ziyuen
Tom started a company with 5 of his friends from the college. They made a software and sold it. Tom sold 15, and his friends each sold at least 1. Did Tom sell more than at least 3 of his friends?
1) The median number of software sold by 5 friends is 14.
2) The average number of software sold by 5 friends is 9.
OFFICIAL EXPLANATION
If you look at the original condition, there are 5 variables (since you have to know the number of software sold by each of his 5 friends), and 1 equation (at least 1 was sold). In order to match the number of variables to the number of equations, there must be 4 more equations. Therefore, E is most likely to be the answer. By solving con 1) and con 2), you get the median by arranging all the numbers in an ascending order, so you get
(1 sell), (1 sell), (14 sells), (14 sells), (15 sells).
This is because the total average of 9 are sold, and the total sum of 5*9=45 should have been sold. Thus, Tom, who always sold 15, sold more than 4 of his other friends, the condition is yes and sufficient. The answer is C.
However, this is an integer question, one of the key questions, “CMT 4(A: if you get C too easily, consider A or B, B: if you get A or B too easily, consider D)”can be applied.
In the case of con 1), the median number of sells is 14, so you get
(14 sells in maximum), (14 sells in maximum), (14 sells), ( ), ( ). Thus, Tom always sold 15 more than 3 of his friends, hence yes it is sufficient.
In the case of con 2), in order for it to be no, it should be
(1 sell), (1 sell), (15 sells), (15 sells), (15sells). However, in this way, the total sum becomes 1+1+15+15+15, so the total average of sells cannot be 9, hence it is impossible. Thus, it is always at least (1 sell), (1 sell), (13 sells),
(15 sells), (15 sells), and the total average of software sold is 9. Therefore, Tom sold 15 sold more than at least 3 of his friends, hence yes, it is sufficient. The answer is D.