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Last year, Company X paid out a total of $1,05,000...

This topic has 3 expert replies and 1 member reply

Last year, Company X paid out a total of $1,05,000...

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Last year, Company X paid out a total of $1,050,000 in salaries to its employees. If no employees earned a salary that is more than 20% greater than any other employee, what is the lowest possible salary that any one employee earned?

(A) $40,000
(B) $41,667
(C) $42,000
(D) $50,000
(E) $60,000

The OA is C.

Please, can any expert explain this PS question for me? I tried to solve it but I can't get the correct answer. I need your help. Thanks.

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GMAT/MBA Expert

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swerve wrote:
Last year, Company X paid out a total of $1,050,000 in salaries to its employees. If no employees earned a salary that is more than 20% greater than any other employee, what is the lowest possible salary that any one employee earned?

(A) $40,000
(B) $41,667
(C) $42,000
(D) $50,000
(E) $60,000

The OA is C.

Please, can any expert explain this PS question for me? I tried to solve it but I can't get the correct answer. I need your help. Thanks.
Hi swerve,

Can you please recheck the question statement?
It seems that there is some information missing or incomplete.

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EconomistGMATTutor wrote:
swerve wrote:
Last year, Company X paid out a total of $1,050,000 in salaries to its employees. If no employees earned a salary that is more than 20% greater than any other employee, what is the lowest possible salary that any one employee earned?

(A) $40,000
(B) $41,667
(C) $42,000
(D) $50,000
(E) $60,000

The OA is C.

Please, can any expert explain this PS question for me? I tried to solve it but I can't get the correct answer. I need your help. Thanks.
Hi swerve,

Can you please recheck the question statement?
It seems that there is some information missing or incomplete.
Oh sorry! Here's the complete question!

Last year, Company X paid out a total of $1,050,000 in salaries to its 21 employees. If no employee earned a salary that is more than 20% greater than any other employee, what is the lowest possible salary that any one employee earned?

(A) $40,000
(B) $41,667
(C) $42,000
(D) $50,000
(E) $60,000

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GMAT/MBA Expert

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swerve wrote:
Last year, Company X paid out a total of $1,050,000 in salaries to its 21 employees. If no employee earned a salary that is more than 20% greater than any other employee, what is the lowest possible salary that any one employee earned?

(A) $40,000
(B) $41,667
(C) $42,000
(D) $50,000
(E) $60,000
We can PLUG IN THE ANSWERS, which represent the smallest possible salary.

To MINIMIZE the smallest salary, we must MAXIMIZE the other 20 salaries.
Thus, each of the other 20 salaries must be the maximum allowed value: 20% greater than the smallest salary.
Since the sum of the salaries is 1,050,000 -- a multiple of 1,000 -- the correct answer choice is almost certainly a multiple of 1,000.
Eliminate B.
When the correct answer is plugged in, the sum of all 21 salaries will be 1,050,000.

Answer choice D: Smallest salary = 50,000.
Maximum value of each of the other 20 salaries = 50,000 + 0.2(50,000) = 60,000.
Sum of the 21 salaries = 50,000 + 20(60,000) = 50,000 + 1,200,000 = 1,250,000.
The sum is too big.
Eliminate D and E.

A: Smallest salary = 40,000
Maximum value of each of the other 20 salaries = 40,000 + 0.2(40,000) = 48,000.
Sum of the 21 salaries = 40,000 + 20(48,000) = 40,000 + 960,000 = 1,000,000.
The sum is too small.
Eliminate A.

The correct answer is C.

Algebraically:
Let x = the smallest salary.
As noted above, to MINIMIZE the smallest salary, we must MAXIMIZE the other 20 salaries.
Thus, each of the other 20 salaries must be the maximum allowed value:
20% greater than the smallest salary = 1.2x.
Sum the 20 greatest salaries = 20(1.2x) = 24x.
Since the sum of all 21 salaries is equal to 1,050,000, we get:
x + 24x = 1,050,000
25x = 1,050,000
x = 42,000.

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swerve wrote:
Last year, Company X paid out a total of $1,050,000 in salaries to its employees. If no employees earned a salary that is more than 20% greater than any other employee, what is the lowest possible salary that any one employee earned?

(A) $40,000
(B) $41,667
(C) $42,000
(D) $50,000
(E) $60,000
Since the sum of all the salaries is a fixed amount (which is given to be $1,050,000), the lowest possible salary is obtained when all the salaries besides the lowest one are maximized. Since the greatest possible difference between any two salaries in this company is 20%, all the salaries besides the lowest salary should be 20% more than the lowest salary.

We can let the lowest salary = x and the greatest = 1.2x and create the following equation:

x + 20(1.2x) = 1,050,000

x + 24x = 1,050,000

25x = 1,050,000

x = 42,000

Answer:C

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Scott Woodbury-Stewart
Founder and CEO
scott@targettestprep.com



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