A scientist has a set of weights {1Kg, 2Kg, 4Kg, 8Kg, 16Kg,

Consider the following example: how many different selections are possible from \(n\) people (including a subset with 0 members and a subset with all \(n\) members)?

\(C^0_n+C^1_n+C^2_n+...+C^n_n=2^n\) --> so, number of different subsets from a set with \(n\) different terms is \(2^n\) (this include one empty subset). Or another way: each person has 2 choices, either to be included or not to be included in the subset, so # of total subsets is \(2^n\).

Next, from a set {1Kg, 2Kg, 4Kg, 8Kg, 16Kg, 32Kg} obviously no term can be obtained by adding any number of other terms.

So, from a set with 6 different terms {1Kg, 2Kg, 4Kg, 8Kg, 16Kg, 32Kg} we can form \(2^6-1=63\) subsets each of which will have different sum (minus one empty subset) --> we can weight 63 different weights;

From a set with 5 different terms {1Kg, 2Kg, 8Kg, 16Kg, 32Kg} we can form \(2^5-1=31\) subsets each of which will have different sum (minus one empty subset) --> we can weight 31 different weights;

Which means that if 4Kg weight is lost 63-31=32 weights can no longer be measured.

Answer: D.