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?  Choices.
A) 0.72 B) 0.74 C) 0.76 D) 0.78 E) 0.82
X is the initial quantity of impurities in that gold.   After a cycle of purification the quantity of impurities left would be X1=X-1/16X i.e. X1=15/16X   Same thing for X2, X3, X4, respectively representing the quantity of impurities left after 2, 3, 4 cycles of purification.   So we have:   X1=15/16 X   X2=15/16 X1   X3=15/16 X2   X4=15/16 X3   By multiplying both ends of the equations we get:   X1*X2*X3*X4 = (15/16)^4 X*X1*X2*X3   Simplification leaves us with:   X4 = (15/16)^4 X   X4 is the quantity of impurities left after four cycles. So the cumulative quantity of impurities (Q4) which has been removed after 4 cycles is: Q4= X-X4=X-(15/16)^4X i.e. Q4 = 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 Q4 = 3.33 * (1-(15/16)^4) = 3.33 * (1-(50625/65536)) = 3.33 * (14911/65536) = 0.757 rounded gives Q4=0.76   Answer: 0.76
<result>C</result>
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?