20. The diagram shows a $2 \times 4$ table in which the numbers in each column except the first column are the sum and the difference of the numbers in the previous column.
Carl completes a $2 \times 7$ table in the same way and obtains the numbers 96 and 64 in the final column. What is the sum of the numbers in the first column of Carl's table?
A 24
B 20
C 12
D 10
E 8
20. B Consider a $2 \times 7$ table with entries $a$ and $b$ in the first column. Since the entries in the following columns are the sum and the difference of the numbers in the previous column, the completed table will be as shown below.

Since the numbers in the final column of Carl's table are 96 and 64 , we have $8 a=96$ and $8 b=64$ which have solution $a=12$ and $b=8$. Therefore the sum of the numbers in the first column of Carl's table is $12+8=20$.