6. Hasan writes down a two-digit number. He then writes the same two-digit number next to his original number to form a four-digit number. What is the ratio of his four-digit number to his two-digit number?
A $2: 1$
B $100: 1$
C 101:1
D $1001: 1$
E It depends on his number
6. Cet Hasan's two-digit number be ' $a b$ ', which is equal to $10 a+b$. The four-digit number he forms is therefore ' $a b a b$ ', which is equal to $1000 a+100 b+10 a+b$ and hence to $100(10 a+b)+10 a+b=101 \times(10 a+b)$. Therefore the ratio of his four-digit number to his two-digit number is $101: 1$.