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31 Mar 2026, 13:48
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Nizomiddin
So basically, what you did was NOT luck — it was actually correct thinking.
You added:
70 + 75 + 80 = 225
Now think of it like this:
There are only 100% people in total, but the total preferences add up to 225%.
So the “extra” is:
225 − 100 = 125
That extra 125% has to come from overlap (people liking more than one fruit).
Now to find the minimum who like all three, we try to push as much overlap as possible into people liking only 2 fruits (not all 3).
Why? Because we are minimizing the 3-way overlap.
So:
- People who like 2 fruits account for 1 extra count each
- People who like all 3 account for 2 extra counts each
Max we can use = 100 (since total people are 100)
So:
125 − 100 = 25 left
This leftover 25 can only come from people who are in all 3 groups.
So minimum people who like all three = 25%
01 Apr 2026, 12:29
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E1+E2+E3=100 assuming ,n(neither)=0
and E1+2E2+3E3=125 at least
on solving we get E2=125 - 2E3 -------i
now we know that as E3 minimizes E1 also minimizes.
so we check with the given choices of E3 that will result in minimum E1.
1. E3=15, E2=95 which gives E1 negative
2. E3=20, E2=85 which again gives E1 negative
3. E3=25,E2=75, which gives E1=0
4 .E3=30,E2=65, E1=05
5. E3=35,E2=55,E1=10
A&B not possible, D&E are not minimum
hence C
[if the question were, the minimum value of E3 that gives the maximum E2 the choice would be same C.
however the minimum value of E3 that results in minimum value of E2 the choice would be E]
and E1+2E2+3E3=125 at least
on solving we get E2=125 - 2E3 -------i
now we know that as E3 minimizes E1 also minimizes.
so we check with the given choices of E3 that will result in minimum E1.
1. E3=15, E2=95 which gives E1 negative
2. E3=20, E2=85 which again gives E1 negative
3. E3=25,E2=75, which gives E1=0
4 .E3=30,E2=65, E1=05
5. E3=35,E2=55,E1=10
A&B not possible, D&E are not minimum
hence C
[if the question were, the minimum value of E3 that gives the maximum E2 the choice would be same C.
however the minimum value of E3 that results in minimum value of E2 the choice would be E]
13 May 2026, 07:47
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the question will feel very simple, once you read this : -
Apple (A) - 70%
Banana (B) - 75%
Cherry (C) - 80%
Since, these are % values, you can't simply (minus) them to get the overlap
for overlap between A&C -
100-80 = 20% folks don't like C ; so these may / may not like "Apple (A)".
but we know for sure that 70% folks like A. Hence, 70-20 = 50% is the min. possible overlap between them - imagine, out of these 70; 50 - for sure likes C; but the 20 may/maynot like C
Similarly if you do for others
A&B = 45%
B&C = 55%
Using the simple 3 set formula
Total = A + B + C - (AB + BC + AC) + {All 3} + None
100 = 70 + 75 + 85 - (50+55+45) + {All 3}
{All 3 } = 25%
Apple (A) - 70%
Banana (B) - 75%
Cherry (C) - 80%
Since, these are % values, you can't simply (minus) them to get the overlap
for overlap between A&C -
100-80 = 20% folks don't like C ; so these may / may not like "Apple (A)".
but we know for sure that 70% folks like A. Hence, 70-20 = 50% is the min. possible overlap between them - imagine, out of these 70; 50 - for sure likes C; but the 20 may/maynot like C
Similarly if you do for others
A&B = 45%
B&C = 55%
Using the simple 3 set formula
Total = A + B + C - (AB + BC + AC) + {All 3} + None
100 = 70 + 75 + 85 - (50+55+45) + {All 3}
{All 3 } = 25%
