My answer is 1950, but the answer sheet says 1949. I think the answer sheet is wrong.
How many digits are in the value of the following expression: $(2^{2001}*5^{1950})/4^{27}$?
I solve this problem as following: $(2^{2001}*5^{1950})/4^{27}=(2*5)^{1950}*2^{51}/2^{54}=10^{1950}/8$, which give total digits of 1950.
$\frac{10^{1950}}{8} = 10^{1947} \times \frac{1000}{8} = 125 \times 10^{1947}$, which is $125$ followed by $1947$ zeros, hence has $1950$ digits.
However, if we divide by $2$ only then would the answer would drop to $1949$ digits. So I think there is a mistake in the answer sheet. You are correct.