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28 Jan 2020, 02:34
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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% _________________ Senior Manager Joined: 16 Feb 2015 Posts: 358 Location: United States Re: If John purchased goods for$1050, and sold 1/3rd of these goods at a  [#permalink]

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28 Jan 2020, 19:54
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% Explanation: 1/3rd of these goods at a loss of 12% = 350 * 0.88 =308 Gain on whole transaction of 18% = 1050 * 1.18 = 1239 Remaing Gain+Cost after 1/3rd of good cost = 1239 - 309 = 931 Gain % with remaing good cost = (931-700/700)x100 = 231/7 = 33% IMO-B GMATWhiz Representative Joined: 07 May 2019 Posts: 700 Location: India Re: If John purchased goods for$1050, and sold 1/3rd of these goods at a  [#permalink]

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28 Jan 2020, 21:22
Bunuel wrote:
If John purchased goods for $1050, and sold 1/3rd of these goods at a loss of 12%, then at what gain percent should remainder goods be sold to gain 18% on the whole transaction? A. 31% B. 33% C. 43% D. 67% E. 77% Solution: Cost price =$ 1050
Cost price of 1/3 of goods =$$1050* \frac{1}{3} =  350$$
Cost price of remaining goods = 1050 – 350 = 700$• 1/3 goods are sold at 12% loss o Loss =$$\frac{12}{100}*350$$ =$42
Overall profit we want = 18%
• Profit = $$\frac{18}{100}$$*1050 = $189 Profit on remaining goods =profit + overcoming the loss = 189 + 42 =$231
• Profit % = $$\frac{231}{700}$$ *100 = 33%
Hence the answer is Option B.
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If John purchased goods for $1050, and sold 1/3rd of these goods at a [#permalink] ### Show Tags 28 Jan 2020, 21:59 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%

Solution:
In this question, we are given percentage values and the answer is also asked in percentage. We can solve this question by assuming the cost price of $$\frac{1}{3}$$ of the goods to be $100 irrespective of what cost price is given in the question. By doing this we can avoid too many fractions here. Let the Cost price of $$\frac{1}{3}$$ goods =$ 100
• It is sold at 12% loss
o Loss = $$\frac{12}{100}$$*100= $12 Overall cost price = 3*cost of $$\frac{1}{3}$$ of the goods = 3*100=$300
• Overall profit we want = 18%
o Overall profit = $$\frac{18}{100}$$*300= $54 Cost price of remaining goods = 300-100=$200
• Profit = overall profit + overcoming the loss = 54 + 12 = $66 o Profit % = $$\frac{66}{200}$$*100= 33% Hence the answer is option B. _________________ GMAT Prep truly Personalized using Technology Prepare from an application driven course that serves real-time improvement modules along with a well-defined adaptive study plan. Start a free trial to experience it yourself and get access to 25 videos and 300 GMAT styled questions. Helpful Links Score Improvement Strategy: How to score Q50+ on GMAT | 5 steps to Improve your Verbal score Study Plan Articles: 3 mistakes to avoid while preparing | How to create a study plan? | The Right Order of Learning | Importance of Error Log Helpful Quant Strategies: Filling Spaces Method | Avoid Double Counting in P&C | The Art of Not Assuming anything in DS | Number Line Method Key Verbal Techniques: Plan-Goal Framework in CR | Quantifiers the tiny Game-changers | Countable vs Uncountable Nouns | Tackling Confusing Words in Main Point GMATWhiz Representative Joined: 07 May 2019 Posts: 700 Location: India Re: If John purchased goods for$1050, and sold 1/3rd of these goods at a  [#permalink]

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28 Jan 2020, 22:31
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% Solution: The shortest and fastest way to solve this problem is by the weighted average method. • $$\frac{1}{3}$$ of the goods are sold at 12% loss. • Let the profit of remaining $$\frac{2}{3}$$ of the goods be x%. o The ratio of$$\frac{ 1}{3}$$ and$$\frac{ 2}{3 }$$= 1: 2 We want the overall profit of 18% We can form the equation as shown below: • $$\frac{1*-12\% + 2*x\%}{3}$$=18% o -12+ 2x = 54 o 2x = 66 o x =33 Hence, the correct answer is Option B. Note- We solved this question without even using the cost price given in the question, this is because the values are given in percentage terms and the answer is also asked in percentage. _________________ GMAT Prep truly Personalized using Technology Prepare from an application driven course that serves real-time improvement modules along with a well-defined adaptive study plan. Start a free trial to experience it yourself and get access to 25 videos and 300 GMAT styled questions. Helpful Links Score Improvement Strategy: How to score Q50+ on GMAT | 5 steps to Improve your Verbal score Study Plan Articles: 3 mistakes to avoid while preparing | How to create a study plan? | The Right Order of Learning | Importance of Error Log Helpful Quant Strategies: Filling Spaces Method | Avoid Double Counting in P&C | The Art of Not Assuming anything in DS | Number Line Method Key Verbal Techniques: Plan-Goal Framework in CR | Quantifiers the tiny Game-changers | Countable vs Uncountable Nouns | Tackling Confusing Words in Main Point Manager Joined: 14 Sep 2019 Posts: 222 Re: If John purchased goods for$1050, and sold 1/3rd of these goods at a  [#permalink]

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28 Jan 2020, 23:00
Total cost price = 1050
Cost price of 1/3 = 1050*(1/3) = 350 and

Selling price of 350 at a loss of 12% = 350*(88/100) = 308
Selling price of 1050 at 18% gain = 1050*(118/100) = 1239

Selling price of remaining cost price of 700 = 1239-308 = 931
Gain percentage of the remainder = (SP- CP)/CP = (931-700)*100/700 = (231/700)*100 = 231/7% = 33% (B)
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If John purchased goods for $1050, and sold 1/3rd of these goods at a [#permalink] ### Show Tags 28 Jan 2020, 23:27 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%

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 = $$[(266 - 200)/200] * 100 = 33%$$

Alternate 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) Admissions Consulting: http://www.oneclickprep.com/admissions-consulting/ 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 _________ Feel free to talk to me about GMAT & GRE | Ask me any question on QA (PS / DS) | Let's converse! Skype: sk_datta, Alt. Email: sujoy.datta@gmail.com VP Joined: 18 Dec 2017 Posts: 1360 Location: United States (KS) GMAT 1: 600 Q46 V27 Re: If John purchased goods for$1050, and sold 1/3rd of these goods at a  [#permalink]

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06 Feb 2020, 04:50
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% We don't need to calculate the units and technically the 1050 is irrelevant. One unit at loss of 12 is -12 and 2 units lets say at the profit of 33 is 66. The resultant value is 66-12=54/3units = 18 Thats what we want. Option B. _________________ The Moment You Think About Giving Up, Think Of The Reason Why You Held On So Long Why You Don’t Deserve A 700 On Your GMAT Learn from the Legend himself: All GMAT Ninja LIVE YouTube videos by topic You are missing on great learning if you don't know what this is: Project SC Butler Re: If John purchased goods for$1050, and sold 1/3rd of these goods at a   [#permalink] 06 Feb 2020, 04:50