If 850+ total printers were donated and 400+ were donated to underprivileged communities, what is the minimum number donated to all other groups combined?

If 850+ total printers were donated and 400+ were donated to underprivileged communities, what is the minimum number donated to all other groups combined?

• A. 450+
• B. 300+
• C. 500+
• D. 600+

Answer: (A)

The key idea is that the total donations include all groups, and the portion going to underprivileged communities is part of that total. To find the smallest amount that could go to all other groups, use the smallest possible total and the smallest possible underprivileged amount that still fit the given bounds: total is at least 850, and the underprivileged share is at least 400. The remaining amount for everyone else must be at least 850 − 400 = 450. So the minimum that could be donated to all other groups combined is 450 or more.

The key idea is that the total donations include all groups, and the portion going to underprivileged communities is part of that total. To find the smallest amount that could go to all other groups, use the smallest possible total and the smallest possible underprivileged amount that still fit the given bounds: total is at least 850, and the underprivileged share is at least 400. The remaining amount for everyone else must be at least 850 − 400 = 450. So the minimum that could be donated to all other groups combined is 450 or more.