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A manufacturer makes umbrellas at the cost of c dollars pe
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Updated on: 27 Feb 2013, 05:53
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60% (02:53) correct 40% (03:10) wrong based on 210 sessions
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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 belowcost rate of b dollars per umbrella and still make a 100% profit on its lot of x total umbrellas? A. \(\frac{b(2cr)}{(xr)}\) B. \(\frac{2x(cr)}{(br)}\) C. \(\frac{x(2cr)}{(br)}\) D. \(\frac{2b(cr)}{(xr)}\) E. \(\frac{2(xcr)}{(xr)}\)
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Originally posted by emmak on 27 Feb 2013, 04:16.
Last edited by Bunuel on 27 Feb 2013, 05:53, edited 1 time in total.
Edited the question.




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Re: A manufacturer makes umbrellas at the cost of c dollars pe
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27 Feb 2013, 04:27
emmak wrote: 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 belowcost rate of b dollars per umbrella and still make a 100% profit on its lot of x total umbrellas?
\(\frac{b(2cr)}{(xr)}\)
\(\frac{2x(cr)}{(br)}\)
\(\frac{x(2cr)}{(br)}\)
\(\frac{2b(cr)}{(xr)}\)
\(\frac{2(xcr)}{(xr)}\) Let "N" be the required answer., (x  N)r + Nb = 2xc xr  Nr + Nb = 2xc N(b  r) = x(2c  r) N = \(\frac{x(2cr)}{(br)}\) Answer is C
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Re: A manufacturer makes umbrellas at the cost of c dollars pe
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28 Feb 2013, 03:33
process of elimination + intuition x and r are not of the same nature (cost in dollar and total umbrellas) => eliminate A,D,E now, with some intuition, if retail price is less than cost, B would be negative => eliminate B Answer is C



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Re: A manufacturer makes umbrellas at the cost of c dollars pe
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11 Jan 2014, 08:36
emmak wrote: 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 belowcost rate of b dollars per umbrella and still make a 100% profit on its lot of x total umbrellas?
A. \(\frac{b(2cr)}{(xr)}\)
B. \(\frac{2x(cr)}{(br)}\)
C. \(\frac{x(2cr)}{(br)}\)
D. \(\frac{2b(cr)}{(xr)}\)
E. \(\frac{2(xcr)}{(xr)}\) Could anybody try smart numbers on this one? I'm having a tough time coming up with the solution Thanks! Cheers! J



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Re: A manufacturer makes umbrellas at the cost of c dollars pe
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13 Sep 2014, 16:44
leekay wrote: process of elimination + intuition x and r are not of the same nature (cost in dollar and total umbrellas) => eliminate A,D,E now, with some intuition, if retail price is less than cost, B would be negative => eliminate B Answer is C Good approach, but still I don´t understand how to choose between B and C.
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A manufacturer makes umbrellas at the cost of c dollars pe
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Updated on: 26 Feb 2019, 07:13
emmak wrote: 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 belowcost rate of b dollars per umbrella and still make a 100% profit on its lot of x total umbrellas?
A. \(\frac{b(2cr)}{(xr)}\)
B. \(\frac{2x(cr)}{(br)}\)
C. \(\frac{x(2cr)}{(br)}\)
D. \(\frac{2b(cr)}{(xr)}\)
E. \(\frac{2(xcr)}{(xr)}\) This is a tough one to use the INPUTOUTPUT 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 belowcost sale price is $0 per umbrella) So, the manufacturer made 10 umbrellas at the cost of $2 per umbrella. So the total cost = $20We 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 belowcost 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 2A. \(\frac{b(2cr)}{(xr)}\) = 0 ELIMINATE A B. \(\frac{2x(cr)}{(br)}\) = 12 ELIMINATE B C. \(\frac{x(2cr)}{(br)}\) = 2 KEEP C D. \(\frac{2b(cr)}{(xr)}\) = 0 ELIMINATE D E. \(\frac{2(xcr)}{(xr)}\) = 6 ELIMINATE E Answer : C Cheers, Brent
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Originally posted by GMATPrepNow on 22 Oct 2015, 11:39.
Last edited by GMATPrepNow on 26 Feb 2019, 07:13, edited 1 time in total.



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Re: A manufacturer makes umbrellas at the cost of c dollars pe
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22 Oct 2015, 11:40
MacFauz and I have demonstrated the two methods (Algebraic and InputOutput) for solving a question type I call Variables in the Answer Choices. If you'd like more information on these approaches, we have some free videos:  Variables in the Answer Choices  http://www.gmatprepnow.com/module/gmat ... /video/933  Tips for the Algebraic Approach  http://www.gmatprepnow.com/module/gmat ... /video/934  Tips for the InputOutput Approach  http://www.gmatprepnow.com/module/gmat ... /video/935 Cheers, Brent
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A manufacturer makes umbrellas at the cost of c dollars pe
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28 Feb 2017, 22:12
emmak wrote: 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 belowcost rate of b dollars per umbrella and still make a 100% profit on its lot of x total umbrellas?
A. \(\frac{b(2cr)}{(xr)}\)
B. \(\frac{2x(cr)}{(br)}\)
C. \(\frac{x(2cr)}{(br)}\)
D. \(\frac{2b(cr)}{(xr)}\)
E. \(\frac{2(xcr)}{(xr)}\) Official solution from Veritas Prep. Correct Answer: C For this problem, it is important to note that \(Profit = Revenue  Cost\). The profit needs to be equal the cost in order to make a 100% profit, so essentially the equation should then be \(Cost = Revenue  Cost\). The cost to the manufacturer is the number of units it makes, x, multiplied by the cost per unit, c, for a product of \(xc\). The revenue that the manufacturer will bring in has two components: the number it sells at the sale price of b multiplied by that price, b, and the rest of the umbrellas, which it sells at r, times r. If we call the number it is allowed to sell at a discount y, then we can solve for y to get our answer. That would make the revenue \(yb + (xy)r\). Therefore, the equation Cost = Revenue  Cost will be: \(xc = yb + (xy)r  xc\). Algebraically, we need to manipulate this equation to solve for y: \(xc = yb + (xy)r  xc\) \(xc = yb + xr  yr  xc\) distribute the multiplication to get y out of the parentheses \(2xc = yb + xr  yr\) add xc to both sides \(2xc  xr = yb  yr\) subtract xr from both sides to get the y terms on their own \(2xc  xr = y(b  r)\) factor the y to get it on its own \(\frac{(2xc−xr)}{(b−r)} = y\) divide both sides by \((b  r)\) to get y on its own \(x \frac{(2c−r)}{(b−r)} = y\) factor the x to make this equation look like the answer choices. Because the solution for y matches answer choice C, the answer is C.
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Re: A manufacturer makes umbrellas at the cost of c dollars pe
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25 Sep 2018, 22:44
emmak wrote: 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 belowcost rate of b dollars per umbrella and still make a 100% profit on its lot of x total umbrellas?
A. \(\frac{b(2cr)}{(xr)}\)
B. \(\frac{2x(cr)}{(br)}\)
C. \(\frac{x(2cr)}{(br)}\)
D. \(\frac{2b(cr)}{(xr)}\)
E. \(\frac{2(xcr)}{(xr)}\) Responding to a pm: Cost of x umbrellas = c*x Profit he intends to make is 100% i.e. = c*x So revenue must be = 2c*x Say, he sells N umbrellas at below cost rate of b and rest of (x  N) umbrellas at retail price of r dollars. \(2c*x = N*b + (x  N)*r\) \(N = \frac{(2cx  rx)}{(b  r)}\) Answer (C)
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Re: A manufacturer makes umbrellas at the cost of c dollars pe
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27 Sep 2018, 01:06
emmak wrote: 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 belowcost rate of b dollars per umbrella and still make a 100% profit on its lot of x total umbrellas?
A. \(\frac{b(2cr)}{(xr)}\)
B. \(\frac{2x(cr)}{(br)}\)
C. \(\frac{x(2cr)}{(br)}\)
D. \(\frac{2b(cr)}{(xr)}\)
E. \(\frac{2(xcr)}{(xr)}\) Had a very hard time understanding the above solutions... So I tried to put it into simpler terms: \(Profit = RevenueCosts\) \(Costs: c*x\) \(Profit = Revenue  cx\) Question stem tells us that the manufacturer needs to make a 100% profit. How do we get a 100% profit? Only when the profit is equal to the costs and the revenue is equal to 2 times the costs. \(cx = Revenue  cx\) \(cx = 2cx  cx\) Therefore the revenue the manufacturer needs to make is equal to \(2cx\)! Now setting up the real equation: Revenue (In terms of cost) = Revenue (In terms of below cost rate and normal cost rate) >\(2cx=\) Revenue below costs + Revenue normal costs Lets use N for the #of terms that sell below cost price. > \(2cx= N*b + (xN)*r\) >\(N = \frac{(2cx  rx)}{(b  r)}\)
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A manufacturer makes umbrellas at the cost of c dollars pe
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26 Feb 2019, 08:48
emmak wrote: 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 belowcost rate of b dollars per umbrella and still make a 100% profit on its lot of x total umbrellas?
A. \(\frac{b(2cr)}{(xr)}\)
B. \(\frac{2x(cr)}{(br)}\)
C. \(\frac{x(2cr)}{(br)}\)
D. \(\frac{2b(cr)}{(xr)}\)
E. \(\frac{2(xcr)}{(xr)}\) How many umbrellas can it afford to sell at the belowcost 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  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. .
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Re: A manufacturer makes umbrellas at the cost of c dollars pe
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01 Mar 2019, 10:49
emmak wrote: 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 belowcost rate of b dollars per umbrella and still make a 100% profit on its lot of x total umbrellas?
A. \(\frac{b(2cr)}{(xr)}\)
B. \(\frac{2x(cr)}{(br)}\)
C. \(\frac{x(2cr)}{(br)}\)
D. \(\frac{2b(cr)}{(xr)}\)
E. \(\frac{2(xcr)}{(xr)}\) Let y = the number of umbrellas the manufacturer sold below cost for b dollars each. Thus, by is the revenue from the belowcost 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 abovecost 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) Answer: C
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Re: A manufacturer makes umbrellas at the cost of c dollars pe
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