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The numbers of cars sold at a certain dealership on six of t
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20 Aug 2020, 10:03
20 Aug 2020, 10:03
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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
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
Re: The numbers of cars sold at a certain dealership on six of t
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20 Aug 2020, 13:26
20 Aug 2020, 13:26
Let x= # of cars sold in the seventh day
x can be 2, 4, or 5
We have
4,7,2,8,3,6,x
Let's put the list in order
2,3,4,6,7,8,x
The average number of cars sold per day is
=(2+3+4+6+7+8+x)/7
=(30+x)/7
We want to find for which value of x will
(30+x)/7 = median of the list
Case 1: x=2
Our list becomes
2,2,3,4,6,7,8
(30+x)/7=(30+2)/7= 32/7
Median= 4
32/7 does not equal 4
Therefore x does not equal 2
Case 2: x=3
Our list becomes
2,3,3,4,6,7,8
(30+x)/7=(30+3)/7= 33/7
Median= 4
33/7 does not equal 4
Therefore x does not equal 2
(At this point we know the answer must be only x=5, since it is the only one left. We'll check it either way)
Case 3: x=5
Our list becomes
2,3,4,5,6,7,8
(30+x)/7=(30+5)/7= 35/7 =5
Median: 5
5=5
Therefore x equals 5
Final Answer: B
x can be 2, 4, or 5
We have
4,7,2,8,3,6,x
Let's put the list in order
2,3,4,6,7,8,x
The average number of cars sold per day is
=(2+3+4+6+7+8+x)/7
=(30+x)/7
We want to find for which value of x will
(30+x)/7 = median of the list
Case 1: x=2
Our list becomes
2,2,3,4,6,7,8
(30+x)/7=(30+2)/7= 32/7
Median= 4
32/7 does not equal 4
Therefore x does not equal 2
Case 2: x=3
Our list becomes
2,3,3,4,6,7,8
(30+x)/7=(30+3)/7= 33/7
Median= 4
33/7 does not equal 4
Therefore x does not equal 2
(At this point we know the answer must be only x=5, since it is the only one left. We'll check it either way)
Case 3: x=5
Our list becomes
2,3,4,5,6,7,8
(30+x)/7=(30+5)/7= 35/7 =5
Median: 5
5=5
Therefore x equals 5
Final Answer: B
gmatclubot
Re: The numbers of cars sold at a certain dealership on six of t [#permalink]
20 Aug 2020, 13:26
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