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
For each of the
d directors, there are
a associates.
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.
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