SOLUTION: 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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Question 998653: 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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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 4, the sum of first four numbers is 4*4 = 16:
+ + + = 16. (1)
Since the average of the last four numbers is 4, the sum of the last four numbers is 4*4 = 16:
+ + + = 16. (2)
Add (1) and (2) and re-group. You will get
( + + + + + + ) + = 32. (3)
Since the average of the seven numbers is 3, their sum is 3*7 = 21:
+ + + + + + = 21.
Comparing it with (3), you get = 32 - 21 = 11.
Answer. = 11.
