Newaz111 wrote:A certain dealership has a number of cars to be sold by its salespeople. How many cars are to be sold?
(1) If each of the salespeople sells 4 of the cars, 23 cars will remain unsold.
(2) If each of the salespeople sells 6 of the cars, 5 cars will remain unsold.
Let T = the total number of cars and n = the total number of salespeople.
Statement 1: If each of the salespeople sells 4 of the cars, 23 cars will remain unsold.
Here, the total number of cars sold by the n salespeople = 4n.
Since 23 cars remain unsold, we get:
T = 4n + 23.
If n=1, then T = (4*1) + 23 = 27.
If n=2, then T = (4*2) + 23 = 31.
Since T can be different values, INSUFFICIENT.
Statement 2: If each of the salespeople sells 6 of the cars, 5 cars will remain unsold.
Here, the total number of cars sold by the n salespeople = 6n.
Since 5 cars remain unsold, we get:
T = 6n + 5.
If n=1, then T = (6*1) + 5 = 11.
If n=2, then T = (6*2) + 5 = 17.
Since T can be different values, INSUFFICIENT.
Statements combined:
Since T = 4n + 23 and T = 6n + 5, we get:
4n + 23 = 6n + 5
18 = 2n
n = 9.
Thus, T = (4*9) + 23 = 59.
SUFFICIENT.
The correct answer is
C.
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