GMAT Question of the Day - Daily to your Mailbox; hard ones only

 It is currently 20 Oct 2019, 21:57

### GMAT Club Daily Prep

#### Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History

# In an election, candidate Smith won 52% of the total vote in

Author Message
TAGS:

### Hide Tags

Senior Manager
Status: Final Countdown
Joined: 17 Mar 2010
Posts: 406
Location: United States (NY)
GPA: 3.82
WE: Account Management (Retail Banking)
In an election, candidate Smith won 52% of the total vote in  [#permalink]

### Show Tags

25 Sep 2012, 06:35
11
00:00

Difficulty:

35% (medium)

Question Stats:

72% (02:03) correct 28% (02:10) wrong based on 393 sessions

### HideShow timer Statistics

In an election, candidate Smith won 52% of the total vote in Counties A and B. He won 61% of the vote in County A. If the ratio of people who voted in County A to County B is 3:1, what percent of the vote did candidate Smith win in County B ?

A.25%
B.27%
C.34%
D.43%
E.49%

Hint:-Choose smart Numbers

_________________
" Make more efforts "
Press Kudos if you liked my post
Intern
Joined: 18 Sep 2012
Posts: 2
Location: United States
Re: In an election, candidate Smith won 52% of the total vote in  [#permalink]

### Show Tags

25 Sep 2012, 06:41
1
(61%)*3x + (y%)*x = (52%)*4x
y = 25%
Director
Joined: 22 Mar 2011
Posts: 588
WE: Science (Education)
Re: In an election, candidate Smith won 52% of the total vote in  [#permalink]

### Show Tags

25 Sep 2012, 07:00
3
1
thevenus wrote:
In an election, candidate Smith won 52% of the total vote in Counties A and B. He won 61% of the vote in County A. If the ratio of people who voted in County A to County B is 3:1, what percent of the vote did candidate Smith win in County B ?

A.25%
B.27%
C.34%
D.43%
E.49%

Hint:-Choose smart Numbers

Use the property of weighted averages:
at-a-certain-company-average-arithmetic-mean-number-of-137851.html#p1115917

$$b$$ - percent of the vote that candidate Smith win in County B
In our case: $$\frac{A}{B}=\frac{3}{1}=\frac{52-b}{61-52}$$, from which $$b = 25%.$$

_________________
PhD in Applied Mathematics
Love GMAT Quant questions and running.
Manager
Joined: 21 Oct 2013
Posts: 178
Location: Germany
GMAT 1: 660 Q45 V36
GPA: 3.51
Re: In an election, candidate Smith won 52% of the total vote in  [#permalink]

### Show Tags

10 Jan 2014, 04:27
A : B : Total
3 : 1 : 4

Say there are a total of 100 votes. 100/4 = 25. Three parts of the 100 are in country A. So 75. Rest is in country B. Thus 25, A.

Wasn't quite sure, so this was an elevated guess, does this work? Or was it luck? :D
Senior Manager
Status: Math is psycho-logical
Joined: 07 Apr 2014
Posts: 402
Location: Netherlands
GMAT Date: 02-11-2015
WE: Psychology and Counseling (Other)
In an election, candidate Smith won 52% of the total vote in  [#permalink]

### Show Tags

24 Feb 2015, 03:27
unceldolan wrote:
A : B : Total
3 : 1 : 4

Say there are a total of 100 votes. 100/4 = 25. Three parts of the 100 are in country A. So 75. Rest is in country B. Thus 25, A.

Wasn't quite sure, so this was an elevated guess, does this work? Or was it luck? :D

I think it should work. It sort of uses the unknown multiplier.

In this sense, since we have 4 parts, 1/4 (which is B) is 25%.

We could for example do this:

3x+1x=100 (if we pick 100 as a smart number)
4x=100
x=25.

Then 1*25=25, so B=25.

Nice way!
Senior Manager
Status: Math is psycho-logical
Joined: 07 Apr 2014
Posts: 402
Location: Netherlands
GMAT Date: 02-11-2015
WE: Psychology and Counseling (Other)
Re: In an election, candidate Smith won 52% of the total vote in  [#permalink]

### Show Tags

24 Feb 2015, 03:34
EvaJager wrote:
thevenus wrote:
In an election, candidate Smith won 52% of the total vote in Counties A and B. He won 61% of the vote in County A. If the ratio of people who voted in County A to County B is 3:1, what percent of the vote did candidate Smith win in County B ?

A.25%
B.27%
C.34%
D.43%
E.49%

Hint:-Choose smart Numbers

Use the property of weighted averages:
at-a-certain-company-average-arithmetic-mean-number-of-137851.html#p1115917

$$b$$ - percent of the vote that candidate Smith win in County B
In our case: $$\frac{A}{B}=\frac{3}{1}=\frac{52-b}{61-52}$$, from which $$b = 25%.$$

Sounds reasonable. I couldn't quite get the denominator 61-52 for B. 61% is only the votes in A. 52% are total votes. So, if we subtract 52% (the total votes) from 61% (only votes from A) we should remain with votes from B?
SVP
Joined: 06 Nov 2014
Posts: 1873
Re: In an election, candidate Smith won 52% of the total vote in  [#permalink]

### Show Tags

28 Feb 2015, 11:31
1
2
thevenus wrote:
In an election, candidate Smith won 52% of the total vote in Counties A and B. He won 61% of the vote in County A. If the ratio of people who voted in County A to County B is 3:1, what percent of the vote did candidate Smith win in County B ?

A.25%
B.27%
C.34%
D.43%
E.49%

Hint:-Choose smart Numbers

Let total votes in County A = 3x.
Let total votes in County B = x.
Hence total votes in Count A & B together = 4x

Given that, 0.52(4x) = 0.61(3x) + n(x)
So, 2.08x = 1.83x + nx
So, n = 0.25 = 25%
Hence option A

--
Optimus Prep's GMAT On Demand course for only \$299 covers all verbal and quant. concepts in detail. Visit the following link to get your 7 days free trial account: http://www.optimus-prep.com/gmat-on-demand-course
EMPOWERgmat Instructor
Status: GMAT Assassin/Co-Founder
Affiliations: EMPOWERgmat
Joined: 19 Dec 2014
Posts: 15294
Location: United States (CA)
GMAT 1: 800 Q51 V49
GRE 1: Q170 V170
Re: In an election, candidate Smith won 52% of the total vote in  [#permalink]

### Show Tags

28 Feb 2015, 15:06
Hi All,

unceldolan wrote:
A : B : Total
3 : 1 : 4

Say there are a total of 100 votes. 100/4 = 25. Three parts of the 100 are in country A. So 75. Rest is in country B. Thus 25, A.

Wasn't quite sure, so this was an elevated guess, does this work? Or was it luck? :D

The answer selected by this user IGNORES the percents that we're meant to use, and it's essentially just 'dumb luck' that the user got the question correct.

Here's how you can TEST VALUES to get to the correct answer.

Since we have 3 times as many voters in Country A as in Country B, let's start there....

Country A = 300 voters
Country B = 100 voters

We're told that the candidate won 61% of the votes in A and 52% of the votes in TOTAL. We're asked for the percent of votes that the candidate won in Country B. From this information, we can set up the following equation...

[(.61)(300) + (X)(100)]/400 = .52

183 + 100X = 208
100X = 25
X = 25/100 = 25%

As a side note, the Official GMAT tends to design questions that won't allow for this type of 'coincidence' to be the correct answer.

GMAT assassins aren't born, they're made,
Rich
_________________
Contact Rich at: Rich.C@empowergmat.com

The Course Used By GMAT Club Moderators To Earn 750+

souvik101990 Score: 760 Q50 V42 ★★★★★
ENGRTOMBA2018 Score: 750 Q49 V44 ★★★★★
Senior SC Moderator
Joined: 22 May 2016
Posts: 3565
In an election, candidate Smith won 52% of the total vote in  [#permalink]

### Show Tags

20 Nov 2017, 18:30
thevenus wrote:
In an election, candidate Smith won 52% of the total vote in Counties A and B. He won 61% of the vote in County A. If the ratio of people who voted in County A to County B is 3:1, what percent of the vote did candidate Smith win in County B ?

A.25%
B.27%
C.34%
D.43%
E.49%

Hint:-Choose smart Numbers

$$\frac{A}{B}=\frac{3}{1}$$

I just used those numbers, as you would in a mixture problem.

Let A = 3
Let B = 1
Resultant percentage = .52(A + B) = .52(4)
Let x = percent of vote won in B

.61(3) + x(1) = .52(4)
1.83 + x = 2.08
x = 2.08 - 1.83
x = .25 * 100 = 25 percent

_________________
SC Butler has resumed! Get two SC questions to practice, whose links you can find by date, here.

Instructions for living a life. Pay attention. Be astonished. Tell about it. -- Mary Oliver
Senior Manager
Status: love the club...
Joined: 24 Mar 2015
Posts: 269
Re: In an election, candidate Smith won 52% of the total vote in  [#permalink]

### Show Tags

21 Nov 2017, 03:47
1
thevenus wrote:
In an election, candidate Smith won 52% of the total vote in Counties A and B. He won 61% of the vote in County A. If the ratio of people who voted in County A to County B is 3:1, what percent of the vote did candidate Smith win in County B ?

A.25%
B.27%
C.34%
D.43%
E.49%

Hint:-Choose smart Numbers

hi

lets think this way

the voters, the weights, in country A and B are in the ratio of 3 : 1

now, set the weighted average equation

61 * 3 + 1 * b
____________ = 52
4

solving for b, we get the desired result: 25%
thanks

cheers through the kudos button if this helps you anyway
Target Test Prep Representative
Affiliations: Target Test Prep
Joined: 04 Mar 2011
Posts: 2815
Re: In an election, candidate Smith won 52% of the total vote in  [#permalink]

### Show Tags

22 Nov 2017, 12:13
thevenus wrote:
In an election, candidate Smith won 52% of the total vote in Counties A and B. He won 61% of the vote in County A. If the ratio of people who voted in County A to County B is 3:1, what percent of the vote did candidate Smith win in County B ?

A.25%
B.27%
C.34%
D.43%
E.49%

We can let the number of votes cast in County B = x and thus the number of votes cast in County A = 3x. We can create the following equation where p = percent of vote candidate Smith won in County B:

0.61(3x) + (p/100)x = .52(3x + x)

61(3x) + px = 52(4x)

183x + px = 208x

183 + p = 208

p = 25

_________________

# Jeffrey Miller

Jeff@TargetTestPrep.com
122 Reviews

5-star rated online GMAT quant
self study course

See why Target Test Prep is the top rated GMAT quant course on GMAT Club. Read Our Reviews

If you find one of my posts helpful, please take a moment to click on the "Kudos" button.

Director
Joined: 08 Jun 2013
Posts: 543
Location: France
GMAT 1: 200 Q1 V1
GPA: 3.82
WE: Consulting (Other)
Re: In an election, candidate Smith won 52% of the total vote in  [#permalink]

### Show Tags

08 Oct 2018, 08:48
To find the percent of votes won in County B, we need to recognize that the total votes won is the sum of the votes in the 2 counties and that the number of votes won in each county is the percentage won multiplied by the number of voters. If we let x% be the percent won in County B, we can write this equation: (61% of County A voters) + (x% of County B voters) = 52% of all voters, or 0.61(County A voters) + (x/100) (County B voters) = 0.52(all voters).

We don't know the number of voters, but we do know that the ratio of County A voters to County B voters is 3:1. Thus, 3/4 of the voters are in County A and 1/4 are in County B. Now suppose that V is the total number of voters, meaning that we have V voters in County A and V voters in County B. So, our original equation becomes 0.61*(3/4) v + (x/100) (1/4) v = 0.52v.

Notice that V appears in each term, so it can be cancelled out. In other words, since we know the proportion of voters in each county, we don't need to know the actual number of voters. In fact, we can simply think of the overall percentage won, 52%, as the weighted average of the percentages won in each county, where the weights are each county's fraction of the total voters.

To solve for x, let's get rid of the fractions by multiplying both sides by 400. This gives us 0.61(300) + x = 208, 183 + x = 208, or x = 208 - 183 = 25. The percent of the voters voting for candidate Smith was 25%. Choice (A) is correct.
_________________
Everything will fall into place…

There is perfect timing for
everything and everyone.
Never doubt, But Work on
improving yourself,
Keep the faith and
It will all make sense.
Re: In an election, candidate Smith won 52% of the total vote in   [#permalink] 08 Oct 2018, 08:48
Display posts from previous: Sort by