kevincan wrote:

In a village of 100 households, 75 have at least one DVD player, 80 have at least one cell phone, and 55 have at least one MP3 player. If x and y are respectively the greatest and lowest possible number of households that have all three of these devices, then x^2-y^2 is a number from

(A) 1000 to 2500

(B) 2501 to 2800

(C) 2801 to 3000

(D) 3001 to 3100

(E) 3001-3150

d = 75

p = 80

m = 55

dpm = x, when dpm is max

dpm = y, when dpm is min

100 = 75 + 80+ 55 - (dp + pm + md) - 2(x)

to maximize dpm (x), minimize (dp + pm + md) to 0.

x = 55

to minimize dpm (y), maximize (dp + pm + md) to the possible extent so that we can get y = 0

x^2-y^2 = 3025 - 0 = 3025.

its D.