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17 Jan 2022, 23:43
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A
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Difficulty:
95%
(hard)
Question Stats:
42% (02:52) correct
58%
(03:22)
wrong
based on 128
sessions
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Not Attempted Yet
At a certain party hall, it is observed that in every party at least 75% of the people take coffee, at least 30% of the people take tea and between 20% to 50% people take cold drink. Each person in the party takes at least one of the beverages but no single person takes all three of them. What is the sum of the minimum possible percentage and maximum possible percentage of people who take both coffee and tea in a party?
A. 85
B. 95
C. 100
D. 105
E. 120
A. 85
B. 95
C. 100
D. 105
E. 120
03 Apr 2022, 21:59
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AbhiroopGhosh
ATLEAST 75% people take coffee so 100% could take coffee.
ATLEAST 30% people take tea so 100% could take tea.
20 - 50% take cold drink and no one takes all three.
To maximise the overlap between tea and coffee, we should maximise both while minimising the ones who take cold drink because no one takes all three so all three cannot overlap. So we should have as few cold drinkers as possible.
So assume 20% drink cold drink (min possible). Then 80% could drink both tea and coffee. This is the maximum possible overlap.
For minimum possible overlap, make 75% drink coffee and 30% drink tea (min possibles) but still there will be an overlap of 5%. Cold drink can be had by any of the other 95% people left who do not have an overlap of tea and coffee.
Hence max % is 80 and min is 5 giving total 85%.
Answer (A)
General Discussion
yashikaaggarwal
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18 Jan 2022, 00:36
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Minimum percentage = minimum of coffee and tea = 75%&30% each. Union of them will lead to minimum percentage as = 30%
For maximum.
Let say only soft drink drinkers are 0%
Tea and soft drink drinkers are 20% (minimum)
And tea drinkers are 80%.
For maximum percentage if tea and coffee drinkers..the percent in excess of 100 goes to both.
So coffee drinkers = 75
Tea drinkers = 80
Adding both = 155
So the maximum percent of tea and coffee drinkers = 55%
Adding maximum and minimum percent of tea and coffee drinkers = 55+30 = 85%
Answer is A
Posted from my mobile device
For maximum.
Let say only soft drink drinkers are 0%
Tea and soft drink drinkers are 20% (minimum)
And tea drinkers are 80%.
For maximum percentage if tea and coffee drinkers..the percent in excess of 100 goes to both.
So coffee drinkers = 75
Tea drinkers = 80
Adding both = 155
So the maximum percent of tea and coffee drinkers = 55%
Adding maximum and minimum percent of tea and coffee drinkers = 55+30 = 85%
Answer is A
Posted from my mobile device
