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Aptitude Day 155

Problems on Average:

1. If the mean of 5 observations x, x+2, x+4, x+6 and x+8 is 10, then the mean of the first 3 observations is:

Solution:
                   Mean = 10              
                   (x+ x+2+ x+4+ x+6 +x+8)/ 5= 10
                   5x+20 = 50
                   x = 6.

                   The numbers are 6, 8, 10, 12 and 14.

                  Mean of 1st 3 observations = (6+8+10)/3
                                                                   = 24/3
                                                                   = 8.

2. If the mean of a, b, c is M and ab+ bc+ ca = 0, then the mean of a2, b2, c2 is:

Solution:
                  As per the given conditions,
                  (a+b+c)/3 = M
                  ab+ bc+ ca = 0
                 
                  (a2+ b2+c2)/3 = ?
        
                 We know that,
                        (a+b+c)2 = a2+ b2+c2+ 2(ab+ bc+ ca)
                                9M2 = (a2+ b2+c2 ) +0

                        (a2+ b2+c2)/3 =  9M2/3

                                                = 3M2.

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