CAT Exam  >  CAT Questions  >  Out of 135 students in a class, 60 play crick... Start Learning for Free
Out of 135 students in a class, 60 play cricket, 80 play football and 75 play tennis. 25 students play both cricket and football, 36 students play both cricket and tennis and 40 students play both football and tennis. How many students play all three sports if each student in the class plays at least one sport?
  • a)
    1
  • b)
    25
  • c)
    21
  • d)
    Cannot be determined
Correct answer is option 'B'. Can you explain this answer?
Verified Answer
Out of 135 students in a class, 60 play cricket, 80 play football and ...
Consider the Venn diagram shown below:
Since all students participate in at least 1 sport,
a + b + c + d + e + f+ g = 135 ... (i)
Also, a + d + f+ g = 60 ... (ii) b + d+e + g = 80... (iii) c + e + f+ g = 75 ... (iv)
(ii) + (iii) + (iv) gives
(a + b + c) + 2 (d + e + f) + 3g = 215 ... (v)
(v) - (i) gives
{d+ e + f) + 2g = 80 ... (vi)
Finally, d+ g = 25 ... (vii) e + g = 40 ... (viii) f + g = 36 ... (ix)
Adding (vii), (viii) and (ix) gives,
(d + e + f) + 3g = 101 ... (x)
(x) - (vi) gives g = 21 Hence, option 2
View all questions of this test
Explore Courses for CAT exam

Top Courses for CAT

Out of 135 students in a class, 60 play cricket, 80 play football and 75 play tennis. 25 students play both cricket and football, 36 students play both cricket and tennis and 40 students play both football and tennis. How many students play all three sports if each student in the class plays at least one sport?a)1b)25c)21d)Cannot be determinedCorrect answer is option 'B'. Can you explain this answer?
Question Description
Out of 135 students in a class, 60 play cricket, 80 play football and 75 play tennis. 25 students play both cricket and football, 36 students play both cricket and tennis and 40 students play both football and tennis. How many students play all three sports if each student in the class plays at least one sport?a)1b)25c)21d)Cannot be determinedCorrect answer is option 'B'. Can you explain this answer? for CAT 2025 is part of CAT preparation. The Question and answers have been prepared according to the CAT exam syllabus. Information about Out of 135 students in a class, 60 play cricket, 80 play football and 75 play tennis. 25 students play both cricket and football, 36 students play both cricket and tennis and 40 students play both football and tennis. How many students play all three sports if each student in the class plays at least one sport?a)1b)25c)21d)Cannot be determinedCorrect answer is option 'B'. Can you explain this answer? covers all topics & solutions for CAT 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Out of 135 students in a class, 60 play cricket, 80 play football and 75 play tennis. 25 students play both cricket and football, 36 students play both cricket and tennis and 40 students play both football and tennis. How many students play all three sports if each student in the class plays at least one sport?a)1b)25c)21d)Cannot be determinedCorrect answer is option 'B'. Can you explain this answer?.
Solutions for Out of 135 students in a class, 60 play cricket, 80 play football and 75 play tennis. 25 students play both cricket and football, 36 students play both cricket and tennis and 40 students play both football and tennis. How many students play all three sports if each student in the class plays at least one sport?a)1b)25c)21d)Cannot be determinedCorrect answer is option 'B'. Can you explain this answer? in English & in Hindi are available as part of our courses for CAT. Download more important topics, notes, lectures and mock test series for CAT Exam by signing up for free.
Here you can find the meaning of Out of 135 students in a class, 60 play cricket, 80 play football and 75 play tennis. 25 students play both cricket and football, 36 students play both cricket and tennis and 40 students play both football and tennis. How many students play all three sports if each student in the class plays at least one sport?a)1b)25c)21d)Cannot be determinedCorrect answer is option 'B'. Can you explain this answer? defined & explained in the simplest way possible. Besides giving the explanation of Out of 135 students in a class, 60 play cricket, 80 play football and 75 play tennis. 25 students play both cricket and football, 36 students play both cricket and tennis and 40 students play both football and tennis. How many students play all three sports if each student in the class plays at least one sport?a)1b)25c)21d)Cannot be determinedCorrect answer is option 'B'. Can you explain this answer?, a detailed solution for Out of 135 students in a class, 60 play cricket, 80 play football and 75 play tennis. 25 students play both cricket and football, 36 students play both cricket and tennis and 40 students play both football and tennis. How many students play all three sports if each student in the class plays at least one sport?a)1b)25c)21d)Cannot be determinedCorrect answer is option 'B'. Can you explain this answer? has been provided alongside types of Out of 135 students in a class, 60 play cricket, 80 play football and 75 play tennis. 25 students play both cricket and football, 36 students play both cricket and tennis and 40 students play both football and tennis. How many students play all three sports if each student in the class plays at least one sport?a)1b)25c)21d)Cannot be determinedCorrect answer is option 'B'. Can you explain this answer? theory, EduRev gives you an ample number of questions to practice Out of 135 students in a class, 60 play cricket, 80 play football and 75 play tennis. 25 students play both cricket and football, 36 students play both cricket and tennis and 40 students play both football and tennis. How many students play all three sports if each student in the class plays at least one sport?a)1b)25c)21d)Cannot be determinedCorrect answer is option 'B'. Can you explain this answer? tests, examples and also practice CAT tests.
Explore Courses for CAT exam

Top Courses for CAT

Explore Courses
Signup for Free!
Signup to see your scores go up within 7 days! Learn & Practice with 1000+ FREE Notes, Videos & Tests.
10M+ students study on EduRev