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In a mayoral election

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by BTGmoderatorDC » Wed Jan 31, 2018 2:54 am
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

Can some experts show me different ways to solve this problem?

OA C
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by Brent@GMATPrepNow » Wed Jan 31, 2018 7:47 am
lheiannie07 wrote: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

Can some experts show me different ways to solve this problem?

OA C
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

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Brent
Brent Hanneson - Creator of GMATPrepNow.com
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by DrMaths » Wed Jan 31, 2018 8:31 am
X = 4/3Y (because 1 + 1/3 = 4/3)
Y = 3/4Z (because 1 - 1/4 = 3/4)
Substituting Y into X gives X = 4/3*3/4Z = Z

Therefore X = Z = 24000
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by Scott@TargetTestPrep » Fri Feb 02, 2018 11:14 am
lheiannie07 wrote: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
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:

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

Answer: C

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