Logical Reasoning - Statement and Conclusion - Discussion
Discussion Forum : Statement and Conclusion - Section 2 (Q.No. 10)
Directions to Solve
In each of the following questions, a statement/group of statements is given followed by some conclusions. Without resolving anything yourself choose the conclusion which logically follows from the given statements).
10.
In a class, three-fourth of the boys play football, one-half play cricket, one-fourth of those who play cricket do not play football.
Discussion:
11 comments Page 1 of 2.
Supriyo said:
12 hours ago
3/4 Plays football,
1/2 plays cricket,
(1/4)*(1/2) = 1/8 plays only cricket.
Now, [Plays Both] = [Plays Cricket] - [Plays Only Cricket]
=> [Plays Both] = 1/2 - 1/8 = 3/8.
Now, [Plays Only Football] = [Plays Football] - [Plays Both]
=> [Plays Only Football] = 3/4 - 3/8 = 3/8.
Now, [Plays Sports] = [Plays Only Cricket] + [Plays Only Football] + [Plays Both]
=> [Plays Sports] = 1/8 + 3/8 + 3/8 = 7/8.
Now, [Does not play Sports] = [Total] - [Plays Sports]
=> [Does not plays Sports] = 1 - 7/8 = 1/8.
Now match each of the options to determine which one will be correct.
1/2 plays cricket,
(1/4)*(1/2) = 1/8 plays only cricket.
Now, [Plays Both] = [Plays Cricket] - [Plays Only Cricket]
=> [Plays Both] = 1/2 - 1/8 = 3/8.
Now, [Plays Only Football] = [Plays Football] - [Plays Both]
=> [Plays Only Football] = 3/4 - 3/8 = 3/8.
Now, [Plays Sports] = [Plays Only Cricket] + [Plays Only Football] + [Plays Both]
=> [Plays Sports] = 1/8 + 3/8 + 3/8 = 7/8.
Now, [Does not play Sports] = [Total] - [Plays Sports]
=> [Does not plays Sports] = 1 - 7/8 = 1/8.
Now match each of the options to determine which one will be correct.
Hitesh said:
4 years ago
Nice explanation, Thanks @Raghu
(1)
Avani said:
5 years ago
Good explanation, thanks @Raghu.
Rubbal said:
5 years ago
Nice explanation, Thanks @Raghu.
Sujeesh said:
9 years ago
1/2 i.e 8/16 students play cricket.
Out of the above 8/16 x 1/4 play only cricket ( = 2/16).
& 8/16 x 3/4 play cricket + Footbal ( = 6/16).
Total students playing foot ball =3/4 = 12/16.
But 6/16 is playing both Cricket + Footbal.
So, total students playing only Footbal= 12/16-6/16 = 6/16.
Remaining students= 1- football players-cricket players- both game players.
= 1-6/16-2/16-6/16.
= 2 /16 =1/8.
Out of the above 8/16 x 1/4 play only cricket ( = 2/16).
& 8/16 x 3/4 play cricket + Footbal ( = 6/16).
Total students playing foot ball =3/4 = 12/16.
But 6/16 is playing both Cricket + Footbal.
So, total students playing only Footbal= 12/16-6/16 = 6/16.
Remaining students= 1- football players-cricket players- both game players.
= 1-6/16-2/16-6/16.
= 2 /16 =1/8.
(1)
Prabu jayabalan said:
9 years ago
Thank you @Raghu.
Raghu said:
1 decade ago
Lets take total number of boys as 8 [some number which is lcm of the denominators].
3/4 play football=f=6.
1/2 play cricket=c=4.
1/4 of those who play cricket play cricket only=A= (1/3) c=1.
So out of four who plays cricket only 1 plays cricket only and other three plays both cricket and football.
So no boys who plays football only is=6-3=3.
So conclusion is:
3 play football only.
1 play cricket only.
3 play both.
So finally 1 is left who neither play cricket nor foot ball.
So answer is.
(1/8) of the total boys that is (1/8) *8 =1 play neither play cricket nor football.
Answer D.
3/4 play football=f=6.
1/2 play cricket=c=4.
1/4 of those who play cricket play cricket only=A= (1/3) c=1.
So out of four who plays cricket only 1 plays cricket only and other three plays both cricket and football.
So no boys who plays football only is=6-3=3.
So conclusion is:
3 play football only.
1 play cricket only.
3 play both.
So finally 1 is left who neither play cricket nor foot ball.
So answer is.
(1/8) of the total boys that is (1/8) *8 =1 play neither play cricket nor football.
Answer D.
(13)
Hoang Le said:
1 decade ago
Answer D. Accept.
The easiest way for these problems is to quantify all the information. For example, assume there are 40 students in the class. 30 (3/4) play football. 20 (1/2) play cricket. 1/4 play cricket but not football, which is 5 students. Thus, 5 students play only cricket. 15 students in the intersection, leaving 15 (30-15) students play only football. Therefore, there are 5 students (40 - 15 - 15 - 5) who play nothing. This ratio is 5/40 = 1/8.
The easiest way for these problems is to quantify all the information. For example, assume there are 40 students in the class. 30 (3/4) play football. 20 (1/2) play cricket. 1/4 play cricket but not football, which is 5 students. Thus, 5 students play only cricket. 15 students in the intersection, leaving 15 (30-15) students play only football. Therefore, there are 5 students (40 - 15 - 15 - 5) who play nothing. This ratio is 5/40 = 1/8.
(1)
Ravi said:
1 decade ago
Use sets you can understand better. given 3/4 plays football, 1/2 boys play cricket. in these boys there are boys who play both. (1/2)*(1/4) boys play cricket but not football. (1/2)-(1/8) = 3/8 boys play both football and cricket. (3/4)-(3/8) =3/8 play only football total boys who play either football or cricket is 1/8 (cricket) +3/8(football) +1/8(both) =7/8 .remaining 1/8 boys play neither cricket nor football.
answer D .
answer D .
(1)
Nikita said:
1 decade ago
no idea how to get thru it ..... can any one help me out on these type of questions ?????
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