20. The multiplication $a b c \times d e=7632$ uses each of the digits 1 to 9 exactly once. What is the value of $b$ ?
A 1
В 4
C 5
D 8
E 9
20. C Note first that $7632=2 \times 2 \times 2 \times 2 \times 3 \times 3 \times 53$. Therefore either the two-digit number $d e=53$ or the three-digit number $a b c$ is a multiple of 53 . Since the multiplication uses each of the digits 1 to 9 once and 7632 contains a 3, the option $d e=53$ is not allowable. Hence we need to find a three-digit multiple of 53 that does not share any digits with 7632 and divides into 7632 leaving an answer that also does not share any digits with 7632. We can reject $2 \times 53=106$ since it contains a 6 but $3 \times 53=159$ is a possibility. The value of $7632 \div 159$ is $2 \times 2 \times 2 \times 2 \times 3=48$ which does not have any digits in common with 7632 nor with 159 . We can also check that no other multiple of 53 will work. Therefore the required multiplication is $159 \times 48=7632$ and hence the value of $b$ is 5 .