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The numbers of cars sold at a certain dealership

This topic has 2 expert replies and 0 member replies
boomgoesthegmat Senior | Next Rank: 100 Posts Default Avatar
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The numbers of cars sold at a certain dealership

Post Mon Apr 25, 2016 2:41 pm
Elapsed Time: 00:00
  • Lap #[LAPCOUNT] ([LAPTIME])
    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

    Answer: B

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    Post Mon Apr 25, 2016 3:43 pm
    Hi boomgoesthegmat,

    This question is essentially a big 'concept' question with a little bit of math thrown in. We're asked which of the 3 Roman Numerals would give us a situation in which the average of the group would equal the median of the group.

    Since we're dealing with a group of 7 numbers (the 6 that we're given and the 7th that is either 2, 4 or 5), the median will be the 4th number (once the values are put in ascending order).

    The total number of cars sold in 6 days is 4+7+2+8+3+6=30.
    In order, those numbers are 2, 3, 4, 6, 7, 8 ...and X, although we don't know what X is yet.

    Since the median will be an integer, we need to add a number to the group that, when the sum of the group is divided by 7, gives us an integer also AND that integer has to match the median.

    Looking at the 3 Roman Numerals, there's only one that fits everything we're looking for: 5

    (30+5)/7 = 5 --> 5 is the average
    2, 3, 4, 5, 6, 7, 8 --> 5 is the median

    Final Answer: B

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    Post Wed Apr 27, 2016 2:14 pm
    We know the mean is

    (4 + 7 + 2 + 8 + 3 + 6 + x) / 7, or (30 + x)/7

    The set has an odd number of terms, so the median will be an integer.

    That means that (30 + x)/7 must ALSO be an integer. For our three options, this will only work if x = 5, so III is the only possibility.

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