OG2015 PS In a certain city

This topic has expert replies
User avatar
Senior | Next Rank: 100 Posts
Posts: 62
Joined: Wed Aug 09, 2017 3:54 pm

OG2015 PS In a certain city

by lionsshare » Wed Sep 13, 2017 3:23 am
In a certain city, 60 percent of the registered voters are Democrats and the rest are Republicans. In a mayoral race, if 75 percent of the registered voters who are Democrats and 20 percent of the registered voters who are Republicans are expected to vote for Candidate A, what percent of the registered voters are expected to vote for Candidate A ?

(A) 50%
(B) 53%
(C) 54%
(D) 55%
(E) 57%

OA: B

Hi, Experts! Please explain how to solve this problem. Many thanks.

GMAT/MBA Expert

User avatar
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] » Wed Sep 13, 2017 6:39 pm
Hi lionsshare,

We're told that 60 percent of the registered voters are Democrats and the rest are Republicans and that 75 percent of the registered voters who are Democrats and 20 percent of the registered voters who are Republicans are expected to vote for Candidate A. We're asked for the percent of the registered voters who are expected to vote for Candidate A. This question can be solved by TESTing VALUES.

IF.... there are 100 TOTAL voters, then...
60% = 60 are registered Democrats
100 - 60 = 40 are registered Republicans

75% of the 60 Democrats = 45
20% of the 40 Republicans = 8
45 + 8 = 53 of the 100 voters will vote for Candidate A.

Final Answer: B

GMAT assassins aren't born, they're made,
Rich
Contact Rich at [email protected]
Image

GMAT/MBA Expert

User avatar
GMAT Instructor
Posts: 3008
Joined: Mon Aug 22, 2016 6:19 am
Location: Grand Central / New York
Thanked: 470 times
Followed by:34 members

by Jay@ManhattanReview » Wed Sep 13, 2017 10:23 pm
lionsshare wrote:In a certain city, 60 percent of the registered voters are Democrats and the rest are Republicans. In a mayoral race, if 75 percent of the registered voters who are Democrats and 20 percent of the registered voters who are Republicans are expected to vote for Candidate A, what percent of the registered voters are expected to vote for Candidate A ?

(A) 50%
(B) 53%
(C) 54%
(D) 55%
(E) 57%

OA: B

Hi, Experts! Please explain how to solve this problem. Many thanks.
Percentage of voters that are registered voters for Democrats = 60%
Thus, the percentage of voters that are registered voters for Republicans = 100% - 60% = 40%

Percentage of registered voters for Democrats who voted for Candidate A = 75% of 60% = (75/100) x 60% = (3/4) x 60% = 45%

Percentage of registered voters for Republicans who voted for Candidate A = 20% of 40% = (20/100) x 40% = (1/5) x 40% = 8%

Percentage of total votes expected for Candidate A = 45% + 8% = 53%

The correct answer: B

Hope this helps!

Download free ebook: Manhattan Review GMAT Quantitative Question Bank Guide

-Jay
_________________
Manhattan Review GMAT Prep

Locations: New York | Jakarta | Nanjing | Berlin | and many more...

Schedule your free consultation with an experienced GMAT Prep Advisor! Click here.

GMAT/MBA Expert

User avatar
GMAT Instructor
Posts: 1462
Joined: Thu Apr 09, 2015 9:34 am
Location: New York, NY
Thanked: 39 times
Followed by:22 members

by Jeff@TargetTestPrep » Tue Sep 19, 2017 2:58 pm
lionsshare wrote:In a certain city, 60 percent of the registered voters are Democrats and the rest are Republicans. In a mayoral race, if 75 percent of the registered voters who are Democrats and 20 percent of the registered voters who are Republicans are expected to vote for Candidate A, what percent of the registered voters are expected to vote for Candidate A ?

(A) 50%
(B) 53%
(C) 54%
(D) 55%
(E) 57%

OA: B
We are given that 60% of the voters are Democrats and the rest are Republicans. This means that 40% are Republicans. We also know that 75% of the voters who are Democrats and 20% of the voters who are Republicans are expected to vote for Candidate A.

The easiest way to solve this problem is to assume that the total number of registered voters is 100 (we could use other numbers, but 100 is an easy number to work with in percentage problems).

We know that 60% of the registered voters are Democrat and 40% are Republicans, so there are 60 Democrat registered voters and 40 Republican registered voters.

Now, since 75% of the 60 Democrat registered voters are expected to vote for Candidate A, we know that 0.75 x 60 = 45 Democrats are expected to vote for Candidate A. Similarly, because 20% of the 40 Republican registered voters are expected to vote for Candidate A, we know that 0.2 x 40 = 8 Republicans are expected to vote for Candidate A.

Thus, there are 45 + 8 = 53 voters expected to vote for Candidate A. Remember, we used 100 as the total number of voters, so this means that 53 out of 100, or 53% of the voters, are expected to vote for Candidate A.

Answer: B

Jeffrey Miller
Head of GMAT Instruction
[email protected]

Image

See why Target Test Prep is rated 5 out of 5 stars on BEAT the GMAT. Read our reviews

Newbie | Next Rank: 10 Posts
Posts: 1
Joined: Tue Apr 17, 2018 8:23 pm

Answer

by prime122 » Tue Apr 17, 2018 8:39 pm
We are given that 60% of the voters are Democrats and the rest are Republicans. This means that 40% are Republicans. We also know that 75% of the voters who are Democrats and 20% of the voters who are Republicans are expected to vote for Candidate A.

The easiest way to solve this problem is to assume that the total number of registered voters is 100 (we could use other numbers, but 100 is an easy number to work with in percentage problems).

We know that 60% of the registered voters are Democrat and 40% are Republicans, so there are 60 Democrat registered voters and 40 Republican registered voters.

Now, since 75% of the 60 Democrat registered voters are expected to vote for Candidate A, we know that 0.75 x 60 = 45 Democrats are expected to vote for Candidate A. Similarly, because 20% of the 40 Republican registered voters are expected to vote for Candidate A, we know that 0.2 x 40 = 8 Republicans are expected to vote for Candidate A.

Thus, there are 45 + 8 = 53 voters expected to vote for Candidate A. Remember, we used 100 as the total number of voters, so this means that 53 out of 100, or 53% of the voters, are expected to vote for Candidate A