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# In the first round of the elections, the only two candidates got exact

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Math Expert
Joined: 02 Sep 2009
Posts: 64318
In the first round of the elections, the only two candidates got exact  [#permalink]

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06 Sep 2016, 03:53
00:00

Difficulty:

45% (medium)

Question Stats:

68% (02:01) correct 32% (02:19) wrong based on 88 sessions

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In the first round of the elections, the only two candidates got exactly the same number of votes. During the second round, 15,000 votes switched from the first candidate to the second one. The total number of votes remained the same in both rounds, and no other votes switched sides. If, in the second round, the winning candidate got four times as many votes as the other candidate, how many people have voted in each round?

A. 15,000
B. 25,000
C. 40,000
D. 50,000
E. 60,000

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In the first round of the elections, the only two candidates got exact  [#permalink]

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06 Sep 2016, 05:24
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Bunuel wrote:
In the first round of the elections, the only two candidates got exactly the same number of votes. During the second round, 15,000 votes switched from the first candidate to the second one. The total number of votes remained the same in both rounds, and no other votes switched sides. If, in the second round, the winning candidate got four times as many votes as the other candidate, how many people have voted in each round?

A. 15,000
B. 25,000
C. 40,000
D. 50,000
E. 60,000

Let A be the first candidate and B be the second one.

Given x+15000 = 4(x-15000) => x = 25000

2x = 50000

IMO option D.
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Re: In the first round of the elections, the only two candidates got exact  [#permalink]

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04 Jan 2018, 15:09
Hi All,

We're told that in the first round of the elections, the only two candidates got exactly the SAME number of votes and during the second round, 15,000 votes switched from the first candidate to the second one. We're also told that the total number of votes remained the same in both rounds, no other votes switched sides and the winning candidate got four times as many votes as the other candidate. We're asked for the number of people who voted in each round. This question can be solved by TESTing THE ANSWERS.

Since 15,000 votes changes sides, the total number of voters has to be well over 30,000. So let's TEST Answer D first...

Round 1: 25,000 votes and 25,000 votes were cast for the two candidates
Round 2: 25,000 - 15,000 = 10,000 and 25,000 + 15,000 = 40,000 were cast
In this scenario, the second number (40,000) is exactly 4 times the first number (10,000). This matches what we were told, so this MUST be the answer.

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Re: In the first round of the elections, the only two candidates got exact  [#permalink]

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21 Jan 2019, 18:13
Bunuel wrote:
In the first round of the elections, the only two candidates got exactly the same number of votes. During the second round, 15,000 votes switched from the first candidate to the second one. The total number of votes remained the same in both rounds, and no other votes switched sides. If, in the second round, the winning candidate got four times as many votes as the other candidate, how many people have voted in each round?

A. 15,000
B. 25,000
C. 40,000
D. 50,000
E. 60,000

We can let the number of votes received in the first round by both applicants = x.

4(x - 15,000) = x + 15,000

4x - 60,000 = x + 15,000

3x = 75,000

x = 25,000

So 2(25,000) = 50,000 voted in each round.

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Re: In the first round of the elections, the only two candidates got exact   [#permalink] 21 Jan 2019, 18:13