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25 Sep 2011, 04:53
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I have solved 2 out of 3. Can somebody help me with Q2.? Thanks.
Q.A survey was conducted among 500 ppl each of whom likes at least one of apple, orange , banana.The number of ppl who like apple is 240, those who like orange are 250 and those who like banana are 290.
Q1. If 60 ppl like only apple and banana, then what is the maximum possible number of ppl who like only orange?
1)120 2) 130 3)140
Q2. If 120 ppl like only apple, then what is the maximum possible number of ppl who like only orange and banana?
1)160 2)170 3)180
Q3. What is the maximum possible number of ppl who like all the 3 fruits?
1)110 2)120 3)130 4)140 5)150
Q.A survey was conducted among 500 ppl each of whom likes at least one of apple, orange , banana.The number of ppl who like apple is 240, those who like orange are 250 and those who like banana are 290.
Q1. If 60 ppl like only apple and banana, then what is the maximum possible number of ppl who like only orange?
1)120 2) 130 3)140
140
Ppl who like apple = A
Ppl who like orange = O
Ppl who like banana = B
Ppl who like all three= x
We know the formula: Total=A+O+B -{Sum of Exactly 2 groups members} - 2*AnOnB + Neither
Sum of Exactly 2 groups members=Sum of ppl who like only apple and orange + Sum of ppl who like only orange and banana + Sum of ppl who like only apple and banana.
To maximize ppl who like only orange we have to minimize Sum of ppl who like only apple and orange and Sum of ppl who like only orange and banana. It will be zero.
Sum of Exactly 2 groups members= 0+0+60 =60
Also, neither=0
Total=A+O+B -{Sum of Exactly 2 groups members} - 2*AnOnB
500=240+290+250-{60} -2x
Solving for x=110.
Hence maximum number of ppl who like Orange= Total who like Orange-Total who like all three
=250-110=140
Ppl who like apple = A
Ppl who like orange = O
Ppl who like banana = B
Ppl who like all three= x
We know the formula: Total=A+O+B -{Sum of Exactly 2 groups members} - 2*AnOnB + Neither
Sum of Exactly 2 groups members=Sum of ppl who like only apple and orange + Sum of ppl who like only orange and banana + Sum of ppl who like only apple and banana.
To maximize ppl who like only orange we have to minimize Sum of ppl who like only apple and orange and Sum of ppl who like only orange and banana. It will be zero.
Sum of Exactly 2 groups members= 0+0+60 =60
Also, neither=0
Total=A+O+B -{Sum of Exactly 2 groups members} - 2*AnOnB
500=240+290+250-{60} -2x
Solving for x=110.
Hence maximum number of ppl who like Orange= Total who like Orange-Total who like all three
=250-110=140
Q2. If 120 ppl like only apple, then what is the maximum possible number of ppl who like only orange and banana?
1)160 2)170 3)180
160
Q3. What is the maximum possible number of ppl who like all the 3 fruits?
1)110 2)120 3)130 4)140 5)150
140
We know the formula: Total=A+O+B -{Sum of Exactly 2 groups members} - 2*AnOnB + Neither
In this case Sum of Exactly 2 groups members = 0
500=240+290+250-0-2x
2x=280
x=140
We know the formula: Total=A+O+B -{Sum of Exactly 2 groups members} - 2*AnOnB + Neither
In this case Sum of Exactly 2 groups members = 0
500=240+290+250-0-2x
2x=280
x=140
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27 Sep 2011, 23:02
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Good questions for learning purpose.
Although seems more of a CAT type question.
2. for only orange and banana to be maximum,
number of people liking all 3 fruits = 0
also, 120(only apple)+ AOr+ABn- AOrBn = 240 (AOr= liking both Apple and orange)
(ABn - liking both Apple and Banana); (AOrBn - liking all 3)
gives AOr+ ABn = 120.
hence,
240+250+290-(120-OrB)-2AOrBn= 500
gives, OrBn= 160.
Although seems more of a CAT type question.
2. for only orange and banana to be maximum,
number of people liking all 3 fruits = 0
also, 120(only apple)+ AOr+ABn- AOrBn = 240 (AOr= liking both Apple and orange)
(ABn - liking both Apple and Banana); (AOrBn - liking all 3)
gives AOr+ ABn = 120.
hence,
240+250+290-(120-OrB)-2AOrBn= 500
gives, OrBn= 160.
jamifahad
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28 Sep 2011, 00:08
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amit2k9
Thanks man. These are for practice purpose only. Just to get totally comfortable with these kinds of question.
