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# The numbers of cars sold at a certain dealership on six of

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The numbers of cars sold at a certain dealership on six of [#permalink]  06 Aug 2012, 01:43
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Question Stats:

85% (02:34) correct 15% (01:43) wrong based on 590 sessions
The numbers of cars sold at a certain dealership on six of the last seven business days were 4, 7, 2, 8, 3, and 6, respectively. If the number of cars sold on the seventh business day was either 2, 4, or 5, for which of the three values does the average (arithmetic mean) number of cars sold per business day for the seven business days equal the median number of cars sold per day for the seven days?

I. 2
II. 4
III. 5

(A) II only
(B) III only
(C) I and II only
(D) II and III only
(E) I, II, and III

Practice Questions
Question: 12
Page: 153
Difficulty: 600
[Reveal] Spoiler: OA

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Re: The numbers of cars sold at a certain dealership on six of [#permalink]  06 Aug 2012, 01:43
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SOLUTION

The numbers of cars sold at a certain dealership on six of the last seven business days were 4, 7, 2, 8, 3, and 6, respectively. If the number of cars sold on the seventh business day was either 2, 4, or 5, for which of the three values does the average (arithmetic mean) number of cars sold per business day for the seven business days equal the median number of cars sold per day for the seven days?

I. 2
II. 4
III. 5

(A) II only
(B) III only
(C) I and II only
(D) II and III only
(E) I, II, and III

The median of a set with odd number of elements is the middle element when arranged in ascending/descending order.

Hence, the median number of cars sold for the 7 (odd) days, is the fourth greatest number of cars sold in these 7 days, therefore the median must be an integer.

Next, the total number of cars sold in 6 days is 4+7+2+8+3+6=30.

The average number of cars sold in 7 days is $$\frac{30+x}{7}$$. Since we need the average to be equal to the median, then the average must also be an integer.

$$\frac{30+x}{7}=integer$$ only if $$x=5$$ (for $$x=2$$ or $$x=4$$ it's not an integer).

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Re: The numbers of cars sold at a certain dealership on six of [#permalink]  06 Aug 2012, 12:31
[Reveal] Spoiler:
B

Since there are a odd number of days the median will be an integer, if the average has to be equal to median then it must be an integer also. Only 5 does this.
Math Expert
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Posts: 30392
Followers: 5093

Kudos [?]: 57403 [0], given: 8811

Re: The numbers of cars sold at a certain dealership on six of [#permalink]  10 Aug 2012, 02:45
Expert's post
SOLUTION

The numbers of cars sold at a certain dealership on six of the last seven business days were 4, 7, 2, 8, 3, and 6, respectively. If the number of cars sold on the seventh business day was either 2, 4, or 5, for which of the three values does the average (arithmetic mean) number of cars sold per business day for the seven business days equal the median number of cars sold per day for the seven days?

I. 2
II. 4
III. 5

(A) II only
(B) III only
(C) I and II only
(D) II and III only
(E) I, II, and III

The median of a set with odd number of elements is the middle element when arranged in ascending/descending order.

Hence, the median number of cars sold for the 7 (odd) days, is the fourth greatest number of cars sold in these 7 days, therefore the median must be an integer.

Next, the total number of cars sold in 6 days is 4+7+2+8+3+6=30.

The average number of cars sold in 7 days is $$\frac{30+x}{7}$$. Since we need the average to be equal to the median, then the average must also be an integer.

$$\frac{30+x}{7}=integer$$ only if $$x=5$$ (for $$x=2$$ or $$x=4$$ it's not an integer).

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Re: The numbers of cars sold at a certain dealership on six of [#permalink]  19 Aug 2012, 13:39
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Best Shortcut for this question:-
If we arrange the numbers in ascending order 2,3,4,x,6,7,8,& observe closely it is a evenly spaced series with one missing number. For a evenly spaced series mean is equal to median. Thus to fulfill the condition of mean = median , x has to be 5 only.
It took app 1 min 10 sec for me
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Re: The numbers of cars sold at a certain dealership on six of [#permalink]  11 Jan 2014, 22:47
Hello from the GMAT Club BumpBot!

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Re: The numbers of cars sold at a certain dealership on six of [#permalink]  09 Sep 2014, 21:44
Bunuel wrote:
The numbers of cars sold at a certain dealership on six of the last seven business days were 4, 7, 2, 8, 3, and 6, respectively. If the number of cars sold on the seventh business day was either 2, 4, or 5, for which of the three values does the average (arithmetic mean) number of cars sold per business day for the seven business days equal the median number of cars sold per day for the seven days?

I. 2
II. 4
III. 5

(A) II only
(B) III only
(C) I and II only
(D) II and III only
(E) I, II, and III

Practice Questions
Question: 12
Page: 153
Difficulty: 600

if the reading part is done carefully, then we could get the solution in 30 secs.

2+3+4+6+7+8 = 30 so if u add 2 then mean= 32/7 not equal to 4(median).
if 4 then 34/7 not equal to median (4).
if % then 35/7 equal to median 5. set will be like [2,3,4,5,6,7,8,]..

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Re: The numbers of cars sold at a certain dealership on six of [#permalink]  12 Sep 2015, 18:05
Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
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Re: The numbers of cars sold at a certain dealership on six of   [#permalink] 12 Sep 2015, 18:05
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