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# All votes cast in a recent presidential election were for

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Updated on: 09 Mar 2012, 23:18
3
3
00:00

Difficulty:

35% (medium)

Question Stats:

73% (01:37) correct 27% (01:40) wrong based on 468 sessions

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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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Originally posted by iwillcrackgmat on 09 Mar 2012, 17:02.
Last edited by Bunuel on 09 Mar 2012, 23:18, edited 1 time in total.
Edited the question and added the OA
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Re: incumbent or the challenger  [#permalink]

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09 Mar 2012, 23:18
1
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 approximately 10%
b.decreased approximately 1%
c.neither increased nor decreased
d.increased approximately 1%
e.increased approximately 2%

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.

Hope it's clear.
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Re: All votes cast in a recent presidential election were for  [#permalink]

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10 Mar 2012, 19:46
thanks Bunuel that's a helpful explanation..
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Re: All votes cast in a recent presidential election were for  [#permalink]

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10 Jun 2013, 04:08
Bumping for review and further discussion*. Get a kudos point for an alternative solution!

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Re: All votes cast in a recent presidential election were for  [#permalink]

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10 Jun 2013, 07:16
2
iwillcrackgmat wrote:
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%

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%

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Re: All votes cast in a recent presidential election were for  [#permalink]

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25 Jun 2013, 22:45
1
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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Re: All votes cast in a recent presidential election were for  [#permalink]

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14 Oct 2013, 07:20

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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Re: All votes cast in a recent presidential election were for  [#permalink]

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07 Nov 2018, 16:52
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.
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Re: All votes cast in a recent presidential election were for  [#permalink]

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09 Nov 2018, 12:24
iwillcrackgmat wrote:
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%

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%.

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Re: All votes cast in a recent presidential election were for &nbs [#permalink] 09 Nov 2018, 12:24
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