iwillcrackgmat wrote:
All votes cast in a recent presidential election were for either the incumbent or the challenger. The challenger received 5.4 million votes and the incumbent received 5 million. If after a recount of the votes and the addition of previously uncounted absentee ballots, the incumbent had 5.2 million votes while the challenger had 5.4 million, then the percentage of the total number of votes that were for the challenger
A. decreased by approximately 10 %
B. decreased approximately 1%
C. neither increased nor decreased
D. increased approximately 1%
E. increased approximately 2%
\({\text{I}}{\text{.}}\,\,\left( {{\text{before}}} \right)\,\,{\text{:}}\,\,\,\frac{{{\text{challenger}}}}{{{\text{total}}}} = \frac{{5.4}}{{5.4 + 5}} = \frac{{54}}{{104}} = \frac{{27}}{{52}}\)
\({\text{II}}{\text{.}}\,\,\left( {{\text{after}}} \right)\,\,{\text{:}}\,\,\,\frac{{{\text{challenger}}}}{{{\text{total}}}} = \frac{{5.4}}{{5.4 + 5.2}} = \frac{{54}}{{106}} = \frac{{27}}{{53}}\)
\(? = \Delta \% \left( {{\text{I}} \to {\text{II}}} \right) = \frac{{\frac{{27}}{{53}} - \frac{{27}}{{52}}}}{{\frac{{27}}{{52}}}} = \frac{{52}}{{53}} - 1 = - \frac{1}{{53}}\,\,\,\mathop \Rightarrow \limits^{{\text{alt}}{\text{.}}\,\,{\text{choices}}} \,\,\,\left( B \right)\)
This solution follows the notations and rationale taught in the GMATH method.
Regards,
Fabio.
_________________
Fabio Skilnik ::
GMATH method creator (Math for the GMAT)
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