1. The median of 11 different positive integers is 15 and seven of those 11 integers are 8, 12, 20, 6, 14, 22, and 13.
Statement I: The difference between the averages of four largest integers and four smallest integers is 13.25.
Statement II: The average of all the 11 integers is 16.
Which of the following statements would be sufficient to find the largest possible integer of these numbers?
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By: anil on 05 May 2019 02.37 am
Median of 11 integers is 15, => In ascending order 6th integer = 15 => Numbers = 6,8,12,13,14,15,20,22 Statement I : Average of four smallest = 6 + 8 + 12 + 13 = $$frac{39}{4} = 9.75$$ It is given that, avg of 4 largest - avg of 4 smallest = 13.25 => Average of 4 largest = 13.25 + 9.75 = 23 => Sum of 4 largest numbers = 23 * 4 = 92 So, we can easily allocate other three numbers different minimum values but more than 15 and maximize the remaining one value Thus, statement I is sufficient. Statement II : Sum of 11 integers = 11 * 16 = 176 Sum of given 8 integers = 6+8+12+13+14+15+20+22 = 110 Sum of remaining numbers = 176 - 110 = 66 So, we can easily allocate other three numbers different minimum values but more than 15 and maximize the remaining one value Thus, statement II is sufficient. $$ herefore$$ Either statement I or II is sufficient.
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