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ariyanak
Joined: 27 Aug 2024
Last visit: 01 Sep 2026
Posts: 18
Given Kudos: 61
Location: Bangladesh
Schools: Yale Booth (Chicago) Wharton UVA Darden
GMAT Focus 1: 645 Q82 V83 DI80 
GPA: 3.29
06 Sep 2024, 00:10
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Mean = Median: 7
Mean > Median: 5
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
85%
(hard)
Question Stats:
55% (03:05) correct
45%
(03:07)
wrong
based on 765
sessions
History
Date
Time
Result
Not Attempted Yet
After taking six practice exams, Albert is reviewing the number of mistakes he made. On the first five exams, he made 7, 4, 8, 6 and 10 mistakes respectively.
In the table below, select a number of mistakes he could make on the 6th exam such that the mean number of mistakes is equal to the median number of mistakes. Then select a number of mistakes he could make on the 6th exam such that the mean (average) is greater than the median. Make only two selections, one in each column.
In the table below, select a number of mistakes he could make on the 6th exam such that the mean number of mistakes is equal to the median number of mistakes. Then select a number of mistakes he could make on the 6th exam such that the mean (average) is greater than the median. Make only two selections, one in each column.
| Mean = Median | Mean > Median | Options |
| 1 | ||
| 3 | ||
| 5 | ||
| 7 | ||
| 8 | ||
| 9 |
ShowHide Answer
Official Answer
Mean = Median: 7
Mean > Median: 5
07 Sep 2024, 03:55
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I believe you have to super quick in calculations with this one
But lets set some preparatory work first
Mistakes arranged in ascending order - 4,6,7,8,10
Sum of mistakes = 35
Let mistake for 6th exam be x
New mean after x = (35+x)/6
Now look at options for median - For first three options it is same (6+7)/2 = 6.5, four forth it is 7 and for last two option it is (7+8)/2 = 7.5
Now lets go one by one for each option
1. 1 -
Mean : (35+1)/6 = 6
Median : (6+7)/2 = 6.5
Nope - fits no case
2. 3
Mean : (35+3)/6 = ~6.3
Median : (6+7)/2 = 6.5
Nope - fits no case
3. 5 :
Mean: (35+5)/6 = 6.67
Median : (6+7)/2 = 6.5
Yes fits case were mean> median
4. 7
Mean : (35+3)/6 = 7
Median : 7
Fits case where both are equal
No need to do further
Only ans 7 and 5 fir our table
But lets set some preparatory work first
Mistakes arranged in ascending order - 4,6,7,8,10
Sum of mistakes = 35
Let mistake for 6th exam be x
New mean after x = (35+x)/6
Now look at options for median - For first three options it is same (6+7)/2 = 6.5, four forth it is 7 and for last two option it is (7+8)/2 = 7.5
Now lets go one by one for each option
1. 1 -
Mean : (35+1)/6 = 6
Median : (6+7)/2 = 6.5
Nope - fits no case
2. 3
Mean : (35+3)/6 = ~6.3
Median : (6+7)/2 = 6.5
Nope - fits no case
3. 5 :
Mean: (35+5)/6 = 6.67
Median : (6+7)/2 = 6.5
Yes fits case were mean> median
4. 7
Mean : (35+3)/6 = 7
Median : 7
Fits case where both are equal
No need to do further
Only ans 7 and 5 fir our table
07 Sep 2024, 19:21
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Mistakes arranged in order: \(4, 6, 7, 8, 10\) - Sum \(=35\) Mean \(=7\) Median \(=7\)
\(Mean=Median=7\)
Case 1: \(Mean=Median\)
\(7\) mistakes made on the 6th exam will keep \(Mean=Median\)
Case 2: \(Mean>Median\)
whatever number be on the 6th exam, the median will be \(6.5\leq{m}\leq{7.5}\)
if the mistakes are \(>7\), the median will be \(7.5\)
mistakes are \(<7\), the median will be \(6.5\)
mistakes are \(=7\), the median will be \(7\)
For \(Mean>6.5\), \(6.5*6=39\), The 6th exam mistakes should be \(>4\)
There is \(5\) in the options.
Answer: 7 & 5
\(Mean=Median=7\)
Case 1: \(Mean=Median\)
\(7\) mistakes made on the 6th exam will keep \(Mean=Median\)
Case 2: \(Mean>Median\)
whatever number be on the 6th exam, the median will be \(6.5\leq{m}\leq{7.5}\)
if the mistakes are \(>7\), the median will be \(7.5\)
mistakes are \(<7\), the median will be \(6.5\)
mistakes are \(=7\), the median will be \(7\)
For \(Mean>6.5\), \(6.5*6=39\), The 6th exam mistakes should be \(>4\)
There is \(5\) in the options.
Answer: 7 & 5
