Log In
Quick search syntax
tags tag:apple
author user:martin
title title:apple
content content:apple
exclude -tag:apple
force match +apple
views views:100
score score:10
answers answers:2
is accepted isaccepted:true
is closed isclosed:true
5 votes

There are 150 students in a class. The number of students who play Cricket, Hockey, and Basketball are 125, 130, 135 respectively. If 5 students do not play any of the three games, the number of students playing all the three games must be at least

  1. 90
  2. 95
  3. 100
  4. 105



in Quantitative Aptitude 7.9k points 234 899 1073 11.4k views
In a class out of 150 studs participated in various games foot ball ,basket ball, cricket are 120, 130,135 respecly and 5 stud are not playing any one of then then find the least no of studs which are are playing all the games  
a)110 b)100 c) 96

2 Answers

2 votes
Best answer

100 should be the correct answer.

We have 125 Cricket Players, 130 Hockey Players & 135 Basketball Players.

Thus we have total (125 + 130 + 135) = 390 game players.

In the class we have 145 Player students & 5 non player students.

Each of these 145 Player students plays at least one of these 3 games( otherwise he/she would come in non player's category),

Now out of these 145 Players students we will have some 1 game players, some 2 game players and some 3 game players.

That is each of the player student can be either a 1 game players, or a 2 game player or a 3 game player.

Also all of these 145 players students will make up 390 game players.

Now suppose if all 145 students are 1 game players, then we will have 145 x 1 = 145 game players.

suppose if all 145 students are 2 game players, then we will have 145 x 2 = 290 game players,

suppose if all 145 students are 3 game players, then we will have 145 x 3 = 435 game players.

It is clear that to make  390 game players out of 145 player students, we need some 3 game player students also, because even if all of 145 students were 2 game players then also we can have only 145 x 2 = 290 players at most, and we are still 100 game players away from given 390 players hence we need at least (390 - 290) = 100, 3 game player students out of 145 player students using pigeon - hole principle.

(125 + 130 + 135) % 145 = 100



1.4k points 3 14
selected by
what is pigeon - hole principle.?
It is a simple but highly useful principle,it states that if n items are put into m containers, with n > m, then at least one container must contain more than one item.
For Example : If you pick five cards from a standard deck of 52 cards, then at least two will be of the same suit. Since each of the five cards can belong to one of four suits and by the pigeonhole principle, two or more must belong to the same suit.
0 votes
410 points 2 4

Related questions

1 vote
1 answer
Out of 100 students, 10 students used to drink milk(M), coffee(C) and Tea(T); 20M and C; 30C and T; 25M and T; 12M only; 5C only and 8T only. The number of students who did not drink any of this is a) 18 b) 24 c) 20 d) 16
asked Jun 7, 2016 in Quantitative Aptitude Aakash Das 30 points 1 1 2 11.6k views
1 vote
3 answers
In a class of 51 students, the difference between the highest mark and the least mark is 70. If the average score is calculated without considering the student who got the highest mark, then the average score decreases by 1%. If the average score is calculated without ... least mark, then the average score increases by 1.33%. What is the original average score of the class? 60 70 80 40
asked Aug 22, 2015 in Quantitative Aptitude makhdoom ghaya 7.9k points 234 899 1073 4.4k views
1 vote
2 answers
In a casino, there were three different coloured tokens - Red, Green, and Blue - with face values of Rs.20, Rs.50 and Rs.100 respectively. The total worth of all the tokens in the casino was Rs.18,500. On a busy day, when the tokens were not sufficient, all ... number of tokens per colour is equal to the number of Green tokens, then find the total number of tokens in the casino. 150 180 270 288
asked Aug 21, 2015 in Quantitative Aptitude makhdoom ghaya 7.9k points 234 899 1073 1.0k views
0 votes
2 answers
In a section of a timber mill, cylindrical logs of wood, all of uniform dimensions, arrive as the input and are cut into smaller cylindrical pieces of the same radius using manual and mechanical saws. To operate a manual saw four workers are needed and to operate a ... logs into four equal pieces each, if they have two mechanized saws and two manual saws? 40 hours 80 hours 120 hours 60 hours
asked Aug 25, 2015 in Quantitative Aptitude makhdoom ghaya 7.9k points 234 899 1073 1.1k views
1 vote
1 answer
Given A = { 1, 3, 9, 27, 81,................................3100 } Y is a subset of A such that the geometric mean of no two elements of Y is 350. N is the maximum possible number of elements in set Y. A. What is the value of N? 50 51 49 52 B. In how many ways can the set Y be formed such that it has exactly N elements? 250 251 350 351
asked Aug 24, 2015 in Quantitative Aptitude makhdoom ghaya 7.9k points 234 899 1073 318 views