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In the department of Mathematics at Green University, more than half o  [#permalink]

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In the department of Mathematics at Green University, more than half of the professors have an income in excess of \$80,000 a year. Which of the following cannot be the average (arithmetic mean) annual income of the professors in the department?

A) \$160,000
B) \$120,000
C) \$50,000
D) \$45,000
E) \$40,000

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Senior Manager  G
Joined: 28 May 2017
Posts: 283
Concentration: Finance, General Management
Re: In the department of Mathematics at Green University, more than half o  [#permalink]

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duahsolo wrote:
In the department of Mathematics at Green University, more than half of the professors have an income in excess of \$80,000 a year. Which of the following cannot be the average (arithmetic mean) annual income of the professors in the department?

A) \$160,000
B) \$120,000
C) \$50,000
D) \$45,000
E) \$40,000

Liked the question....Made me think for a while

Question states that more than half of the professors have an income in excess of \$80,000 a year

Let's assume on a CONSERVATIVE side that exactly 51% of the population has an average income of 80000, so the contribution to average income is 40,800

Let's assume on a CONSERVATIVE side that remaining 49% of the population has an average income of 0, so the contribution to average income is 0

Combining both statements,
average income cant be less than 40,800

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Re: In the department of Mathematics at Green University, more than half o  [#permalink]

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duahsolo wrote:
In the department of Mathematics at Green University, more than half of the professors have an income in excess of \$80,000 a year. Which of the following cannot be the average (arithmetic mean) annual income of the professors in the department?

A) \$160,000
B) \$120,000
C) \$50,000
D) \$45,000
E) \$40,000

Let’s assume that exactly half of the professors make exactly \$80,000 a year. Even if the other half of the professors do not make a penny, the average annual income of all of the professors would be exactly \$40,000. However, since we are given that more than half of the professors make more than \$80,000 a year, even if the other half of the professors do not make a penny, the average annual income would still be more than \$40,000. Thus, answer choice E can’t be the average annual income.

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Director  V
Joined: 27 May 2012
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In the department of Mathematics at Green University, more than half o  [#permalink]

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ScottTargetTestPrep wrote:
duahsolo wrote:
In the department of Mathematics at Green University, more than half of the professors have an income in excess of \$80,000 a year. Which of the following cannot be the average (arithmetic mean) annual income of the professors in the department?

A) \$160,000
B) \$120,000
C) \$50,000
D) \$45,000
E) \$40,000

Let’s assume that exactly half of the professors make exactly \$80,000 a year. Even if the other half of the professors do not make a penny, the average annual income of all of the professors would be exactly \$40,000. However, since we are given that more than half of the professors make more than \$80,000 a year, even if the other half of the professors do not make a penny, the average annual income would still be more than \$40,000. Thus, answer choice E can’t be the average annual income.

sorry, the solutions are not clear .

lets say there are 6 professors.( more than half is 4.)
now if the average is 50,000 then the total is(6 *50,000) 300,000
more than half earn in excess of 80,000 but even if they earn just 80,000 then half their salary totals :
4*80,000= 320,000, which is already more than the total of 6 professors hence even 50,000 cannot be the average.

lets say there are 6 professors.( more than half is 4.)
now if the average is 45,000 then the total is(6 *45,000) 270,000
more than half earn in excess of 80,000 but even if they earn just 80,000 then half their salary totals :
4*80,000= 320,000, which is already more than the total of 6 professors hence even 45,000 cannot be the average.

hence 3 options seem to satisfy this question.
Am i missing anything ?
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Joined: 02 Jan 2016
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Re: In the department of Mathematics at Green University, more than half o  [#permalink]

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ScottTargetTestPrep wrote:
duahsolo wrote:
In the department of Mathematics at Green University, more than half of the professors have an income in excess of \$80,000 a year. Which of the following cannot be the average (arithmetic mean) annual income of the professors in the department?

A) \$160,000
B) \$120,000
C) \$50,000
D) \$45,000
E) \$40,000

Let’s assume that exactly half of the professors make exactly \$80,000 a year. Even if the other half of the professors do not make a penny, the average annual income of all of the professors would be exactly \$40,000. However, since we are given that more than half of the professors make more than \$80,000 a year, even if the other half of the professors do not make a penny, the average annual income would still be more than \$40,000. Thus, answer choice E can’t be the average annual income.

let's say there are 10 professors:

more than half is 6, if they are earning 80,000 than there earnings combined reaches 4,80,000 and lets say there rest 4 do not make any money, then in such a case total would be 480000.

and the average would be 4,80,000/10 = 48000, thus there are two options answer now, 45000 and 40,000.

I believe there is some issue with the questions. Re: In the department of Mathematics at Green University, more than half o   [#permalink] 23 Feb 2018, 00:46
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