XAT 2012 Question 59

Question 59

Ramesh analysed the monthly salary figures of five vice presidents of his company. All the salary figures are integers. The mean and the median salary figures are 5 lakh, and the only mode is 8 lakh. Which of the options below is the sum (in lakh) of the highest and the lowest salaries?

Solution

Median = 5 , Mode = 8

Mean = 5, => Sum of 5 salaries = $$25$$

As mode is 8, it will occur 2 times but not 3 ($$\because$$ sum is 25)

Also, median is 5, the third salary is 5 and the first two are less than 5

=> Sum of third , fourth and fifth salary = 5 + 8 + 8 = 21

Sum of first two = 25 - 21 = 4

First and second salaries cannot be same ($$\because$$ mode is 8)

=> First and second salary = 1 and 3

$$\therefore$$ Sum (in lakh) of the highest and the lowest salaries = 1 + 8 = 9



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