BTGmoderatorLU wrote:Source: Manhattan Prep

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

Given that on the first day, 3 cars are sold and on each subsequent day of the event, 3 more cars are sold than on the previous day, we have an arithmetic progression in place. Since we know the first term and the common difference, we know a pattern.

Let's take each statement one by one.

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.

=> Say the sale lasted for n days, then sale on (n + 2)the day = 3 + 84 = 87

Thus, sale on the nth day = 87 - 3 - 3 = 81

81 = 3 + 3*(n - 1) => n = 27 days. Sufficient.

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

The arithmetic progression is 3, 6, 9, 12, 15, 18, ...

We see that every third number is a multiple of 9; thus, on 9 days of the events, we would have 3*9 = 27 multiples of 9. Though it suggests that we have the unique answer: n = 27; however, it is not. What if the event ran for 28 or 29 days? Since sale figure for the 28th and 29th day will not be a multiple of 9, we have three answers for n: 27, 28 and 29. Note that the 9th multiple of 9 would fall on the 27th day and 10th multiple of 9 would fall on the 30th day. No unique answer. Insufficient.

The correct answer: A

Hope this helps!

-Jay
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