Of the 30 cricket players selected for England tour, half are allotted

Question

Of the 30 cricket players selected for England tour, half are allotted to the Senior Team and half to the Junior Team. However, 60 percent of the players prefer the Senior Team and 40 percent prefer the Junior Team. What is the least possible number of players who will not be assigned to the team they prefer?

(A) 3
(B) 4
(C) 5
(D) 6
(E) 7

(A) 3
(B) 4
(C) 5
(D) 6
(E) 7

APram · Answer

60% of 30 = 18
40% of 30 = 12

Half of 30 is 15
So clearly 3 students will not get their preferred choice

SSPatil · Answer

1. Calculate the number of players in each team: 
 
 Total players = 30 
 Senior Team = 30 / 2 = 15 players 
 Junior Team = 30 / 2 = 15 players

2. Calculate the number of players preferring each team0.60×30=18 players 0.40×30=12 players

3. Determine the number of players who cannot be assigned their preferred team:

For the Senior Team: 18 players prefer the Senior Team, but only 15 spots are available. This means 
 18−15=3, players who prefer the Senior Team cannot be assigned to it.

Zosima08 · Answer

I always prefer visualizing these types of questions using a 2x2 table:

Junior 
 Senior

Prefer Junior

18 
 
  Prefer Senior

12 
 
  Total 
 15 
 15 
 30

Once you get that laid out, just read the question and fill in the blanks. If we want the least number of players who won't be assigned to the preferred team, it means we need to MAX out people who are assigned to preferred team:

Junior 
 Senior

Prefer Junior 
  15  
   3   
 18 
 
  Prefer Senior 
 0 
  12  
 12 
 
  Total 
 15 
 15 
 30

Of the 30 cricket players selected for England tour, half are allotted

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Of the 30 cricket players selected for England tour, half are allotted

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