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A retail store employs only clerks

This topic has 1 expert reply and 1 member reply

A retail store employs only clerks

Post Wed Dec 06, 2017 4:33 am
A retail store employs only clerks and managers and the clerks earn $11.50/hour while the managers earn $19/hour. Last year, the store had 20 employees and its average employee earned $13/hour. Thus far this year, the store has hired 4 clerks and promoted some of last year’s clerks to manager. If the store has undergone no other personnel changes and the average employee now earns $14/hour, how many clerks were promoted to manager?

A. 2
B. 4
C. 6
D. 7
E. 8

Can experts show me the best solution in this problem?

OA B

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DavidG@VeritasPrep Legendary Member
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Post Wed Dec 06, 2017 9:46 am
lheiannie07 wrote:
A retail store employs only clerks and managers and the clerks earn $11.50/hour while the managers earn $19/hour. Last year, the store had 20 employees and its average employee earned $13/hour. Thus far this year, the store has hired 4 clerks and promoted some of last year’s clerks to manager. If the store has undergone no other personnel changes and the average employee now earns $14/hour, how many clerks were promoted to manager?

A. 2
B. 4
C. 6
D. 7
E. 8

Can experts show me the best solution in this problem?
OA B
Plot the initial wages on a number line:
11.50-------13------------------19
Gap:----1.5------------6--------

First notice that the average is much closer to the low end than the high, so we know there are more clerks than managers. Next, if we examine the difference between each respective group and the overall average, we can see that there's a ratio of 6:1.5, or 4:1, meaning that for every 4 clerks, there will be 1 manager.

Number of clerks: 4x
Number of managers: x
Total employees: 20
4x + x = 20 --> 5x = 20--> x = 4.

Number of clerks: 4*4 = 16
Number of managers: 4.

If 4 clerks are added, there will be 20 clerks and 4 managers, and a total of 24 employees.

Next we're told that the average pay rose to 14. Again let's plot the figures on the number line
11.50---------14------------------19
Gap:----2.5------------5--------

Ratio of clerks : managers = 5:2.5 = 2:1.
If there are 24 employees, now we have

Clerks: 2y
Managers: y
Total 24
2y + y = 24 --> 3y = 24 --> y = 8.

Clerks:16 and Managers: 8.

If we previously had 20 clerks and 4 managers, and now we have 16 clerks and 8 managers, then 4 clerks must have been promoted. The answer is B

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GMATWisdom Master | Next Rank: 500 Posts Default Avatar
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Post Wed Dec 06, 2017 11:49 am
lheiannie07 wrote:
A retail store employs only clerks and managers and the clerks earn $11.50/hour while the managers earn $19/hour. Last year, the store had 20 employees and its average employee earned $13/hour. Thus far this year, the store has hired 4 clerks and promoted some of last year’s clerks to manager. If the store has undergone no other personnel changes and the average employee now earns $14/hour, how many clerks were promoted to manager?

A. 2
B. 4
C. 6
D. 7
E. 8

Can experts show me the best solution in this problem?

OA B
number of employees initially = 20
average earning = $13/ hour
therefore total earning = 20 x 13 = $260/hour

later 4 more clerks are employed so total earning @ $14/hour = 24 x 14 = $336/hour
earning of the 4 new clerks @ $11.5/hour = 4 x 11.5 = $46/hour
therefore total earning of the initial 20 employees = 336 - 46 = 290/hour

therefore increase in total earning of
initial 20 employees(due to some clerks promoted to managers) = 290 - 260 = $30/hour
that is clerks promoted as managers shall get a total of $30 more

earnings increased of each clerk promoted as manager = 19 - 11.5 = $ 7.5/hour
therefore number of clerks promoted as managers = 30/7.5 = 4

so the correct answer is B

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