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# A new electric car company holds a limited-time sales event.

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A new electric car company holds a limited-time sales event.  [#permalink]

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Updated on: 20 May 2013, 11:18
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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, the average number of cars sold per day would have increased by 3.

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

Originally posted by guerrero25 on 20 May 2013, 09:36.
Last edited by guerrero25 on 20 May 2013, 11:18, edited 1 time in total.
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Re: A new electric car company holds a limited-time sales event.  [#permalink]

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20 May 2013, 10:11
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guerrero25 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, the average number of cars sold per day would have increased by 3.

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

OA to follow.

The question is a lil unclear, but If I were to go with sumthing, I'd go with [E].

For the car company, the sales for n days of sale would be in the set {3,6,9,.....3n}
Hence total cars sold on n days would be 3n*(n+1)/2

With that in mind, Statement 1, says that if the event had lasted 2 more days, the average number of cars sold per day would have increased by 3. Hence the event lasted for n+2 days.

So Average of cars sold in n+2 days = 3(n+2)*(n+3)/2*(n+2) = (3n + 9)/2
Average of cars sold in n days = 3(n+1)/2 = (3n + 3)/2
Hence the difference is 3, which was calculated for all n. Hence it does not depend on the number of cars sold. Not sufficient.

Statement 2 says, On exactly 9 days during the event, the number of cars for the day is a multiple of 9.
Assuming n = 9, the total number of cars sold = 3*9*10/2 = 15*9 a multiple of 9. Hence the statement is true, but does not specify if n is ultimately 9 or not. It simple states 'On exactly 9 days', and no mention is made if the event ended after the same.

The question is a little confusing. Probably the purpose of it was to do so! Nevertheless, Please verify my answer guerrero25! Hope its correct!

Regards,
Arpan
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Re: A new electric car company holds a limited-time sales event.  [#permalink]

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20 May 2013, 10:14
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guerrero25 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, the average number of cars sold per day would have increased by 3.

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

The no of cars sold on the 1st day,2nd day,3rd day,4th day = 3,6,9,12 and so on.

Assuming the no of days the event lasted = 2, thus the average no of cars sold - (6+3)/2 = 4.5.Also, for the event to last for 2+2=4 days, the average no of cars sold = (3+6+9+12)/4 = 30/4 = 7.5-->7.5-4.5 =3.

Similarly if the event lasted for 1 day, average = 3/1 = 3.If the event lasted for 1+2 = 3 days, the average = 18/3 = 6 --> 6-3 = 3.Thus the relationship given in the F.S 1 is not sufficient.The relation provided will hold good, irrespective of the no of days involved for d and d+2 days.

From F.S 2, we know that the first time a multiple of 9 occurs is on the 3rd day. Thus, the no of cars sold were a multiple of 9 on 3rd,6th,9th... 27th day.However, it might so happen that some cars were sold on 28th day also, which is not a multiple of 9. Insufficient.

Taking both statements together, it is again insufficient.
E.
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Re: A new electric car company holds a limited-time sales event.  [#permalink]

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20 May 2013, 10:49
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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, the average number of cars sold per day would have increased by 3.
This is always true, and there is no need to say it...
As my collegues correctly say

(2) On exactly 9 days during the event, the number of cars for the day is a multiple of 9.
So the event lasted at least 81/3 days = 27, but it's not sufficient.
If the event lasted 28 or 29 days this would still hold true

1+2) Because 1 do not add info to 2, the answer is E
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A new electric car company holds a limited-time sales event.  [#permalink]

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05 Sep 2013, 00:14
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, the average number of cars sold per day would have increased by 3.

(2) On exactly 9 days during the event, the number of cars for the day is a multiple of 9.
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Re: A new electric car company holds a limited-time sales event.  [#permalink]

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05 Sep 2013, 01:20
Stiv 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, the average number of cars sold per day would have increased by 3.

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

Merging similar topics.
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Re: A new electric car company holds a limited-time sales event.  [#permalink]

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22 Mar 2018, 20:47
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, the average number of cars sold per day would have increased by 3.

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

no of cars on nth day - 3n. So the list is 3,6,9,12...
Option 1 -
Average on nth day -3/2(n+1)
Average on (n+2)th day - 3/2(n+3) -> so diff irrespective of n is always 3. Doesn't give us no of days - Insuff

Option 2 -
on 9th day, the number of car is a multiple of 9. Something we already know, beacuse car on nth day is 3n. Doesn't tell us the no of days - insuff

Combined Together as well we dont derive anything that we didnt already know - hence Ans is E
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Re: A new electric car company holds a limited-time sales event.  [#permalink]

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16 May 2019, 21:25
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Re: A new electric car company holds a limited-time sales event.   [#permalink] 16 May 2019, 21:25
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