There are 6 consecutive odd numbers in increasing order. The difference between the average of the squares of the first four numbers and the last four numbers is 64. If the sum of the squares of the first and the last number (i.e. odd numbers) is 178, then the averages of all the six numbers is:
A) 8
B) 10
C) 12
D) 16
E) None of these
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Answer:
8 or -8
Step-by-step explanation:
Let 6nos. be x,x+2,x+4,x+6,x+8,x+10.
a. Sum of square of first and last element is 178.
x.x+x.x+100+20x=178
2x.x+20x-78=0
x.x+10x-39=0
(x+13)(x-3)=0
x=3,-13
When x=3
No's. are 3,5,7,9,11,13
Their avg. is 3+5+7+9+11+13/6
=48/6=8
When=-13
No's. are-13,-11,-9,-7,-5,-3
Their avg. is -13-11-9-7-5-3/6
=-48/6=-8
So avg of these no's.are(+-8).
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