution:

Let’s round all the numbers. From the final statement of the problem, we know we’ll sell about 1,000 sets. The initial outlay is about 12,000 and manufacturing costs are about (20) (1000) = 20,000. Thus, costs are about 32,000. Revenue is a bit greater than (50)(1000) = 50,000. Thus, revenue - cost = 50,000 - 32,000 = 18,000. Thus, profit is a bit greater than $18,000.

Answer: A

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ACME’s manufacturing costs for sets of horseshoes

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ACME’s manufacturing costs for sets of horseshoes

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