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
network of car dealerships
This topic has expert replies
-
- Senior | Next Rank: 100 Posts
- Posts: 73
- Joined: Sun May 06, 2012 2:19 am
- Location: Cape Town
- Thanked: 6 times
d sales directors
a sales assocaites
d sold 10 cars each = d * 10
s sold 20 cars each = s * 20
Number of cars sold = (d*10) + (d(a*20))
Statement 1
(d*10) + (d(a*20)) = 270
10d + 20ad = 270...... (1)
There are 2 combination of a and d which satisfies the eq
a = 4 and d = 3
a = 1 and d = 9
Therefore not sufficient
Statement 2
a > d > 2
Alone is not sufficient as we do not know the number of cars.
Statement 1 and Statement 2 Sufficent
a = 4 and d = 3 to satisfy eq 10d + 20ad = 270 and in equality a > d > 2.
Answer C
Hope this helps.
a sales assocaites
d sold 10 cars each = d * 10
s sold 20 cars each = s * 20
Number of cars sold = (d*10) + (d(a*20))
Statement 1
(d*10) + (d(a*20)) = 270
10d + 20ad = 270...... (1)
There are 2 combination of a and d which satisfies the eq
a = 4 and d = 3
a = 1 and d = 9
Therefore not sufficient
Statement 2
a > d > 2
Alone is not sufficient as we do not know the number of cars.
Statement 1 and Statement 2 Sufficent
a = 4 and d = 3 to satisfy eq 10d + 20ad = 270 and in equality a > d > 2.
Answer C
Hope this helps.
- GMATGuruNY
- GMAT Instructor
- Posts: 15539
- Joined: Tue May 25, 2010 12:04 pm
- Location: New York, NY
- Thanked: 13060 times
- Followed by:1906 members
- GMAT Score:790
For each of the d directors, there are a associates.himu 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
(2) a > d > 2
Thus, the total number of associates = d*a.
Each director sells 10 cars, for a total of 10d cars.
Each associate sells 20 cars, for a total of 20ad cars.
Thus:
Total cars sold = 10d + 20ad.
Statement 1: The total number of cars sold was 270.
10d + 20ad = 270.
d + 2ad = 27.
d(1 + 2a) = 27.
Thus, d is a factor of 27: 1, 3, 9, or 27.
Since d can be different values, INSUFFICIENT.
Statement 2: a > d > 2
Since a and d can be different values, INSUFFICIENT.
Statements combined: d(2a+1) = 27 and a>d>2.
d is a factor of 27 greater than 2: 3, 9, or 27.
If d=3, we get:
3(2a+1) = 27
2a+1 = 9
2a=8
a=4.
If the value of d INCREASES, then the value of a must DECREASE, violating the constraint that a>d.
Thus, d=3 and a=4.
SUFFICIENT.
The correct answer is C.
Private tutor exclusively for the GMAT and GRE, with over 20 years of experience.
Followed here and elsewhere by over 1900 test-takers.
I have worked with students based in the US, Australia, Taiwan, China, Tajikistan, Kuwait, Saudi Arabia -- a long list of countries.
My students have been admitted to HBS, CBS, Tuck, Yale, Stern, Fuqua -- a long list of top programs.
As a tutor, I don't simply teach you how I would approach problems.
I unlock the best way for YOU to solve problems.
For more information, please email me (Mitch Hunt) at [email protected].
Student Review #1
Student Review #2
Student Review #3
Followed here and elsewhere by over 1900 test-takers.
I have worked with students based in the US, Australia, Taiwan, China, Tajikistan, Kuwait, Saudi Arabia -- a long list of countries.
My students have been admitted to HBS, CBS, Tuck, Yale, Stern, Fuqua -- a long list of top programs.
As a tutor, I don't simply teach you how I would approach problems.
I unlock the best way for YOU to solve problems.
For more information, please email me (Mitch Hunt) at [email protected].
Student Review #1
Student Review #2
Student Review #3
here if d=7 and a =10 also satisfies the criteria of selling 270 cars..Hence to possiblities d=3 a=4 and d=7 a=10 .Two values.hence Insufficient..Can some one tell me why am getting insufficient.Whats the mistake i am making
GMAT/MBA Expert
- Anju@Gurome
- GMAT Instructor
- Posts: 511
- Joined: Wed Aug 11, 2010 9:47 am
- Location: Delhi, India
- Thanked: 344 times
- Followed by:86 members
No.skamal7 wrote:here if d=7 and a =10 also satisfies the criteria of selling 270 cars..Hence to possiblities d=3 a=4 and d=7 a=10 .Two values.hence Insufficient..Can some one tell me why am getting insufficient.Whats the mistake i am making
Read the problem statement again : "... a group of d sales directors each has a team of a sales associates"
Hence, total number of sales associates = d*a
Now, if d = 7 and a = 10, total number of sales associates = 7*10 = 70
So, number of cars sold by sales directors = 7*10 = 70 and number of cars sold by sales associates = 70*20 = 1400
Total number of cars sold = (70 + 1400) > 270
Hope that helps.
Anju Agarwal
Quant Expert, Gurome
Backup Methods : General guide on plugging, estimation etc.
Wavy Curve Method : Solving complex inequalities in a matter of seconds.
§ GMAT with Gurome § Admissions with Gurome § Career Advising with Gurome §
Quant Expert, Gurome
Backup Methods : General guide on plugging, estimation etc.
Wavy Curve Method : Solving complex inequalities in a matter of seconds.
§ GMAT with Gurome § Admissions with Gurome § Career Advising with Gurome §