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The numbers of cars sold at a certain dealership on six of [#permalink]
 06 Aug 2012, 02:43
Question Stats:
90% (02:21) correct
9% (01:41) wrong based on 4 sessions
The Official Guide for GMAT® Review, 13th Edition - Quantitative Questions ProjectThe 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
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Re: The numbers of cars sold at a certain dealership on six of [#permalink]
06 Aug 2012, 02:43
SOLUTIONThe 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). Answer: B.
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Re: The numbers of cars sold at a certain dealership on six of [#permalink]
06 Aug 2012, 13:31
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.
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Re: The numbers of cars sold at a certain dealership on six of [#permalink]
10 Aug 2012, 03:45
SOLUTIONThe 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). Answer: B.
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Re: The numbers of cars sold at a certain dealership on six of [#permalink]
19 Aug 2012, 14:39
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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
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19 Aug 2012, 14:39
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