MGMAT 6 | Statistics

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MGMAT 6 | Statistics

by [email protected] » Wed Jul 17, 2013 2:18 am
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.

Can anyone explain this in a simplified manner. I dont understand the MGMAT Explanation.

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by GMATGuruNY » Wed Jul 17, 2013 3:17 am
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.

kindly help me tackle this problem.thanks!
The number of cars sold increases by 3 each day:
3, 6, 9, 12, 15...
The result is an EVENLY SPACED SET.

Statement 1: If the event had lasted 2 more days, the average number of cars sold per day would have increased by 3.
3
3, 6, 9
3, 6, 9, 12, 15
3, 6, 9, 12, 15, 18, 21
With an evenly spaced set, average = median.
As shown here, EVERY TIME two more days are included, the median -- and thus the average -- increases by 3.
Thus, statement 1 is IRRELEVANT.
ANY NUMBER OF DAYS will satisfy statement 1.
If the event lasts 1 day, then adding 2 more days will increase the average number of cars sold per day by 3.
If the event lasts 2 days, then adding 2 more days will increase the average number of cars sold per day by 3.
If the event lasts 3 days, then adding 2 more days will increase the average number of cars sold per day by 3.
And so on.
Since statement 1 does not constrain the number of days in any way, eliminate A, D, and C.

Statement 2: On exactly 9 days during the event, the number of cars for the day is a multiple of 9.
The number of cars sold per day could look like this:
3, 6, 9...75, 78, 81.
The list above will include exactly 9 multiples of 9:
9, 18, 27, 36, 45, 54, 63, 72, 81.
But if the event lasts one more day, it will still be true that on exactly 9 days the number of cars sold per day will be a multiple of 9:
3, 6, 9...75, 78, 81...84.
Since the number of days can be different values, INSUFFICIENT.
Eliminate B.

The correct answer is E.
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by [email protected] » Fri Jul 19, 2013 2:16 am
Mitch what I don't understand is why in the second example you have taken values of mutiples of 3 after 27. The question stem says the event lasts for only 9 days so isn't the value going to be only till 27 and that would also be divisible by 9?

Please explain the second statement in a little detail.

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by GMATGuruNY » Fri Jul 19, 2013 3:29 am
[email protected] wrote:Mitch what I don't understand is why in the second example you have taken values of mutiples of 3 after 27. The question stem says the event lasts for only 9 days so isn't the value going to be only till 27 and that would also be divisible by 9?

Please explain the second statement in a little detail.
Question stem: On each subsequent day of the event, 3 more cars are sold than on the previous day.
Statement 2: On exactly 9 days during the event, the number of cars for the day is a multiple of 9.

In my post above, the values listed under statement 2 represent the NUMBER OF CARS SOLD each day.
To illustrate:
3, 6, 9...
These three values represent the first 3 days, with 3 cars sold the FIRST day, 6 cars sold the SECOND day, and 9 cars sold the THIRD day.

Number of cars sold each day in CASE 1:
3, 6, 9, 12, 15, 18, 21, 24, 27, 30
33, 36, 39, 42, 45, 48, 51, 54, 57, 60
63, 66, 69, 72, 75, 78, 81.
The values in red satisfy the constraint that, on exactly 9 days, the number of cars sold is a multiple of 9.
The total number of values in the list = 27, implying that the event lasts for a total of 27 days.

Number of cars sold each day in CASE 2:
3, 6, 9, 12, 15, 18, 21, 24, 27, 30
33, 36, 39, 42, 45, 48, 51, 54, 57, 60
63, 66, 69, 72, 75, 78, 81, 84.
The values in red satisfy the constraint that, on exactly 9 days, the number of cars sold is a multiple of 9.
The total number of values in the list = 28, implying that the event lasts for a total of 28 days.

Since the total number of days can be different values, statement 2 is INSUFFICIENT.
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