A gold purification process cycle, is able to remove 1/16 of impurities in gold. If we have a 10 grams of gold ore dust containing 16/24 pure gold. How much impurities would have been removed from that old after 4 cycles of purification using that method? Select the correct option
A) 0.72 B) 0.74 C) 0.76 D) 0.78 E) 0.82

Rationale: x is the initial quantity of impurities in that gold . after a cycle of purification the quantity of impurities left would be x 1 = x - 1 / 16 x i . e . x 1 = 15 / 16 x same thing for x 2 , x 3 , x 4 , respectively representing the quantity of impurities left after 2 , 3 , 4 cycles of purification . so we have : x 1 = 15 / 16 x x 2 = 15 / 16 x 1 x 3 = 15 / 16 x 2 x 4 = 15 / 16 x 3 by multiplying both ends of the equations we get : x 1 * x 2 * x 3 * x 4 = ( 15 / 16 ) ^ 4 x * x 1 * x 2 * x 3 simplification leaves us with : x 4 = ( 15 / 16 ) ^ 4 x x 4 is the quantity of impurities left after four cycles . so the cumulative quantity of impurities ( q 4 ) which has been removed after 4 cycles is : q 4 = x - x 4 = x - ( 15 / 16 ) ^ 4 x i . e . q 4 = x ( 1 - ( 15 / 16 ) ^ 4 ) in this case , given x was : x = ( 1 - 16 / 24 ) * 10 g = 3.33 g ( remember we had 16 / 24 pure gold ) so we have q 4 = 3.33 * ( 1 - ( 15 / 16 ) ^ 4 ) = 3.33 * ( 1 - ( 50625 / 65536 ) ) = 3.33 * ( 14911 / 65536 ) = 0.757 rounded gives q 4 = 0.76 answer : c
Answer: C