Data Sufficiency

AAPL wrote:A new electric car company holds a limited-time sales event. On the first day, 3 cars are sold. On each subsequent day of the event, 3 more cars are sold than on the previous day. For how many days does the event last?

(1) If the event had lasted 2 more days, there would have been 84 more cars sold on the last day of the event than on the first.
(2) On exactly 9 days during the event, the number of cars for the day is a multiple of 9.

The OA is A.

Please, can any expert assist me with this DS question? I don't have it clear and I appreciate if any explain it for me. Thanks.

The number of cars sold on the event days are: 3, 6, 9, 12, 15, 18, ...

(1) If the event had lasted 2 more days, there would have been 84 more cars sold on the last day of the event than on the first.

Since the number of cars sold on the first day = 3, the number of cars would have been sold on 2 days hence after the last day = 3 + 84 = 87.

=> The number of cars sold on the last day = 87 - 3 - 3 = 81

Since we know that the number of cars sold on the event days are: 3, 6, 9, 12, 15, 18, ..., 81, the number of days are countable -- finite. Sufficient. There is no need to count the number of event days as this is a DS question; we just need to be sure that we get the unique answer.

(2) On exactly 9 days during the event, the number of cars for the day is a multiple of 9.

Nine numbers of multiples of 9 are: 9, 18, 27, 36, 45, 54, 63, 72, and 81

Case 1: If the number of cars sold on the envet days are: 3, 6, 9, 12, 15, 18, ..., 81. Say the number of days of the event = x.
Case 2: If the number of cars sold on the envet days are: 3, 6, 9, 12, 15, 18, ..., 81, 84. Say the number of days of the event = x + 1. Note that 84 is not a multiple of 9.
Case 3: If the number of cars sold on the envet days are: 3, 6, 9, 12, 15, 18, ..., 81, 84, 87. Say the number of days of the event = x + 2. Note that 84 and 87 are not a multiple of 9.

The number of days can be x, (x + 1), or (x + 2). No unique value. Insufficient.

The correct answer: A

Hope this helps!

-Jay
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