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100 points for $49 worth of Veritas practice GMATs FREE VERITAS PRACTICE GMAT EXAMS Earn 10 Points Per Post Earn 10 Points Per Thanks Earn 10 Points Per Upvote ## A manufacturer makes umbrellas at the cost of c dollars per tagged by: AAPL ##### This topic has 3 expert replies and 0 member replies ### Top Member ## A manufacturer makes umbrellas at the cost of c dollars per ## Timer 00:00 ## Your Answer A B C D E ## Global Stats Difficult Veritas Prep A manufacturer makes umbrellas at the cost of c dollars per umbrella, and sells them at the retail price of r dollars each. How many umbrellas can it afford to sell at the below-cost rate of b dollars per umbrella and still make a 100% profit on its lot of x total umbrellas? $$A.\ \frac{2\left(2c-r\right)}{\left(x-r\right)}$$ $$B.\ \frac{2x\left(c-r\right)}{\left(b-r\right)}$$ $$C.\ \frac{x\left(2c-r\right)}{\left(b-r\right)}$$ $$D.\ \frac{2b\left(c-r\right)}{\left(x-r\right)}$$ $$E.\ \frac{2\left(xc-r\right)}{\left(x-r\right)}$$ OA C ### GMAT/MBA Expert GMAT Instructor Joined 08 Dec 2008 Posted: 12975 messages Followed by: 1249 members Upvotes: 5254 GMAT Score: 770 AAPL wrote: Veritas Prep A manufacturer makes umbrellas at the cost of c dollars per umbrella, and sells them at the retail price of r dollars each. How many umbrellas can it afford to sell at the below-cost rate of b dollars per umbrella and still make a 100% profit on its lot of x total umbrellas? $$A.\ \frac{2\left(2c-r\right)}{\left(x-r\right)}$$ $$B.\ \frac{2x\left(c-r\right)}{\left(b-r\right)}$$ $$C.\ \frac{x\left(2c-r\right)}{\left(b-r\right)}$$ $$D.\ \frac{2b\left(c-r\right)}{\left(x-r\right)}$$ $$E.\ \frac{2\left(xc-r\right)}{\left(x-r\right)}$$ OA C This is a tough one to use the INPUT-OUTPUT approach, but here is goes: Let c =$2 (it cost $2 to make each umbrella) Let x = 10 (we make 10 umbrellas) Let r =$5 (the retail price is $5 per umbrella) Let b =$0 (the below-cost sale price is $0 per umbrella) So, the manufacturer made 10 umbrellas at the cost of$2 per umbrella. So the total cost = $20 We need a 100% profit. So, we must earn$40 in revenue. In other words, we must sell 8 umbrellas at $5 each. This means we can "sell" 2 umbrellas at the below-cost sale price of$0 each.

At this point, we must plug c = 2, x = 10, r = 5 and b = 0 into each expression and see which one yields an OUTPUT of 2

A. 2(2c-r)/(x-r) = -2/5 ELIMINATE A

B. 2x(c-r)/(b-r) = 12 ELIMINATE B

C. x(2c-r)/(b-r) = 2 KEEP C

D. 2b(c-r)/(x-r) = 0 ELIMINATE D

E. 2(xc-r)/(x-r) = 6 ELIMINATE E

Cheers,
Brent

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AAPL wrote:
Veritas Prep

A manufacturer makes umbrellas at the cost of c dollars per umbrella, and sells them at the retail price of r dollars each. How many umbrellas can it afford to sell at the below-cost rate of b dollars per umbrella and still make a 100% profit on its lot of x total umbrellas?
$$A.\ \frac{2\left(2c-r\right)}{\left(x-r\right)}$$
$$B.\ \frac{2x\left(c-r\right)}{\left(b-r\right)}$$
$$C.\ \frac{x\left(2c-r\right)}{\left(b-r\right)}$$
$$D.\ \frac{2b\left(c-r\right)}{\left(x-r\right)}$$
$$E.\ \frac{2\left(xc-r\right)}{\left(x-r\right)}$$
OA C
How many umbrellas can it afford to sell at the below-cost rate of b dollars per umbrella and still make a 100% profit?
If c=1 and r=2 -- implying that the cost per umbrella = $1 and that the retail price per umbrella =$2 -- then 100% profit will be yielded only if ALL of the umbrellas are sold at the retail price.
Since this case requires that NONE of the umbrellas be sold at a discount, the correct answer must yield a value of 0 when c=1 and r=2.
Only A and C are guaranteed to yield a value of 0 when c=1 and r=2.

Given c=1 and r=2, it is possible that x=2 umbrellas are sold at the retail price.
In A, x=2 and r=2 will yield a denominator of 0, rendering A invalid.

The correct answer is C.

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### GMAT/MBA Expert

GMAT Instructor
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AAPL wrote:
Veritas Prep

A manufacturer makes umbrellas at the cost of c dollars per umbrella, and sells them at the retail price of r dollars each. How many umbrellas can it afford to sell at the below-cost rate of b dollars per umbrella and still make a 100% profit on its lot of x total umbrellas?
$$A.\ \frac{2\left(2c-r\right)}{\left(x-r\right)}$$
$$B.\ \frac{2x\left(c-r\right)}{\left(b-r\right)}$$
$$C.\ \frac{x\left(2c-r\right)}{\left(b-r\right)}$$
$$D.\ \frac{2b\left(c-r\right)}{\left(x-r\right)}$$
$$E.\ \frac{2\left(xc-r\right)}{\left(x-r\right)}$$
OA C
Let y = the number of umbrellas the manufacturer sold below cost for b dollars each. Thus, by is the revenue from the below-cost part of the sale.

Since x is the total number of umbrellas sold, then he sold x - y umbrellas for r dollars each. Thus, r(x - y) is the revenue from the above-cost part of the sale. Since we want to have 100% profit, the revenue R has to be twice the cost:

R = 2c

by + r(x - y) = 2cx

by + rx - ry = 2cx

by - ry = 2cx - rx

y(b - r) = 2cx - rx

y = (2cx - rx)/(b - r)

y = x(2c - r)/(b - r)

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