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In a city council election, Candidate X received more votes than Cand

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In a city council election, Candidate X received more votes than Cand [#permalink]

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New post 04 Jan 2018, 23:51
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In a city council election, Candidate X received 1/3 more votes than Candidate Y, and Candidate Y received 1/4 fewer votes than Candidate Z. If the average (arithmetic mean) of votes per candidate was 22,000, how many votes did Candidate X receive?

A. 18,000
B. 20,000
C. 21,000
D. 22,000
E. 24,000
[Reveal] Spoiler: OA

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Re: In a city council election, Candidate X received more votes than Cand [#permalink]

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New post 05 Jan 2018, 05:39
Bunuel wrote:
In a city council election, Candidate X received 1/3 more votes than Candidate Y, and Candidate Y received 1/4 fewer votes than Candidate Z. If the average (arithmetic mean) of votes per candidate was 22,000, how many votes did Candidate X receive?

A. 18,000
B. 20,000
C. 21,000
D. 22,000
E. 24,000


Candidate X received 1/3 more votes than Candidate Y
ie. X = (4/3)Y


Candidate Y received 1/4 fewer votes than Candidate Z
i.e. Y = (3/4)Z


If the average (arithmetic mean) of votes per candidate was 22,000
i.e. (X+Y+Z)/3 = 22000


i.e. X+(3/4)X+(4/3)(3/4)X = 66000

i.e. (11/4)X = 66000
i.e. X = 24000

Answer: Option E
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Re: In a city council election, Candidate X received more votes than Cand [#permalink]

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New post 05 Jan 2018, 07:00
Bunuel wrote:
In a city council election, Candidate X received 1/3 more votes than Candidate Y, and Candidate Y received 1/4 fewer votes than Candidate Z. If the average (arithmetic mean) of votes per candidate was 22,000, how many votes did Candidate X receive?

A. 18,000
B. 20,000
C. 21,000
D. 22,000
E. 24,000


z = z
y =3z/4
x = z

x+y+z = 66000
z+3z/4+z = 66000
11z/4 = 66000
z = 24000
X received 24000 votes
E
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In a city council election, Candidate X received more votes than Cand [#permalink]

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New post 05 Jan 2018, 15:41
Bunuel wrote:
In a city council election, Candidate X received 1/3 more votes than Candidate Y, and Candidate Y received 1/4 fewer votes than Candidate Z. If the average (arithmetic mean) of votes per candidate was 22,000, how many votes did Candidate X receive?

A. 18,000
B. 20,000
C. 21,000
D. 22,000
E. 24,000

Y = \(\frac{3}{4}\)Z => Z = \(\frac{4}{3}\)Y
X = \(\frac{4}{3}\)Y
X = Z = \(\frac{4}{3}\)Y

\(\frac{X + Y + Z}{3}\) = 22,000
X + Y + Z = 66,000

\(\frac{4}{3}\)Y + Y + \(\frac{4}{3}\)Y = 66,000

\(\frac{11}{3}\)Y = 66,000
Y = 66,000 * \(\frac{3}{11}\) = 18,000

X = \(\frac{4}{3}\) * 18,000 = 24,000

Answer E
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In a city council election, Candidate X received more votes than Cand   [#permalink] 05 Jan 2018, 15:41
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