Bunuel wrote:

If John purchased goods for $1050, and sold 1/3rd of these goods at a loss of 12%, then at what gain percent should remainder goods be sold to gain 18% on the whole transaction?

A. 31%

B. 33%

C. 43%

D. 67%

E. 77%

Understand that the question is asking about

gain PERCENT.

To determine a percentage value, we can, actually ignore the $1050 information and solve it using any suitable value as well, say $300 instead (this makes the calculations way easier). Let us see:

Let the total purchase price be $300

Thus, purchase price of \(1/3rd\) of these = \(1/3 * $300 = $100\)

Loss incurred = 12%

=> Selling price of these \(1/3rd\) goods = $88

Required gain overall = 18%

=> Required TOTAL selling price = \(118% of $300 = $354\)

Thus, selling price of the remaining \((1 - 1/3 =) 2/3rd\) goods = \($(354 - 88) = $266\)

Purchase price of this stock of \(2/3rd\) goods = \(2/3 * $300 = $200\)

=> Required percent profit = \([(266 - 200)/200] * 100 = 33%\)

Answer BAlternate approach: Now that we are clear that the actual price of $1050 is NOT necessary, let us try to solve this using a method where we do NOT need to assume any values at all!

Let us look at the data available:

You have some goods (Note: the cost price per unit is the SAME since the goods are identical)

You sell \(1/3rd\) making 12% loss =>

Net contribution = \(1/3 * (-12) = -4\)

You need to make overall 18% profit =>

Net overall = \(+18\)

Thus, contribution required from the remaining \(2/3rd\) = \(18 - (-4) = 22\)

(Note: If we add 22 with '-4', only then we get 18)

Thus, from the \(2/3rd\) stock, you intend to get a contribution of 22

=> Required profit % of this remaining \(2/3rd\) stock = \(22/(2/3) = 22 * 3/2\) =

33%[Relate to the first step: 2/3rd making 33% gain => Net contribution = 2/3 * (+33) = +22]

Voila! A simple 30 second approach to solve this question

_________________

Sujoy Kumar Datta

Director - CUBIX Educational Institute Pvt. Ltd. (https://www.cubixprep.com)

IIT Kharagpur, TU Dresden Germany

Linked-in:

https://www.linkedin.com/in/sujoy-kumar-datta/GMAT - Q51 & CAT (MBA @ IIM) 99.98 Overall with 99.99 QA

Ask me anything about GMAT Quant_________

Feel free to talk to me about GMAT & GRE | Ask me any question on QA (PS / DS)

Let's converse!

Skype: sk_dattaAlt. Email: sujoy.datta@gmail.com