Bunuel wrote:
A googol is the number that is written as 1 followed by 100 zeros. if G represents a googol, what is the sum of the digits of \(\frac{G}{8} + \frac{G}{5} + \frac{G}{4} + \frac{G}{2}\) ?
A. 13
B. 22
C. 107
D. 400
E. 1075
\(G=10^{100}\)
\(\frac{G}{8}\)\(=10^{100}/2^{3}=10^{97}•5^3\)
\(\frac{G}{5}\)\(=10^{100}/5=10^{99}•2\)
\(\frac{G}{4}\)\(=10^{100}/2^{2}=10^{98}•5^2\)
\(\frac{G}{2}\)\(=10^{100}/2=10^{99}•5\)
\(\frac{G}{8} + \frac{G}{5} + \frac{G}{4} + \frac{G}{2}=…\)
\(10^{97}•5^3+10^{99}•2+10^{98}•5^2+10^{99}•5…=\)
\(10^{97}(5^3+10^{2}•2+10•5^2+10^{2}•5)=…\)
\(10^{97}(125+200+250+500)=…\)
\(10^{97}(1075)=…\)
\(digits:1+7+5=13\)
Answer (A).