Q1. The numbers 24, 34, 46, 48, 2x + 1, 4x + 3, 105, 110, 114 and 123 are written in ascending order, and the median is 77. The value of x is:
Explanation
There are 10 numbers, already stated to be in ascending order. For an even number of observations, the median is the average of the 5th and 6th terms. Here those terms are 2x + 1 and 4x + 3. So [(2x + 1) + (4x + 3)] / 2 = 77, giving 6x + 4 = 154 and x = 25. The values 20, 22 and 30 do not make the average of the two middle terms equal to 77, so they cannot satisfy the given median.
