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26 Mar 2026, 19:00
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C
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Difficulty:
95%
(hard)
Question Stats:
45% (02:12) correct
55%
(02:50)
wrong
based on 47
sessions
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13 students in a class had a median score of 10 and an average score of 15. If all scores were in integers and Mike scored higher than all other students in the quiz, what can be the lowest possible score of Mike?
A. More than 23
B. 23
C. 22
D. 21
E. 20
A. More than 23
B. 23
C. 22
D. 21
E. 20
26 Mar 2026, 23:09
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Question would have a been a bit more tricky if all were unique integers but as we have it here, again I will take the deviation method.
Since we minimize max value we will have the least deviation from the mean to the left as we have a median that is really low compared to median.
Take all 10s from 1-7.
Deviation = 7*5 = 35
Now Right side we need to minimise thus divide by 6, 35/6=close to 6. So lets take 36 as the deviation in that case 6 for each.
15+6 = 21 But max is unique thus add 1.
Hence lowest possible score of Mike = 22.
Answer: Option C
Since we minimize max value we will have the least deviation from the mean to the left as we have a median that is really low compared to median.
Take all 10s from 1-7.
Deviation = 7*5 = 35
Now Right side we need to minimise thus divide by 6, 35/6=close to 6. So lets take 36 as the deviation in that case 6 for each.
15+6 = 21 But max is unique thus add 1.
Hence lowest possible score of Mike = 22.
Answer: Option C
ExpertsGlobal5
26 Mar 2026, 23:59
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the max score all first six students get is 10 each.
now the next five students after the 7th students gets n score each and mike gets n+1.
so total = 70 + 5n + n + 1 = 195
6n+1 = 125
6n= 124
n = 20.6
but since score is integer, n=21
so for mike n= 22
ans is C
now the next five students after the 7th students gets n score each and mike gets n+1.
so total = 70 + 5n + n + 1 = 195
6n+1 = 125
6n= 124
n = 20.6
but since score is integer, n=21
so for mike n= 22
ans is C
ExpertsGlobal5
