Question 998653
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In seven given numbers, the average of first four numbers is 4 and that of the last four numbers is also 4. If the average of these seven numbers is 3, the fourth number is :
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Since the average of first four numbers is &nbsp;4, &nbsp;the sum of first four numbers is &nbsp;4*4 = 16:

{{{a[1]}}} + {{{a[2]}}} + {{{a[3]}}} + {{{a[4]}}} = 16. &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;(1)

Since the average of the last four numbers is &nbsp;4, &nbsp;the sum of the last four numbers is &nbsp;4*4 = 16:

{{{a[4]}}} + {{{a[5]}}} + {{{a[6]}}} + {{{a[7]}}} = 16. &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;(2)

Add (1) and (2) and re-group. You will get

({{{a[1]}}} + {{{a[2]}}} + {{{a[3]}}} + {{{a[4]}}} + {{{a[5]}}} + {{{a[6]}}} + {{{a[7]}}}) + {{{a[4]}}} = 32. &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;(3)


Since the average of the seven numbers is &nbsp;3, &nbsp;their sum is &nbsp;3*7 = 21:

{{{a[1]}}} + {{{a[2]}}} + {{{a[3]}}} + {{{a[4]}}} + {{{a[5]}}} + {{{a[6]}}} + {{{a[7]}}} = 21.

Comparing it with (3), you get {{{a[4]}}} = 32 - 21 = 11.

<U>Answer</U>. {{{a[4]}}} = 11.
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