Jul 20 07:00 AM PDT  09:00 AM PDT Attend this webinar and master GMAT SC in 10 days by learning how meaning and logic can help you tackle 700+ level SC questions with ease. Jul 21 07:00 AM PDT  09:00 AM PDT Attend this webinar to learn a structured approach to solve 700+ Number Properties question in less than 2 minutes Jul 26 08:00 AM PDT  09:00 AM PDT The Competition Continues  Game of Timers is a teambased competition based on solving GMAT questions to win epic prizes! Starting July 1st, compete to win prep materials while studying for GMAT! Registration is Open! Ends July 26th Jul 27 07:00 AM PDT  09:00 AM PDT Learn reading strategies that can help even nonvoracious reader to master GMAT RC
Author 
Message 
TAGS:

Hide Tags

Manager
Joined: 03 Aug 2010
Posts: 89
GMAT Date: 08082011

A rental car agency purchases fleet vehicles in two sizes: a
[#permalink]
Show Tags
02 Dec 2010, 14:14
Question Stats:
80% (01:08) correct 20% (01:03) wrong based on 1298 sessions
HideShow timer Statistics
A rental car agency purchases fleet vehicles in two sizes: a fullsize 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.
Official Answer and Stats are available only to registered users. Register/ Login.




Math Expert
Joined: 02 Sep 2009
Posts: 56300

Re: Car Dealer  Data Sufficiency
[#permalink]
Show Tags
02 Dec 2010, 17:03
Yalephd wrote: A rental car agency purchases fleet vehicles in two sizes: a fullsize 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 Ctrap question. Ctrap 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 fullsize 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 nonnegative 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=6610F 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: eunicesoldseveralcakesifeachcakesoldforeither109602.htmlmarthaboughtseveralpencilsifeachpencilwaseithera100204.htmlarentalcaragencypurchasesfleetvehiclesintwosizesa105682.htmljoeboughtonlytwentycentstampsandthirtycentstamps106212.htmlacertainfruitstandsoldapplesfor070eachandbananas101966.htmljoannaboughtonly015stampsand029stampshowmany101743.htmlatanamusementparktomboughtanumberofredtokensand126814.htmlcollectionsconfusedneedahelp81062.htmlHope it helps.
_________________




Manager
Joined: 03 Aug 2010
Posts: 89
GMAT Date: 08082011

Re: Car Dealer  Data Sufficiency
[#permalink]
Show Tags
02 Dec 2010, 17:46
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 fullsize 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 Ctrap question. Ctrap 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 fullsize 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 nonnegative 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=6610F 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: gmatprep292785.html?hilit=linear%20typeHope it helps.



Veritas Prep GMAT Instructor
Joined: 16 Oct 2010
Posts: 9443
Location: Pune, India

Re: Car Dealer  Data Sufficiency
[#permalink]
Show Tags
02 Dec 2010, 19:46
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/integralsolutionsofaxbyc.html
_________________
Karishma Veritas Prep GMAT Instructor
Learn more about how Veritas Prep can help you achieve a great GMAT score by checking out their GMAT Prep Options >



Math Expert
Joined: 02 Sep 2009
Posts: 56300

Re: A rental car agency purchases fleet vehicles in two sizes: a
[#permalink]
Show Tags
31 May 2013, 05:43
Bumping for review and further discussion*. Get a kudos point for an alternative solution! *New project from GMAT Club!!! Check HERE
_________________



Verbal Forum Moderator
Joined: 10 Oct 2012
Posts: 604

Re: A rental car agency purchases fleet vehicles in two sizes: a
[#permalink]
Show Tags
31 May 2013, 22:16
Yalephd wrote: A rental car agency purchases fleet vehicles in two sizes: a fullsize 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: 57
Location: United States
GMAT Date: 06112013
GPA: 3.5
WE: Marketing (Consumer Products)

Re: A rental car agency purchases fleet vehicles in two sizes: a
[#permalink]
Show Tags
02 Jun 2013, 14:13
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: 44

Re: A rental car agency purchases fleet vehicles in two sizes: a
[#permalink]
Show Tags
18 Nov 2013, 11:32
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 



Manager
Joined: 02 Jan 2017
Posts: 71
Location: Pakistan
Concentration: Finance, Technology
GPA: 3.41
WE: Business Development (Accounting)

Re: A rental car agency purchases fleet vehicles in two sizes: a
[#permalink]
Show Tags
15 Dec 2017, 08:14
VeritasPrepKarishma wrote: 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/integralsolutionsofaxbyc.htmlYour blog posts in comments are always helpful, thankyou.



Intern
Joined: 09 Feb 2018
Posts: 1

Re: A rental car agency purchases fleet vehicles in two sizes: a
[#permalink]
Show Tags
11 Feb 2018, 09:34
Bunuel wrote: Bumping for review and further discussion*. Get a kudos point for an alternative solution! We know that X and Y must be integers and prices are 9.000 or 10.000 Regardless the tens of thousand number, the only way to obtain 6 is if we sold 104 cars at 9.000 so we have 4 times 9.000 = 36.000 thus we can determine X which is 3. So B is sufficient while A is not as said in other posts. Not sure how clear it is but in my head it goes quicker to do 104 = 6 so I need 6 * 9.000 than trying to find for which value we have a multiple of 9



Manager
Joined: 21 Jul 2018
Posts: 193

Re: A rental car agency purchases fleet vehicles in two sizes: a
[#permalink]
Show Tags
05 Oct 2018, 03:28
Does C trap question like this does really fall under sub600 level? BunuelBunuel wrote: Yalephd wrote: A rental car agency purchases fleet vehicles in two sizes: a fullsize 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 Ctrap question. Ctrap 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 fullsize 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 nonnegative 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=6610F 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: http://gmatclub.com/forum/eunicesolds ... 09602.htmlhttp://gmatclub.com/forum/marthabought ... 00204.htmlhttp://gmatclub.com/forum/arentalcar ... 05682.htmlhttp://gmatclub.com/forum/joeboughton ... 06212.htmlhttp://gmatclub.com/forum/acertainfru ... 01966.htmlhttp://gmatclub.com/forum/joannabought ... 01743.htmlhttp://gmatclub.com/forum/atanamuseme ... 26814.htmlhttp://gmatclub.com/forum/collectionsc ... 81062.htmlHope it helps.
_________________
______________________________ Press +1 Kudos if my post helped you a little and help me to ulcock the tests Wish you all success I'd appreciate learning about the grammatical errors in my posts
Please let me know if I'm wrong somewhere and help me to learn



Math Expert
Joined: 02 Sep 2009
Posts: 56300

Re: A rental car agency purchases fleet vehicles in two sizes: a
[#permalink]
Show Tags
05 Oct 2018, 05:45
parthos wrote: Does C trap question like this does really fall under sub600 level? BunuelBunuel wrote: Yalephd wrote: A rental car agency purchases fleet vehicles in two sizes: a fullsize 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 Ctrap question. Ctrap 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 fullsize 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 nonnegative 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=6610F 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: http://gmatclub.com/forum/eunicesolds ... 09602.htmlhttp://gmatclub.com/forum/marthabought ... 00204.htmlhttp://gmatclub.com/forum/arentalcar ... 05682.htmlhttp://gmatclub.com/forum/joeboughton ... 06212.htmlhttp://gmatclub.com/forum/acertainfru ... 01966.htmlhttp://gmatclub.com/forum/joannabought ... 01743.htmlhttp://gmatclub.com/forum/atanamuseme ... 26814.htmlhttp://gmatclub.com/forum/collectionsc ... 81062.htmlHope it helps. The difficulty level of a question is calculated automatically based on the timer stats from the users which attempted the question. So our stats say that it's sub600 level.
_________________



Retired Moderator
Joined: 23 May 2018
Posts: 487
Location: Pakistan

A rental car agency purchases fleet vehicles in two sizes: a
[#permalink]
Show Tags
07 Oct 2018, 03:20
Yalephd wrote: A rental car agency purchases fleet vehicles in two sizes: a fullsize 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. (1) It could be any combination for the two. INSUFFICIENT(2) For $66,000, a maximum of 6 fullsize cars can be bought but that will leave only $6,000 and a compact car is of $9,000. This cannot be the combinationIf 5 full size cars are bought, that leaves $16,000. 1 compact car can be bought and $7,000 This cannot be the combinationIf 4 full size cars are bought, that leaves $26,000. 2 compact cars can be bought and $8,000 This cannot be the combinationIf 3 full size cars are bought, that leaves $36,000. 4 compact cars can be bought with no remaining amount This is the combination we are looking forTherefore, B is the answer
_________________
If you can dream it, you can do it.
Practice makes you perfect.
Kudos are appreciated.




A rental car agency purchases fleet vehicles in two sizes: a
[#permalink]
07 Oct 2018, 03:20






