In a mayoral election, Candidate X received 1/3 more votes than Candid

Question

In a mayoral election, Candidate X received 1/3 more votes than Candidate Y, and Candidate Y received 1/4 fewer votes than Candidate Z. If Candidate Z received 24,000 votes, how many votes did Candidate X receive?

(A) 18,000
(B) 22,000
(C) 24,000
(D) 26,000
(E) 32,000

Show Answer

Official Answer

C

(A) 18,000
(B) 22,000
(C) 24,000
(D) 26,000
(E) 32,000

b2bt · Accepted Answer

Z = 100%
Y = 1/4th less than Z = 3/4(Z)
X = 1/3rd more that Y = 4/3 (Y)

Hence X = 4/3*3/4*Z = Z

Answer C
Time Taken 1:05
Difficulty level 550

Bunuel · Answer

SOLUTION

In a mayoral election, Candidate X received 1/3 more votes than Candidate Y, and Candidate Y received 1/4 fewer votes than Candidate Z. If Candidate Z received 24,000 votes, how many votes did Candidate X receive?

(A) 18,000
(B) 22,000
(C) 24,000
(D) 26,000
(E) 32,000

Show Answer

Official Answer

C

(A) 18,000
(B) 22,000
(C) 24,000
(D) 26,000
(E) 32,000

Z=24 --> Y received 1/4 fewer votes than Z --> Y=3/4*Z=18;
X received 1/3 more votes than Y --> X=Y+1/3*Y=24.

Answer: C.

ashreena · Answer

Candidate X= Candidate Y+1/3 CandidateY....1
Candidate Y= Candidate Z-1/4 Candidate Z...2

Candidate Z= 24000 (given)

Solve eq.2
 Candidate Y= 18000

Then solve eq. 1

Candidate X= 24000

Answer: C

DJ1986 · Answer

Another problem where you should put off doing the math!

X=(4/3)(3/4)24
x=24

Abhishek009 · Answer

Let the total no of votes received by z be 12 ( LCM of 3 and 4)

Y received 9 ( 1/4 fewer votes than Candidate Z.)

X received 12 (1/3 more votes than Candidate Y)

So, that means both X and Z received same number of votes.

Hence X received 24,000 votes!!

BrentGMATPrepNow · Answer

GIVEN: Candidate Z received  24,000  votes

Candidate Y received 1/4 fewer votes than Candidate Z   
In other words, Candidate Y received 3/4 of the votes that Candidate Z received
3/4 of  24,000  = (3/4)(  24,000 ) =  18,000

Candidate X received 1/3 more votes than Candidate Y   
1/3 of  18,000  =  6,000 
Number of votes that Candidate X received =  18,000  +  6,000  =  24,000

Answer: C

Cheers,
Brent

Kinshook · Answer

z=24K
y=3/4*34K = 18K
x=4/3*18K = 24K

IMO C

ScottTargetTestPrep · Answer

Since Candidate Y received 1/4 fewer votes than Candidate Z, and Candidate Z received 24,000 votes:

Y = (3/4)(24,000) = 18,000

Since Candidate X received 1/3 more votes than Candidate Y:

X = 4/3 x 18,000 = 24,000

Answer: C

21savage21 · Answer

This isn't a solution but, I wanted to post my error because I think it is a common error.

I simplified the problem.

X:Y Y:Z
3:1 1:4

4x = 24 --> x=6

At this point, I multiplied 6*3 to get 18 and chose A.

MahmudulRonee · Answer

Ratio Approach :

X : Y = 4 : 3 & Y : Z = 3 : 4

Hence, X : Y : Z = 4 : 3 : 4

Notice, X = Z = 4

Therefore, If Z = 24,000, then X = also 24,000 ✌✌✌

Posted from my mobile device

AnirudhaS · Answer

Z = 24000
Y = 24000*3/4 = 18000
X = 18000*4/3 = 24000

Answer:  C

Nipungupta9081 · Answer

we can work backwards in this question.

Votes given to Z = 24000

Votes given to Y 1/4 fewer = 24000 * 1/4 = 24000 - 6000 = 18000
Votes given to X = 1/3 more then Y = 18000 * 1/3 = 18000 + 6000 = 24000
 
 Answer C

Kimberly77 · Answer

Hi  BrentGMATPrepNow  , when I calculate it with 
Y= Z-1/4 , Z= 24,000
Y = 4(24000) -1/4
Y = 23999.75

not sure what did I get it wrong here? Could you help? Thanks

BrentGMATPrepNow · Answer

I think you have misinterpreted the information in the question.

Candidate Y received 1/4 fewer votes than Candidate Z   tells us that candidate Y received 25% fewer votes than candidate Z did. 
This means: Y = Z - (25% of Z)
Plug in values: Y = 24,000 - (25% of 24,000) = 24,000 - 6000 - 18,000

Kimberly77 · Answer

Brilliant thanks BrentGMATPrepNow for the clarification

. Understood now and will watch out for this in future.

ArnauG · Answer

Let's break down the information given step by step to solve the problem.

Candidate Z received 24,000 votes.

Candidate Y received 1/4 fewer votes than Candidate Z.
Candidate Y = Candidate Z - 1/4 * Candidate Z

Candidate X received 1/3 more votes than Candidate Y.
Candidate X = Candidate Y + 1/3 * Candidate Y

Now, let's substitute the values and calculate the number of votes for each candidate.

Candidate Y = 24,000 - 1/4 * 24,000
Candidate Y = 24,000 - 6,000
Candidate Y = 18,000

Candidate X = 18,000 + 1/3 * 18,000
Candidate X = 18,000 + 6,000
Candidate X = 24,000

Therefore, Candidate X received 24,000 votes.

The correct answer is (C) 24,000.

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