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 1^st 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.