Laura sells encyclopaedias, and her monthly income has two components, a fixed component of $1000, and a variable component of $C for each set of encyclopaedias that she sells in that month over a sales target of n sets, where n>0. How much did she earn in March?
(1) If Laura had sold three fewer sets in March, her income for that month would have been $600 lower than it was.
(2) If Laura had sold 10 sets of encyclopaedias in March, her income for that month would have been over $4000
The first n sets do not earn a bonus.
Statement 1: If Laura had sold three fewer sets in March, her income for that month would have been $600 lower than it was.
Case 1: 1 set earned a bonus of $600, and the remaining n sets did not earn a bonus.
Case 2: 2 sets each earned a bonus of $300, and the remaining n sets did not earn a bonus.
Case 3: 3 sets each earned a bonus of $200, and the remaining n sets did not earn a bonus.
Case 4: More than 3 sets each earned a bonus of $200, and the remaining n sets did not earn a bonus.
In any of these cases, selling 3 fewer sets would decrease the total income by $600.
No way to determine the total income.
INSUFFICIENT.
Statement 2: If Laura had sold 10 sets of encyclopaedias in March, her income for that month would have been over $4000
Since the first n sets earn a total of $1000, the total bonus earned by the remaining sets is more than $3000.
The minimum value of c -- the bonus earned by each set sold after the first n sets -- occurs if n=1, with the result that 9 of the 10 sets here each earn a bonus.
If 9 sets here each earn a bonus of c dollars, we get:
9c > 3000
c > 333.33.
No way to determine the total income.
INSUFFICIENT.
Statements combined:
Since c > 333.33, only Case 1 above is viable:
1 set earned a bonus of $600, and the remaining n sets did not earn a bonus.
Thus:
Total income = base income + bonus = 1000 + 600 = 1600.
SUFFICIENT.
The correct answer is
C.
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