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iwillcrackgmat
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All votes cast in a recent presidential election were for either the Updated on: 14 May 2019, 22:43
Originally posted by iwillcrackgmat on 09 Mar 2012, 18:02.
Last edited by Bunuel on 14 May 2019, 22:43, edited 2 times in total.
Edited the question and added the OA
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All votes cast in a recent presidential election were for either the incumbent or thechallenger. The challenger received 5.4 million votes and the incumbent received 5million. If after a recount of the votes and the addition of previously uncountedabsentee 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%
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B
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Bunuel
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All votes cast in a recent presidential election were for either the 10 Mar 2012, 00:18
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iwillcrackgmat
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 approximately 10%
b.decreased approximately 1%
c.neither increased nor decreased
d.increased approximately 1%
e.increased approximately 2%
Show more

Before a recount the percentage of the total number of votes that were for the challenger was \(\frac{5.4}{5+5.4}*100=\frac{5.4}{10.4}*100\);
After the recount the percentage of the total number of votes that were for the challenger was \(\frac{5.4}{5.2+5.4}*100=\frac{5.4}{10.6}*100\);

Since the total # of votes increased (denominator increased from 10.4 to 10.6) and the # of votes for the challenger remained the same then the percentage of the total number of votes that were for the challenger clearly decreased, though since the increase in the total # of votes were minimal then the decrease in the percentage of the total number of votes that were for the challenger would also be minimal. Only answer choice B fits.

Answer: B.

Hope it's clear.
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All votes cast in a recent presidential election were for either the 10 Mar 2012, 20:46
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thanks Bunuel that's a helpful explanation..
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All votes cast in a recent presidential election were for either the 10 Jun 2013, 05:08
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Bumping for review and further discussion*. Get a kudos point for an alternative solution!

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All votes cast in a recent presidential election were for either the 10 Jun 2013, 08:16
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iwillcrackgmat
All votes cast in a recent presidential election were for either the incumbent or thechallenger. The challenger received 5.4 million votes and the incumbent received 5million. If after a recount of the votes and the addition of previously uncountedabsentee 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%
Show more

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
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All votes cast in a recent presidential election were for either the 25 Jun 2013, 23:45
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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%)
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All votes cast in a recent presidential election were for either the 14 Oct 2013, 08:20
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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 :)
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All votes cast in a recent presidential election were for either the 07 Nov 2018, 17:52
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iwillcrackgmat
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%
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\({\text{I}}{\text{.}}\,\,\left( {{\text{before}}} \right)\,\,{\text{:}}\,\,\,\frac{{{\text{challenger}}}}{{{\text{total}}}} = \frac{{5.4}}{{5.4 + 5}} = \frac{{54}}{{104}} = \frac{{27}}{{52}}\)

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

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

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

Regards,
Fabio.
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All votes cast in a recent presidential election were for either the 09 Nov 2018, 13:24
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iwillcrackgmat
All votes cast in a recent presidential election were for either the incumbent or thechallenger. The challenger received 5.4 million votes and the incumbent received 5million. If after a recount of the votes and the addition of previously uncountedabsentee 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%
Show more


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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All votes cast in a recent presidential election were for either the 06 May 2019, 04:38
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Bunuel
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 approximately 10%
B. decreased approximately 1%
C. neither increased nor decreased
D. increased approximately 1%
E. increased approximately 2%
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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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All votes cast in a recent presidential election were for either the 02 Jul 2024, 10:00
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%age of total number of votes for the challenger before the absentee ballots = 5.4/(5.4 + 5) = 5.4/10.4 ≈ 51.9%.

%age of total number of votes for the challenger after the absentee ballots = 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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