Author 
Message 
TAGS:

Hide Tags

Math Expert
Joined: 02 Sep 2009
Posts: 44388

Question Stats:
71% (01:32) correct 29% (01:58) wrong based on 112 sessions
HideShow timer Statistics
A car dealership sold two cars: the first car at a 10% profit and the second car at a 10% loss, which gave them an overall profit of 5% from these two sales. If the dealership's total profit was $1000, what was the cost price of each car? A. $5,000 and $1,000 B. $9,000 and $5,000 C. $11,000 and $9,000 D. $15,000 and $5,000 E. $20,000 and $10,000
Official Answer and Stats are available only to registered users. Register/ Login.
_________________
New to the Math Forum? Please read this: Ultimate GMAT Quantitative Megathread  All You Need for Quant  PLEASE READ AND FOLLOW: 12 Rules for Posting!!! Resources: GMAT Math Book  Triangles  Polygons  Coordinate Geometry  Factorials  Circles  Number Theory  Remainders; 8. Overlapping Sets  PDF of Math Book; 10. Remainders  GMAT Prep Software Analysis  SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS)  Tricky questions from previous years.
Collection of Questions: PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.
What are GMAT Club Tests? Extrahard Quant Tests with Brilliant Analytics



Math Expert
Joined: 02 Sep 2009
Posts: 44388

Official Solution:A car dealership sold two cars: the first car at a 10% profit and the second car at a 10% loss, which gave them an overall profit of 5% from these two sales. If the dealership's total profit was $1000, what was the cost price of each car? A. $5,000 and $1,000 B. $9,000 and $5,000 C. $11,000 and $9,000 D. $15,000 and $5,000 E. $20,000 and $10,000 Since 5% profit equals to $1,000 of profit, then total cost price of two cars was $20,000 (\(0.05*x=1,000\) giving \(x=20,000\)). Now, options C and D both fit. Let's check one of them: C. $11,000 and $9,000. The profit from the first car would be \(0.1*\$11,000=\$1,100\) and the loss from the second car would be \(0.1*\$9,000=\$900\). So, the overall profit would be \($1,100$900=$200 \ne $1,000\). So, the answer must be D. Answer: D
_________________
New to the Math Forum? Please read this: Ultimate GMAT Quantitative Megathread  All You Need for Quant  PLEASE READ AND FOLLOW: 12 Rules for Posting!!! Resources: GMAT Math Book  Triangles  Polygons  Coordinate Geometry  Factorials  Circles  Number Theory  Remainders; 8. Overlapping Sets  PDF of Math Book; 10. Remainders  GMAT Prep Software Analysis  SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS)  Tricky questions from previous years.
Collection of Questions: PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.
What are GMAT Club Tests? Extrahard Quant Tests with Brilliant Analytics



Intern
Joined: 06 Jan 2013
Posts: 11
Location: United States
Concentration: Finance, Economics
GMAT Date: 11152013
GPA: 3.5
WE: Education (Education)

Re: M0332 [#permalink]
Show Tags
07 Oct 2014, 02:45
1
This post was BOOKMARKED
Is it valid to set this up as a weighted average? If the overall % gain was 5% then we could solve this as:
(+10)x + (15)y = 0 yielding that x = 3y. The only combination of prices which matches the ratio is (D)



Math Expert
Joined: 02 Sep 2009
Posts: 44388

Re: M0332 [#permalink]
Show Tags
07 Oct 2014, 03:23



Intern
Joined: 20 Apr 2015
Posts: 4

Re: M0332 [#permalink]
Show Tags
02 Jun 2015, 17:15
1
This post received KUDOS
Bunuel wrote: imperfectdark wrote: Is it valid to set this up as a weighted average? If the overall % gain was 5% then we could solve this as:
(+10)x + (15)y = 0 yielding that x = 3y. The only combination of prices which matches the ratio is (D) Yes, that's correct. Hi Bunuel, can you elaborate more about how we go about setting up the weighted average equation? Thanks.



Current Student
Joined: 12 Aug 2015
Posts: 296
Concentration: General Management, Operations
GMAT 1: 640 Q40 V37 GMAT 2: 650 Q43 V36 GMAT 3: 600 Q47 V27
GPA: 3.3
WE: Management Consulting (Consulting)

1
This post received KUDOS
josegf1987 wrote: Bunuel wrote: imperfectdark wrote: Is it valid to set this up as a weighted average? If the overall % gain was 5% then we could solve this as:
(+10)x + (15)y = 0 yielding that x = 3y. The only combination of prices which matches the ratio is (D) Yes, that's correct. Hi Bunuel, can you elaborate more about how we go about setting up the weighted average equation? Thanks. Hi this shortcut looks the following way: please the pic. 1. Draw a number line and place values (5 is midpoint, Y is 15 points from the midpoint because it is a loss) 2. The closer to average the greater the weight (X is greater that Y) 3. Configure a proportion where X gets the corresponding value (greater value because weight is greater) 4. X relates to Y just the same way as 15 relates to 5, because X weighs more than Y. 5. Only answer D matches our fraction 15:5
>> !!!
You do not have the required permissions to view the files attached to this post.
_________________
KUDO me plenty
Last edited by shasadou on 08 Sep 2015, 08:58, edited 2 times in total.



Current Student
Joined: 12 Aug 2015
Posts: 296
Concentration: General Management, Operations
GMAT 1: 640 Q40 V37 GMAT 2: 650 Q43 V36 GMAT 3: 600 Q47 V27
GPA: 3.3
WE: Management Consulting (Consulting)

hi an algebraic solution + back solving: 1. We are given that we derived profit from sale of car 1 that translates into 10% of cost1 or 0.1*cost1. We are given that we encountered loss on a standalone sale of the other car: (10% of cost2)  eventually (0.1 * cost2)2. We are also given that the toal profits sums up to: 1000 = 0.1*c1 + (0.1*c2) 3. Now let us test the values the answers provide to us. I usually start with C: 0.1 of 11 000 = 1 100 (profit) and 0.1 of 9 000 is 900 (loss). The sum is 1 100  900 = 200. INCORRECT. D: 10% of 15 000 is 1 500 (gain). 10% of 5 000 is 500 (loss). This sums up to 1500  500 = 1000. CORRECT
_________________
KUDO me plenty



Verbal Forum Moderator
Joined: 15 Apr 2013
Posts: 195
Location: India
Concentration: General Management, Marketing
GMAT Date: 11232015
GPA: 3.6
WE: Science (Other)

Re: M0332 [#permalink]
Show Tags
25 Oct 2015, 01:47
1
This post was BOOKMARKED
Hello Bunuel,
Thanks for a very good question.
Don't you feel question needs rewording for better clarity:
......Overall profit of 5% from these two sales. If the dealership's total profit was $1000....
While reading through the question I interpreted it at 5% of profits from two sales and Total profits were $1000.
Hence amount of profit from two sales 50 (5% of 1000).
Please suggest.



Intern
Joined: 04 Sep 2015
Posts: 6

Re M0332 [#permalink]
Show Tags
27 Jan 2016, 23:28
I think this is a poorquality question and the explanation isn't clear enough, please elaborate.



Math Expert
Joined: 02 Sep 2009
Posts: 44388

Re: M0332 [#permalink]
Show Tags
27 Jan 2016, 23:34



Intern
Joined: 04 Sep 2015
Posts: 6

Re: M0332 [#permalink]
Show Tags
27 Jan 2016, 23:50
Hi Bunuel,
sorry I just clicked on the feedback button of the question. I think I probably misunderstood the question stem. Are the 20,000 the total sales price of the cars? And don't I have to calculate the profit/loss of each car like that: 1,1x=15,000 =>~13,636 => 15,000  13,636 is the actual profit of this car?
Thanks for your Support.



Math Expert
Joined: 02 Sep 2009
Posts: 44388

Re: M0332 [#permalink]
Show Tags
28 Jan 2016, 02:18
Erina89 wrote: Hi Bunuel,
sorry I just clicked on the feedback button of the question. I think I probably misunderstood the question stem. Are the 20,000 the total sales price of the cars? And don't I have to calculate the profit/loss of each car like that: 1,1x=15,000 =>~13,636 => 15,000  13,636 is the actual profit of this car?
Thanks for your Support. Profit and loss are on costs price. So, $20,000 was total cost price of two cars.
_________________
New to the Math Forum? Please read this: Ultimate GMAT Quantitative Megathread  All You Need for Quant  PLEASE READ AND FOLLOW: 12 Rules for Posting!!! Resources: GMAT Math Book  Triangles  Polygons  Coordinate Geometry  Factorials  Circles  Number Theory  Remainders; 8. Overlapping Sets  PDF of Math Book; 10. Remainders  GMAT Prep Software Analysis  SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS)  Tricky questions from previous years.
Collection of Questions: PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.
What are GMAT Club Tests? Extrahard Quant Tests with Brilliant Analytics



Manager
Joined: 05 Jul 2015
Posts: 106
Concentration: Real Estate, International Business
GPA: 3.3

Re: M0332 [#permalink]
Show Tags
25 Feb 2016, 14:07
With the Allegation method this question takes 2 seconds.
+10____5____10
The distance from average is 5:15.



Manager
Joined: 23 Jun 2009
Posts: 197
Location: Brazil
GMAT 1: 470 Q30 V20 GMAT 2: 620 Q42 V33

My approach was
0.1*x0.1*y=0.5*(x+y)
.05x=.15y
x=3y
which one of the options proves the equation above? Just D
15=3*5
Last edited by felippemed on 01 Aug 2016, 06:13, edited 1 time in total.



Manager
Joined: 23 Jun 2009
Posts: 197
Location: Brazil
GMAT 1: 470 Q30 V20 GMAT 2: 620 Q42 V33

Re: M0332 [#permalink]
Show Tags
01 Aug 2016, 06:06
Bunuel wrote: Official Solution:
Since 5% profit equals to $1,000 of profit, then total cost price of two cars was $20,000 (\(0.05*x=1,000\) giving \(x=20,000\)).
Hi Bunuel, Can I suggest an edition to your answer explanation? The passage above would be more clear if you had used (\(0.05*(x+y)=1,000\) giving \(x+y=20,000\)) then the following "C and D are the only possible answers" would be also more clear since, x + y = 20 then, 15 + 5 = 20 and 11 + 9 = 20



Current Student
Joined: 08 Jan 2015
Posts: 86

Re: M0332 [#permalink]
Show Tags
09 Aug 2016, 23:24
Bunuel wrote: Erina89 wrote: Hi Bunuel,
sorry I just clicked on the feedback button of the question. I think I probably misunderstood the question stem. Are the 20,000 the total sales price of the cars? And don't I have to calculate the profit/loss of each car like that: 1,1x=15,000 =>~13,636 => 15,000  13,636 is the actual profit of this car?
Thanks for your Support. Profit and loss are on costs price. So, $20,000 was total cost price of two cars. Bunuel, I agree with Erina, that the question stem is quiet confusing. There should be an indication that the profit/loss is on the cost price, and not the sale price, or the question should be somehow restated. The reasoning is that profit, which in this case, I guess, means profit margin, is always on the sale price. I haven't met profit on the cost price, since it doesn't make sense.



Intern
Joined: 16 Dec 2016
Posts: 2

Re: M0332 [#permalink]
Show Tags
22 Dec 2016, 16:20
1
This post received KUDOS
I am doing mathematical approach.
1. 1.1x + 0.9y = 1.05(x+y) 2. 0.05(x+y) = 1,000
if you solve the two equations above, you will get x=15,000 y=5,000



Intern
Joined: 15 Dec 2016
Posts: 2
Location: India
GPA: 3.5
WE: Marketing (Real Estate)

Re: M0332 [#permalink]
Show Tags
18 Mar 2017, 22:18
Hello friends, sharing with you the pure algebraic approach. Let A & B be two cars. As per the given info, we can deduce two equations. As per the profit, which is 10% of A  10% of B = 1000 that is 0.1A  0.1B = 1000, Multiplying the above equation we get that A  B = 10,000. 5% of total cost of A & B = 1000. So, 100% of the cost is 20,000. OR 5/100 = 1000/x, then x=20,000. OR 0.5(A+B) = 1000, A+B = 20,000. Now we have two equations A+B = 20,000 & AB = 10,000 Solving those we get that A = 15,000 That is one of the options so no need to solve for B. CORRECT ANSWER D. If it helped you then quickly hit that +Kudos button



Intern
Joined: 23 Oct 2013
Posts: 4
WE: Consulting (Law)

Re: M0332 [#permalink]
Show Tags
20 Mar 2017, 21:25
Hi I was so confused with the question. $20,000 should be the sale price of both cars (cause including 5% profit). So, the question should be finding the sale price of each car (not sale price). Please help make it clear. Thanks



Math Expert
Joined: 02 Sep 2009
Posts: 44388

Re: M0332 [#permalink]
Show Tags
21 Mar 2017, 04:05







Go to page
1 2
Next
[ 29 posts ]



