In the first round of the elections, the only two...

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AAPL: Moderator; Posts: 2599; Joined: Sun Oct 29, 2017 2:08 pm; Followed by:2 members

In the first round of the elections, the only two...

by AAPL » Sun Nov 19, 2017 2:55 pm

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

The OA is D.

Please, can any expert assist me with this PS question? I don't have it clear and I appreciate if any explain it for me. Thanks.

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Source: Beat The GMAT — Problem Solving | Sun Nov 19, 2017 2:55 pm

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ErikaPrepScholar: Legendary Member; Posts: 503; Joined: Thu Jul 20, 2017 9:03 am; Thanked: 86 times; Followed by:15 members; GMAT Score:770

by ErikaPrepScholar » Mon Nov 20, 2017 10:09 am

Let x be the number of people who voted for each candidate in round 1. This means that in round 2, x - 15,000 people voted for the losing candidate and x + 15,000 people voted for the winning candidate.

If the winning candidate received 4 times as many votes as the losing candidate, we can build the following equation:

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

Then we can solve

4x - 60,000 = x + 15,000
3x = 75,000
x = 25,000

Since in round 1, each candidate received x votes, the total number of people who voted in each round is 2x, giving 50,000 people in total.

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[email protected]: Elite Legendary Member; Posts: 10392; Joined: Sun Jun 23, 2013 6:38 pm; Location: Palo Alto, CA; Thanked: 2867 times; Followed by:511 members; GMAT Score:800

by [email protected] » Mon Nov 20, 2017 3:10 pm

Hi AAPL,

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...

Answer D: 50,000 total voters

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.

Final Answer: D

GMAT assassins aren't born, they're made,
Rich

Contact Rich at [email protected]

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Scott@TargetTestPrep: GMAT Instructor; Posts: 8083; Joined: Sat Apr 25, 2015 10:56 am; Location: Los Angeles, CA; Thanked: 43 times; Followed by:29 members

by Scott@TargetTestPrep » Tue Oct 15, 2019 6:50 pm

AAPL 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

The OA is D.

Please, can any expert assist me with this PS question? I don't have it clear and I appreciate if any explain it for me. Thanks.

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

During the second round, the first candidate had (x - 15,000) votes, and the second candidate had (x + 15,000) votes; thus:

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.

Answer: D

Scott Woodbury-Stewart
Founder and CEO
[email protected]