A rental car agency purchases fleet vehicles in two sizes: a : GMAT Data Sufficiency (DS)
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# A rental car agency purchases fleet vehicles in two sizes: a

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Manager
Joined: 03 Aug 2010
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GMAT Date: 08-08-2011
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A rental car agency purchases fleet vehicles in two sizes: a [#permalink]

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02 Dec 2010, 13:14
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Question Stats:

79% (01:46) correct 21% (00:49) wrong based on 762 sessions

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A rental car agency purchases fleet vehicles in two sizes: a full-size car costs $10,000, and a compact costs$9,000. How many compact cars does the agency own?

(1) The agency owns 7 total cars.

(2) The agency paid $66,000 for its cars. [Reveal] Spoiler: OA Math Expert Joined: 02 Sep 2009 Posts: 37113 Followers: 7255 Kudos [?]: 96618 [11] , given: 10770 Re: Car Dealer - Data Sufficiency [#permalink] ### Show Tags 02 Dec 2010, 16:03 11 This post received KUDOS Expert's post 5 This post was BOOKMARKED Yalephd wrote: A rental car agency purchases fleet vehicles in two sizes: a full-size car costs$10,000, and a compact costs $9,000. How many compact cars does the agency own? (1) The agency owns 7 total cars. (2) The agency paid$66,000 for its cars.

Don't have the OA. I think this is an easy question but I am afraid that it might be deceptively simple. I just want to double check.

This is classic C-trap question. C-trap questions are the questions which are obviously sufficient if we take statements together. When we see such questions we should become very suspicious.

Let # of full-size car be F and # of compact cars be C. Question: C=?

(1) The agency owns 7 total cars --> F+C=7. Clearly insufficient to get C.

(2) The agency paid $66,000 for its cars --> 10,000F+9,000C=66,000 --> 10F+9C=66. Here comes the trap: generally such kind of linear equations (ax+by=c) have infinitely many solutions for x and y, and we cannot get single numerical values for the variables. But since F and C represent # of cars then they must be non-negative integers and in this case 10F+9C=66 is no longer simple linear equation it's Diophantine equation (equations whose solutions must be integers only) and for such kind on equations there might be only one combination of x and y (F and C in out case) possible to satisfy it. When you encounter such kind of problems you must always check by trial and error whether it's the case. Now, it's quite easy to check whether 10F+9C=66 has one or more solutions. 9C=66-10F so 66 minus multiple of 10 must be multiple of 9: 66 is not a multiple of 9; 56 is not; 46 is not; 36 IS A MULTIPLE OF 9 (F=3 and C=4); 26 is not; 16 is not and 6 is not. So only one combination of F and C satisfies equation 10F+9C=66, namely F=3 and C=4. Sufficient. Answer: B. For more on this type of questions check: eunice-sold-several-cakes-if-each-cake-sold-for-either-109602.html martha-bought-several-pencils-if-each-pencil-was-either-a-100204.html a-rental-car-agency-purchases-fleet-vehicles-in-two-sizes-a-105682.html joe-bought-only-twenty-cent-stamps-and-thirty-cent-stamps-106212.html a-certain-fruit-stand-sold-apples-for-0-70-each-and-bananas-101966.html joanna-bought-only-0-15-stamps-and-0-29-stamps-how-many-101743.html at-an-amusement-park-tom-bought-a-number-of-red-tokens-and-126814.html collections-confused-need-a-help-81062.html Hope it helps. _________________ Manager Joined: 03 Aug 2010 Posts: 106 GMAT Date: 08-08-2011 Followers: 1 Kudos [?]: 69 [0], given: 63 Re: Car Dealer - Data Sufficiency [#permalink] ### Show Tags 02 Dec 2010, 16:46 Thank you, Bunuel. I thought it was C. Your explanation was clear as always. Bunuel wrote: Yalephd wrote: A rental car agency purchases fleet vehicles in two sizes: a full-size car costs$10,000, and a compact costs $9,000. How many compact cars does the agency own? (1) The agency owns 7 total cars. (2) The agency paid$66,000 for its cars.

Don't have the OA. I think this is an easy question but I am afraid that it might be deceptively simple. I just want to double check.

This is classic C-trap question. C-trap questions are the questions which are obviously sufficient if we take statements together. When we see such questions we should become very suspicious.

Let # of full-size car be F and # of compact cars be C. Question: C=?

(1) The agency owns 7 total cars --> F+C=7. Clearly insufficient to get C.

(2) The agency paid $66,000 for its cars --> 10,000F+9,000C=66,000 --> 10F+9C=66. Here comes the trap: generally such kind of linear equations (ax+by=c) have infinitely many solutions for x and y, and we can not get single numerical values for the variables. But since F and C represent # of cars then they must be non-negative integers and in this case 10F+9C=66 is no longer simple linear equation it's Diophantine equation (equations whose solutions must be integers only) and for such kind on equations there might be only one combination of x and y (F and C in out case) possible to satisfy it. When you encounter such kind of problems you must always check by trial and error whether it's the case. Now, it's quite easy to check whether 10F+9C=66 has one or more solutions. 9C=66-10F so 66 minus multiple of 10 must be multiple of 9: 66 is not multiple of 9; 56 is not; 46 is not; 36 IS MULTIPLE OF 9 (F=3 and C=4); 26 is not; 16 is not and 6 is not. So only one combination of F and C satisfies equation 10F+9C=66, namely F=3 and C=4. Sufficient. Answer: B. Similar problems: gmat-prep2-92785.html?hilit=linear%20type Hope it helps. Veritas Prep GMAT Instructor Joined: 16 Oct 2010 Posts: 7187 Location: Pune, India Followers: 2170 Kudos [?]: 14036 [1] , given: 222 Re: Car Dealer - Data Sufficiency [#permalink] ### Show Tags 02 Dec 2010, 18:46 1 This post received KUDOS Expert's post 1 This post was BOOKMARKED In my blog post given below, I have discussed in detail how to find integer solutions to linear equations in 2 variables (i.e. equations such as this one) See if it helps. http://gmatquant.blogspot.com/2010/11/integral-solutions-of-ax-by-c.html _________________ Karishma Veritas Prep | GMAT Instructor My Blog Get started with Veritas Prep GMAT On Demand for$199

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Re: A rental car agency purchases fleet vehicles in two sizes: a [#permalink]

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31 May 2013, 04:43
Bumping for review and further discussion*. Get a kudos point for an alternative solution!

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Re: A rental car agency purchases fleet vehicles in two sizes: a [#permalink]

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31 May 2013, 21:16
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Yalephd wrote:
A rental car agency purchases fleet vehicles in two sizes: a full-size car costs $10,000, and a compact costs$9,000. How many compact cars does the agency own?

(1) The agency owns 7 total cars.

(2) The agency paid $66,000 for its cars. F.S 1 clearly insufficient. F.S 2 states that 10*f+9*c = 66 [f is the # full size cars;c of compact car] The only way in which we could get a 6 in the units digit for the RHS is through the factor 9*c --> 9*4 = 36. Thus, the no of compact cars = 4.Sufficient. B. _________________ Manager Joined: 27 Apr 2012 Posts: 62 Location: United States GMAT Date: 06-11-2013 GPA: 3.5 WE: Marketing (Consumer Products) Followers: 1 Kudos [?]: 53 [1] , given: 21 Re: A rental car agency purchases fleet vehicles in two sizes: a [#permalink] ### Show Tags 02 Jun 2013, 13:13 1 This post received KUDOS Stmt 1 : f + c = 7 …insufficient since we can not determine a specific number Stmt 2 : 10000f + 9000c = 66000 Dividing both sides by 1000 10f + 9c = 66 Since cars can only be represented by integers, we can set the following equation : 9c = 66 – 10f C = (66 – 10f)/9 We are looking for a number that is divisible by 9.We need to plug in numbers and arrive at a multiple of 9. C = (66 – 10*3)/9 = 36/9 = 4 Hence the number of compact cars owned is 4. Answer : B Intern Joined: 20 Jun 2011 Posts: 46 Followers: 1 Kudos [?]: 96 [0], given: 1 Re: A rental car agency purchases fleet vehicles in two sizes: a [#permalink] ### Show Tags 18 Nov 2013, 10:32 Alt.: st. 2) $10.000 \$9000 Total # of cars 7 0 70.000 6 1 69.000 5 2 68.000 4 3 67.000 3 4 66.000 ---> Bingo it matches
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Re: A rental car agency purchases fleet vehicles in two sizes: a [#permalink]

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20 Nov 2015, 20:01
Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

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Re: A rental car agency purchases fleet vehicles in two sizes: a [#permalink]

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08 Feb 2017, 03:46
Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
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Re: A rental car agency purchases fleet vehicles in two sizes: a   [#permalink] 08 Feb 2017, 03:46
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