Question 1134236
<font color="black" face="times" size="3">Yes it is possible, and here's why:


Focus on the phrase " 23 of the students got a score of 63 or lower". Let's assume that all 23 students got the same score of 63, which is the highest possible for this group. This would mean that the total sum of the scores so far is 23*63 = 1449. Basically if you had 23 copies of "63" added up, you'd get to 1449.


Add on 5*x which represents the idea of having 5 other students score some other value x. Keep in mind that x is in the interval from 0 to 100. Anything outside this interval does not make sense. You can't get a negative score. You cannot get a score over 100 (assume there's no extra credit)


So we add 5x to 1449 to get 5x+1449. This total sum is divided over the number of students, which is 28, to get this expression {{{(5x+1449)/28}}}. This expression represents the average of all 28 students. The first 23 scored a 63, while the other 5 got a score of 'x' (to be determined)


Set this expression equal to the target average we want, which is 68. Let's solve for x


{{{(5x+1449)/28 = 68}}}


{{{5x+1449 = 28*68}}} Multiply both sides by 28


{{{5x+1449 = 1904}}} 


{{{5x+1449-1449 = 1904-1449}}} Subtract 1449 from both sides


{{{5x = 455}}}


{{{5x/5 = 455/5}}} Divide both sides by 5


{{{x = 91}}}


Therefore, the other five students must score 91 on each test so that the entire class averages a 68.


So it is possible, and I'm sure there are other scenarios where you can have the class average a 68 even if you don't have two groups scoring the same. Though of course, if the first group has too low of scores then at some point the other group won't have enough to bring up the overall average. 
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