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In a network of car dealerships, a group of d sales director

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In a network of car dealerships, a group of d sales director [#permalink]  22 Apr 2013, 20:57
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In a network of car dealerships, a group of d sales directors each has a team of a sales associates. In a given month, if the directors each sold 10 cars and each sales associate sold 20 cars, and all cars were sold by either a sales director or a sales associate, how many people total sold cars?

(1) The total number of cars sold was 270

(2) a > d > 2
[Reveal] Spoiler: OA

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Last edited by Bunuel on 17 Sep 2013, 23:23, edited 1 time in total.
Edited the question and the OA.
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Re: n a network of car dealerships, a group of d sales [#permalink]  22 Apr 2013, 21:25
In a network of car dealerships, a group of d sales directors each has a team of a sales associates. In a given month, if the directors each sold 10 cars and each sales associate sold 20 cars, and all cars were sold by either a sales director or a sales associate, how many people total sold cars?

(1) The total number of cars sold was 270
$$a=13,$$ $$d=1,$$ $$20*13+10*1=270$$ or $$a=12,$$ $$d=3,$$ $$20*12+10*3=270$$ Not sufficient

(2) a > d > 2
Clearly not sufficient

1+2
$$a=10, d=7, 10*20+7*10=270$$ or $$a=11,d=5,11*20+5*10=270$$. Not sufficient
E
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Senior Manager
Joined: 02 Sep 2012
Posts: 259
Location: United States
Concentration: Entrepreneurship, Finance
GMAT Date: 07-25-2013
GPA: 3.83
WE: Architecture (Computer Hardware)
Followers: 4

Kudos [?]: 135 [0], given: 99

Re: n a network of car dealerships, a group of d sales [#permalink]  22 Apr 2013, 21:30
statement 2 says:
2) a > d > 2
but in test case u have taken " a=5,d=10 .So a<d which contradicts the question stem
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Senior Manager
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Concentration: Entrepreneurship, Finance
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Kudos [?]: 135 [0], given: 99

Re: n a network of car dealerships, a group of d sales [#permalink]  22 Apr 2013, 21:40
Ya now its correct and thanks for editing ur posts
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A network of car dealerships, employs d sales directors, who [#permalink]  16 Sep 2013, 21:47
A network of car dealerships, employs d sales directors, who each supervise a sales associates. If each director sells 10 cars and each sales associate sells 20 cars, and no other cars were sold by the dealership, how many people total sold cars?

(1) The total number of cars sold was 270

(2) a>d>2

Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient to answer the question asked
Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient to answer the question asked
Both statements (1) and (2) TOGETHER are sufficient to answer the question asked; but NEITHER statement ALONE is sufficient
Statements (1) and (2) TOGETHER are NOT sufficient to answer the question asked, and additional data specific to the problem are needed

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Re: n a network of car dealerships, a group of d sales [#permalink]  16 Sep 2013, 22:32
Zarrolou wrote:
In a network of car dealerships, a group of d sales directors each has a team of a sales associates. In a given month, if the directors each sold 10 cars and each sales associate sold 20 cars, and all cars were sold by either a sales director or a sales associate, how many people total sold cars?

(1) The total number of cars sold was 270
$$a=13,$$ $$d=1,$$ $$20*13+10*1=270$$ or $$a=12,$$ $$d=3,$$ $$20*12+10*3=270$$ Not sufficient

(2) a > d > 2
Clearly not sufficient

1+2
$$a=10, d=7, 10*20+7*10=270$$ or $$a=11,d=5,11*20+5*10=270$$. Not sufficient
E

dx10 + ax20 = 270
here a=d

d=9
2d total number pf person who sold the car = 2 X9 = 18 A is the correct answer
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Re: n a network of car dealerships, a group of d sales [#permalink]  16 Sep 2013, 22:45
2
KUDOS
Zarrolou wrote:
In a network of car dealerships, a group of d sales directors each has a team of a sales associates. In a given month, if the directors each sold 10 cars and each sales associate sold 20 cars, and all cars were sold by either a sales director or a sales associate, how many people total sold cars?

(1) The total number of cars sold was 270
$$a=13,$$ $$d=1,$$ $$20*13+10*1=270$$ or $$a=12,$$ $$d=3,$$ $$20*12+10*3=270$$ Not sufficient

(2) a > d > 2
Clearly not sufficient

1+2
$$a=10, d=7, 10*20+7*10=270$$ or $$a=11,d=5,11*20+5*10=270$$. Not sufficient
E

Hi Zarrolou,

Isn't the answer suppose to be C

Below is my explanation

St 1 and 2 are clearly not sufficient so we rule out option A, D, and B.

Combining we get

10d+ 20 a= 270 and that a>d>2

Possible cases are

let us say d=1, a =13 so Total no . of people =14
d=3, a=12, Total= 15
d=9,a=9, Total 18
d=5, a=11, Total 16 and so one
We see that as D increases A will decrease and hence the given condition that each sales director handle "a" sales associates will not hold.

From the above condition there is only 1 case possible which d=3, a=12 and T=15. Note that each Sales director handles 4 Sales associates.

Where am I wrong on this one???
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Re: A network of car dealerships, employs d sales directors, who [#permalink]  16 Sep 2013, 23:06
1
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Expert's post
honchos wrote:
A network of car dealerships, employs d sales directors, who each supervise a sales associates. If each director sells 10 cars and each sales associate sells 20 cars, and no other cars were sold by the dealership, how many people total sold cars?

(1) The total number of cars sold was 270

(2) a>d>2

Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient to answer the question asked
Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient to answer the question asked
Both statements (1) and (2) TOGETHER are sufficient to answer the question asked; but NEITHER statement ALONE is sufficient
Statements (1) and (2) TOGETHER are NOT sufficient to answer the question asked, and additional data specific to the problem are needed

Merging similar topics.
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Re: n a network of car dealerships, a group of d sales [#permalink]  17 Sep 2013, 09:50
(1) d*10 + d*a*20=270
d*(10 + a*20)=270 ---> multiple answers are possible: a=1 & d=9; a=4 & d=3; a=3 & d=4.

(2) a>d>2 ----> the only possible combination d=3 & a=4

btw, beatthegmat has the same post discussed with C as correct answer

Last edited by bettyseven on 17 Sep 2013, 10:00, edited 1 time in total.
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Re: In a network of car dealerships, a group of d sales [#permalink]  17 Sep 2013, 18:41
1
KUDOS
Many values could solve this equation, Not Sufficient

(2) --> a>d>2
Clearly insufficient

(1)+(2),
The first value of d and a is 3 and 4 (a and d must be integer), then
d(10+2a)=270 --> 3(10+2*4)=270 --> so d must be 4 and a must be 3.
If we increase d to 4 and a to 5, then the value is to big to get 270. Sufficient, answer C
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Re: In a network of car dealerships, a group of d sales director [#permalink]  17 Sep 2013, 23:31
Expert's post
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In a network of car dealerships, a group of d sales directors each has a team of a sales associates. In a given month, if the directors each sold 10 cars and each sales associate sold 20 cars, and all cars were sold by either a sales director or a sales associate, how many people total sold cars?

The total # of directors = d;
The total # of associates = ad;

Total # of cars sold = 10d + 20ad.

(1) The total number of cars sold was 270 --> 10d + 20ad = 270 --> d(1 + 2a) = 27. Four cases are possible:
d = 1 and a = 13,
d = 3 and a = 4,
d = 9 and a = 1,
d = 27 and a = 0.

Not sufficient.

(2) a > d > 2. Clearly insufficient.

(1)+(2) Since from (2) a > d > 2, then only one case remains from (1): d = 3 and a = 4. Sufficient.

Hope it's clear.
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Re: In a network of car dealerships, a group of d sales director [#permalink]  11 Mar 2015, 05:14
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