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

Expert's post

4

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00:00

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Difficulty:

5% (low)

Question Stats:

85% (02:31) correct
15% (01:40) wrong based on 494 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

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 _________________

If you like my Question/Explanation or the contribution, Kindly appreciate by pressing KUDOS. Kudos always maximizes GMATCLUB worth-Game Theory

If you have any question regarding my post, kindly pm me or else I won't be able to reply

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

1

This post received KUDOS

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).

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.

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).

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!

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).

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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,]..

Answer B

gmatclubot

Re: The numbers of cars sold at a certain dealership on six of
[#permalink]
09 Sep 2014, 21:44

Back to hometown after a short trip to New Delhi for my visa appointment. Whoever tells you that the toughest part gets over once you get an admit is...