Question 1134236
.
<pre>
If the class of 28 students took a 100 point test and if the mean was 68, then the total points was 28*68 = 1904.


Let assume that for some 23 students their average score was 63 or lower - then the total score for these 23 students was 23*63 = 1449 or lower.


Hence, the difference is  1904 - 1449 = 455 or greater, and it is what the rest of 28-23 = 5 students get altogether.


Since {{{455/5}}} = 91 is less than 100,  there is NO CONTRADICTION, which means that the given outcome IS POSSIBLE.
</pre>


---------------


Usually, &nbsp;the problems of this kind are designed to get a contradiction and thus disprove the possibility.


But in the given / (posted) case, &nbsp;this hypothetical design / ("solution strategy") &nbsp;does not work.




<U>INTERESTING &nbsp;NOTICE / addition</U>.



If, &nbsp;on the contrary, &nbsp;I slightly change the problem formulation in this way


<pre>
    A class of 28 students took a 90 point test. If the mean was 68, is it possible that 23 of the students got a score of 63 or lower?
</pre>

then the answer is &nbsp;"<U>IT &nbsp;IS &nbsp;IMPOSSIBLE</U>",  &nbsp;and the proof is as follows:



<pre>
    If the class of 28 students took a 90 point test and if the mean was 68, then the total points was 28*68 = 1904.


    Let assume that for some 23 students their average score was 63 or lower - then the total score for these 23 students was 23*63 = 1449 or lower.


    Hence, the difference is  1904 - 1449 = 455 or greater, and it is what the rest of 28-23 = 5 students get altogether.


    But  90*5 = 450  is LESS than 455,  so in the 90-point test 5 students CAN NOT obtain  455 points cumulatively.


    CONTRADICTION (!).


    Which proves that  <U>IT  IS  IMPOSSIBLE  (!)</U>
</pre>


Hope my explanations make the general picture more clear to you . . .