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All votes cast in a recent presidential election were for

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by BTGmoderatorLU » Wed Nov 07, 2018 2:37 pm

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Source: Princeton Review

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 5million. 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 5.4million, 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%

The OA is B.
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by fskilnik@GMATH » Wed Nov 07, 2018 4:40 pm
BTGmoderatorLU wrote:Source: Princeton Review

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 5million. 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 5.4million, 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%
All numbers presented below are in million votes.
\[{\text{I}}{\text{.}}\,\,\left( {{\text{before}}} \right)\,\,{\text{:}}\,\,\,\frac{{{\text{challenger}}}}{{{\text{total}}}} = \frac{{5.4}}{{5.4 + 5}} = \frac{{54}}{{104}} = \frac{{27}}{{52}}\]
\[{\text{II}}{\text{.}}\,\,\left( {{\text{after}}} \right)\,\,{\text{:}}\,\,\,\frac{{{\text{challenger}}}}{{{\text{total}}}} = \frac{{5.4}}{{5.4 + 5.2}} = \frac{{54}}{{106}} = \frac{{27}}{{53}}\]
\[? = \Delta \% \left( {{\text{I}} \to {\text{II}}} \right) = \frac{{\frac{{27}}{{53}} - \frac{{27}}{{52}}}}{{\frac{{27}}{{52}}}} = \frac{{52}}{{53}} - 1 = - \frac{1}{{53}}\,\,\,\mathop \Rightarrow \limits^{{\text{alt}}{\text{.}}\,\,{\text{choices}}} \,\,\,\left( B \right)\]

This solution follows the notations and rationale taught in the GMATH method.

Regards,
Fabio.
Fabio Skilnik :: GMATH method creator ( Math for the GMAT)
English-speakers :: https://www.gmath.net
Portuguese-speakers :: https://www.gmath.com.br
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by Scott@TargetTestPrep » Fri Nov 09, 2018 12:18 pm
BTGmoderatorLU wrote:Source: Princeton Review

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 5million. 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 5.4million, 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%
The percent of the total number of votes for the challenger before the absentee ballots is 5.4/(5.4 + 5) = 5.4/10.4 ≈ 51.9%.

The percent of the total number of votes for the challenger after the absentee ballots is 5.4/(5.4 + 5.2) = 5.4/10.6 ≈ 50.9%.

Therefore, the percent of the total number of votes for challenger decreased approximately 1%.

Answer: B

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