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In an election between two candidates, the winner has a marg

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In an election between two candidates, the winner has a marg  [#permalink]

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New post 24 Sep 2013, 22:16
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In an election between two candidates, the winner has a margin of 10% of the votes polled. If 1500 people change their mind and vote for the loser, the loser would have won by a margin of 10% of the votes polled. Find the total number of votes polled in the election?

a. 30,000
b. 15,450
c. 45,000
d. 60,000
e. 15,000
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Re: In an election between two candidates, the winner has a marg  [#permalink]

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New post 24 Sep 2013, 22:32
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b2bt wrote:
In an election between two candidates, the winner has a margin of 10% of the votes polled. If 1500 people change their mind and vote for the loser, the loser would have won by a margin of 10% of the votes polled. Find the total number of votes polled in the election?

a. 30,000
b. 15,450
c. 45,000
d. 60,000
e. 15,000


Total # of votes cast = 100x, out of these, let the # of votes won by the winner = w, and for the loser(l) = 100x-w. Given that w-(100x-w) = 10% of total votes cast = 10x

Thus, 2w-100x = 10x \(\to\) w = 55x and l = 100x-55x = 45x.

According to the new condition, if the loser had won 45x+1500 votes, then , (45x+1500)-(55x-1500) = 10 % of total votes cast = 10x

Thus, 3000 = 20x and 100x = 15000.

E.
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Re: In an election between two candidates, the winner has a marg  [#permalink]

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New post 25 Sep 2013, 01:03
1
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b2bt wrote:
In an election between two candidates, the winner has a margin of 10% of the votes polled. If 1500 people change their mind and vote for the loser, the loser would have won by a margin of 10% of the votes polled. Find the total number of votes polled in the election?

a. 30,000
b. 15,450
c. 45,000
d. 60,000
e. 15,000


Winner - Looser
55% - 45%

If 1500 people change their mind and vote for the loser:
Winner - Looser
45% - 55%

Thus 1,500 people compose 10% of all voters, which means that the total number of votes is 15,000.

Answer: E.
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Re: In an election between two candidates, the winner has a marg  [#permalink]

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New post 25 Sep 2013, 01:28
Condition 1 : W-L=0.1V

Condition 2: L+1500-(W-1500) = 0.1V

So, V=15000

Hence, E :)
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Re: In an election between two candidates, the winner has a marg  [#permalink]

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New post 25 Sep 2013, 08:56
Bunuel wrote:
b2bt wrote:
In an election between two candidates, the winner has a margin of 10% of the votes polled. If 1500 people change their mind and vote for the loser, the loser would have won by a margin of 10% of the votes polled. Find the total number of votes polled in the election?

a. 30,000
b. 15,450
c. 45,000
d. 60,000
e. 15,000


Winner - Looser
55% - 45%

If 1500 people change their mind and vote for the loser:
Winner - Looser
45% - 55%

Thus 1,500 people compose 10% of all voters, which means that the total number of votes is 15,000.

Answer: E.



Hi Bunuel, How are we concluding 55-45 here?
I took it as 60-40 and messed up but however got the answer right.

I want to know how "logically" we can conclude it (55-45)
mau5 method is too alegbric for me :) :P
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Re: In an election between two candidates, the winner has a marg  [#permalink]

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New post 25 Sep 2013, 08:58
1
1
b2bt wrote:
Bunuel wrote:
b2bt wrote:
In an election between two candidates, the winner has a margin of 10% of the votes polled. If 1500 people change their mind and vote for the loser, the loser would have won by a margin of 10% of the votes polled. Find the total number of votes polled in the election?

a. 30,000
b. 15,450
c. 45,000
d. 60,000
e. 15,000


Winner - Looser
55% - 45%

If 1500 people change their mind and vote for the loser:
Winner - Looser
45% - 55%

Thus 1,500 people compose 10% of all voters, which means that the total number of votes is 15,000.

Answer: E.



Hi Bunuel, How are we concluding 55-45 here?
I took it as 60-40 and messed up but however got the answer right.

I want to know how "logically" we can conclude it (55-45)
mau5 method is too alegbric for me :) :P


The winner has a margin of 10% of the votes polled --> x+(x+10)=100 --> x=45 and x+10=55.
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Resources:
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Collection of Questions:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


What are GMAT Club Tests?
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Re: In an election between two candidates, the winner has a marg  [#permalink]

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New post 03 Jun 2016, 09:51
b2bt wrote:
In an election between two candidates, the winner has a margin of 10% of the votes polled. If 1500 people change their mind and vote for the loser, the loser would have won by a margin of 10% of the votes polled.Find the total number of votes polled in the election?

a. 30,000
b. 15,450
c. 45,000
d. 60,000
e. 15,000


Attachment:
Voters.PNG
Voters.PNG [ 3.03 KiB | Viewed 3629 times ]


So, 10--------->1500
Or, 100-------->15000

Hence correct answer will be (E)
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Re: In an election between two candidates, the winner has a marg  [#permalink]

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Re: In an election between two candidates, the winner has a marg &nbs [#permalink] 02 Dec 2018, 00:33
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