Question

Positive integers from 1 to 21 are arranged in 3 groups of 7 integers each, in some particular order.
Then the highest possible mean of the medians of these 3 groups is-
NTSE Stage-II (2016)
(A) 16
(B) 12.5
(C) 11
(D) 14
numbers among​

Answer 1

Answer:

14

Step-by-step explanation:

(18 + 14 + 10 )/ 3

= 14

We need to maximize the median in each group in order to maximize the average of all the medians.

The highest possible median is 18 as there should be 3 numbers higher than the median in a group of 7.

The median of the group 1, 2, 3, 18, 19, 20, 21 will be 18.

The next group will be 4, 5, 6, 14, 15, 16, 17. The median will be 36.

To maximize medians in all the 3 groups, the medians of the 3 groups have to be 10, 14 and 18

The mean of these three numbers is 14

Answer 2

Given: positive integers from 1 to 21 in 3 groups of 7 integers in some order.

to find: the highest possible mean of the medians of these 3 groups?

explanation:

• first, we need to maximize the median in each group to maximize the average of all median.
• The highest possible median is 18 there should be 3 numbers higher than a group of 7.

as we have,

                   1         2         3        18         19        20          21

similarly,

                  4         5         6         14         15         16          17

then,

                  7         8          9         10         11         12          13

as we can see medians are in the group is 18, 14 and 10.

we know,

                        mean = $\frac{18+14+10}{3}$

                                  = $\frac{42}{3}$

                                  = 14

hence the highest possible mean of the medians of these 3 groups is 14.