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
A new electric car company holds a limited-time sales event. On the first day, 3 cars are sold. On each subsequent day..
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On day 1, 3 cars are sold.
On each subsequent day, 3 more cars than the previous day are sold
Target question: For how many days does the event last?
Expressing it as an arithmetic progression, first term = 3, and difference = 3; find n.
Statement 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.
$$T_1=a\ \ \ and\ a=3$$
$$T_2=T_1+3\ =3+3=6$$
$$T_3=T_2+3\ =6+3=9$$
Since the event did not last 2 more days, total cars sold = 84 - 6 = 78
From the analysis above;
$$No.\ of\ days=\frac{total\ cars}{3}$$
$$No.\ of\ days=\frac{78}{3}=26\ days;\ Statement\ 1\ is\ SUFFICIENT$$
Statement 2: On exactly 9 days during the event, the number of cars for the day is a multiple of 9.
This does not tell us about the total number of vehicles sold. So the total days cannot be evaluated. Hence, statement 2 is NOT SUFFICIENT.
Since the only statement 1 is SUFFICIENT, answer = A
On each subsequent day, 3 more cars than the previous day are sold
Target question: For how many days does the event last?
Expressing it as an arithmetic progression, first term = 3, and difference = 3; find n.
Statement 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.
$$T_1=a\ \ \ and\ a=3$$
$$T_2=T_1+3\ =3+3=6$$
$$T_3=T_2+3\ =6+3=9$$
Since the event did not last 2 more days, total cars sold = 84 - 6 = 78
From the analysis above;
$$No.\ of\ days=\frac{total\ cars}{3}$$
$$No.\ of\ days=\frac{78}{3}=26\ days;\ Statement\ 1\ is\ SUFFICIENT$$
Statement 2: On exactly 9 days during the event, the number of cars for the day is a multiple of 9.
This does not tell us about the total number of vehicles sold. So the total days cannot be evaluated. Hence, statement 2 is NOT SUFFICIENT.
Since the only statement 1 is SUFFICIENT, answer = A