All votes cast in a recent presidential election were for either the

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Full algebraic answer:
Before recount and absentee ballots: challenger = 5.4, incumbent = 5, total = 5.4 + 5 = 10.4
After recount and absentee ballots: challenger = 5.4, incumbent 5.2, total 5.4 + 5.2 = 10.6
\(\frac{5.4}{10.6} - \frac{5.4}{10.4}\)

\(\frac{54}{106} - \frac{54}{104}\)

\(\frac{54(104)}{106(104)} - \frac{54(106)}{104(106)}\)

\(\frac{54(104-106)}{106(104)}\)

\(\frac{54(-2)}{106(104)}\)

\(\frac{-108}{11024}\)

\(\frac{-1.08}{110.24}\)

approximately -1%

Answer is B

challenger = 5.4 (after recount) challenger = 5.4
incumbent = 5 (after recount) incumbent = 5.2
Total = 10.4 (after recount) Total = 10.6

Ratio1 = 5.4/10.4 Ratio2 = 5.4/10.6
Only Denominator increase from 10.4 to 10.6 (around 2% increase) = so ratio decreases (around 1%)

The answer is B.

I did it without any 'notes'. first I estimated the Challenger's share by 5.4/10.4*100. Here by approximation it would come to around 51%.

After the recalculation, Challenger's share 5.4/10.6*100. Here by approximation it would come to around 52%.

The numerator is the same but the denominator has changed so it will be decrease for sure. so C,D,E are ruled out.

out of A and B, in B 10% is too large.

A is most suitable as 1% is nearest to the actual answer.

Hope my explanation makes sense

\({\text{I}}{\text{.}}\,\,\left( {{\text{before}}} \right)\,\,{\text{:}}\,\,\,\frac{{{\text{challenger}}}}{{{\text{total}}}} = \frac{{5.4}}{{5.4 + 5}} = \frac{{54}}{{104}} = \frac{{27}}{{52}}\)

\({\text{II}}{\text{.}}\,\,\left( {{\text{after}}} \right)\,\,{\text{:}}\,\,\,\frac{{{\text{challenger}}}}{{{\text{total}}}} = \frac{{5.4}}{{5.4 + 5.2}} = \frac{{54}}{{106}} = \frac{{27}}{{53}}\)

\(? = \Delta \% \left( {{\text{I}} \to {\text{II}}} \right) = \frac{{\frac{{27}}{{53}} - \frac{{27}}{{52}}}}{{\frac{{27}}{{52}}}} = \frac{{52}}{{53}} - 1 = - \frac{1}{{53}}\,\,\,\mathop \Rightarrow \limits^{{\text{alt}}{\text{.}}\,\,{\text{choices}}} \,\,\,\left( B \right)\)

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

Regards,
Fabio.

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

earlier ; c= 5.4 and i = 5
total % of C ; 5.4/10.4 ~ 52%
after recound ; x = 5.4 and i = 5.2
total % C ; 5.4/10/6 ~ 51 %
decreased approximately 1%
IMO C

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