At a certain party hall, it is observed that in every party at least 7

Question

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

KarishmaB · Accepted Answer

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)

yashikaaggarwal · Answer

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

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Karan0912 · Answer

Lets try to simplify and understand.

Important information in que stem : All 3 and None of the 3 = 0.

For maximising both Tea and Coffee, we need to minimize Cold drink. Fair enough? So minimum % of people who consume cold drink is 20% so the rest 80% can be attributed to both Tea and coffee (Here to maximise consumption of both Tea and Coffee we are assuming Only Tea and Only Coffee as zero).

Now let's find the minmum value. This is slightly tricky. For minimising both Tea and Coffee, we need to maximise others. The tea and coffee consumption is atleast 75% and 30% respectively so there is atleast 5% overlap between Tea and Coffee, which is basically Both Teas and Coffee group. Now this is atleast 5% and it could be bigger number but our objective is to minimize it. We can do that if we make the rest 95% as follows: (50% as cold drink group (since this is max.) and rest 45% as Only Tea and Only Coffee group).

Now add the max and min, you get 80 + 5 = 85.
Option A is correct.

Kinshook · Answer

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?

Maximum people taking coffee = 100%
Maximum people taking tea = 100%

Since no one takes all 3 drinks, minimum people taking cold drink = 20%
Maximum people taking both tea and coffee = 100% -20% = 80%

Minimum people taking both tea and coffee will be 5%, since there will be minimum overlap of 5% between 75% & 30%.

The sum of the minimum possible percentage and maximum possible percentage of people who take both coffee and tea in a party = 5% + 80% = 85%

IMO A

At a certain party hall, it is observed that in every party at least 7

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At a certain party hall, it is observed that in every party at least 7

Prep Toolkit

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

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