All 3 maximum can be 65
All 3 minimum can be 15

2 items maximum = when all 3 minimum therefore 2 items maximum = 100-15 = 85
2 items minimum = 0

Whats the OA?

My non-formula approach:

Min Number of people who has pencil and pen
(80+65 -100) = 45

Min number of people who has pencil, pen and slate
(45+70)-100 = 15

Max is 65, no problem.

My question is: How do you do this formulaically?

If formula is Total = Group1 + Group 2 + Group3 -Double -2Triple +Neither:

Total-Group(1,2,3)=-D-2T

1) To MAX Double you MIN Triple and Min Neither: (per the formula: Total-Group(1,2,3)+2T-N=-D)
2) Max double: 85,65,70. Pair 85 with 70; you get 70 pairs with 15 left over. Pair the remaining 15 with the 65; you get 15. Total Double= 85

-115=-85-2t
115=85+2t
T=15

Whats the OA?

I m getting:

For 2 only - MIN=1, MAX=115
For 3 only - MIN=0, MAX=57

Sorry I did this all wrong. The problem said [u]at least[/u] 65. So max all 3 is actually 100%. Disregard everything I wrote.