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

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Joined: 02 Sep 2009
Posts: 58427

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04 Jan 2018, 23:51
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Difficulty:

35% (medium)

Question Stats:

72% (02:40) correct 28% (03:07) wrong based on 56 sessions

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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

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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

ie. X = (4/3)Y

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

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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
E
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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

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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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