Question 1119146
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<pre>
Since the average is 100, the sum of the 5 numbers is 5*100 = 500.


The largest number is 120;  hence, the second, third and fourth of the integers (by their magnitude) are not greater than 119, 118 and 117.


Thus


500 = 120 + {{{a[2]}}} + {{{a[3]}}} + {{{a[4]}}} + {{{a[5]}}},

 
{{{a[2]}}} + {{{a[3]}}} + {{{a[4]}}} + {{{a[5]}}} = 500 - 120 = 380,


119 + 118 + 117 + {{{a[5]}}} >= 380,

{{{a[5]}}} >= 380 - 119 - 118 - 117 = 26.


<U>Answer</U>.  {{{a[5]}}} >= 26.  
</pre>

Solved.