I28-19

Question

At a regional food festival, there were 240 attendees in total.
 
• 150 attendees chose pasta dishes.
 
• 100 attendees chose grilled dishes.
 
• At least 25 attendees chose other food options—neither pasta nor grilled dishes.
 
Select for  Minimum  the minimum number of attendees who could have chosen both pasta and grilled dishes, and select for  Maximum  the maximum number of attendees who could have chosen both. Make only two selections, one in each column.

Bunuel · Answer

Official Solution:

Total = Pasta + Grilled - Both + Neither
 
240 = 150 + 100 - Both + Neither
 
Both = Neither + 10
 
Since Neither is at least 25, Both is at least 35, making the minimum for Both 35.
 
For the maximum, Both cannot exceed the smallest group, so it cannot be more than 100. Can it be exactly 100? Yes, when Neither = 90:
 
240 = 150 + 100 - 100 + 90

Correct answer:

Minimum  "35"

Maximum  "100"

rashis700 · Answer

I did not quite understand the solution. Not able to understand why 100 is considered to be equal to max Both as it is already belonging to the subset of grilled dishes. and also the concept of neither to be at 90. IF we are given that Neither is equal to 25, we should only consider that. In that case, the max both will be equal to 90.

Bunuel · Answer

We are not told that Neither equals 25. It says “at least 25,” meaning 25 or more. For the minimum, use 25, so Both = 35. For the maximum, if Both = 100, then Neither = 90, which satisfies the condition. Check alternative solutions here: https://gmatclub.com/forum/12-days-of-c ... 39424.html

sequimaxime · Answer

So guys a interesting problem which can be solved easily using Matrix
    
 Pasta 
 pasta' 
 total 
 
  Grilled 
 min 
 max 
 100 
 
  Grilled' 
 max 
 25(min) 
 140

150 
 90 
 240

So it we want ro minimize both we have to take 25 as a value. So solving matrix we get 
35 as a answer.
Now we want to Maximize,for this using the same matrix but changing both to max , we 
See that we have to maximize neither from close values we choose 90and hence solving for same will give us results of 100.
Hope you like this approach , its useful.

I28-19

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My Rewards

	Pasta	pasta'	total
Grilled	min	max	100
Grilled'	max	25(min)	140
	150	90	240