Problem $1$: An inorganic soil sample with the following characteristics was tested for liquid limit using the percussion cup method, see table of results below and answer the following:

Initial moisture content $=18\mathrm{.}2\%$

$\%$ passing No$.4$ sieve $=100\%$

$\%$ passing No$.200$ sieve $=80\%$

Plastic limit $=8$

$\backslash$table$[[$Number of Blows, $N,$Moisture Content, $\%$wt$],[14,35],[16,32],[20,27],[28,16]]$

A$.$ Determine the liquid limit of the clay $(3$ pts$)$

B$.$ Calculate the plasticity index $(2$ pts$)$

C$.$ Calculate the liquidity index $(2$ pts$)$

D$.$ Classify the soil based on the AASHTO classification system $(3$ pts$)$

E$.$ Classify the soil based on the Unified Soil Classification System $($USCS$)($w$/$ ASTM names$)(3$ pts$)$

F$.$ If the "fines" consist of $70\%$ clay and $30\%$ silt, what is the soil named under the USDA system? $(3$ pts$)$