jamifahad wrote:

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

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

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

HI everyone just wanted to bring this question out in the open

I got stumped in the very first option

in order to maximize only orange from the Diagram I can see only orange is 250 -( x+y+z)= only orange

so in order to maximize I would minimize x+y+z so I would take x+y+z= 0 so maximum only orange = 250

so what is wrong with this logic !! ( assuming actual answer is correct ) why cannot be assume people who like all three (apple . orange and Banana) to be 0?

They have to like at least one, not necessarily there must be some who like all three , so we should be able to take Z=0 in order to maximize only orange unless I am messing up somewhere. Please do help

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- Stne