swerve wrote:Which of the following is closest to the value of (2^23)(5^26)?
A. 10^23
B. 10^24
C. 10^25
D. 10^26
E. 10^27
Source: Veritas Prep
\[{2^{23}} \cdot {5^{26}}\,\, \cong \,\,\,{10^{\,?}}\,\]
\[{2^{23}} \cdot {5^{26}} = {2^{23}} \cdot {5^{23}} \cdot {5^3} = \,\,\,125\,\,{\left( {10} \right)^{23}}\]
\[\underline {1 \cdot {{10}^{25}}} = 100 \cdot {\left( {10} \right)^{23}} < \underline {125\,\,{{\left( {10} \right)}^{23}}} < 200 \cdot {\left( {10} \right)^{23}} = \underline {2 \cdot {{10}^{25}}} \,\,\,\,\,\, \Rightarrow \,\,\,\,\,\left( C \right)\]
This solution follows the notations and rationale taught in the GMATH method.
Regards,
Fabio. 
