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18 May 2017, 00:17
14
00:00

Difficulty:

45% (medium)

Question Stats:

72% (03:14) correct 28% (03:10) wrong based on 139 sessions

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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

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18 May 2017, 06:05
Bunuel 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

let x be the number of clerks who got promoted.
(1) $$\frac{(11.5C + 19M)}{(C+M)}$$ = 13
(2) $$\frac{(11.5(C+4-X) + 19(M+x))}{(C+M+4)}$$ = 14
(3) C+M = 20

From (1) & (3); C=16,M=4
substitute C,M into (2);x = 4
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Re: A retail store employs only clerks and managers and the clerks earn $1 [#permalink] ### Show Tags 18 May 2017, 11:12 1 Given: clerks earn$11.50/hour
managers earn $19/hour Total Number of Clerks currently working = c Total Number of Managers currently working = m Given c+m=20 11.50c+19m = (c+m)13 Solving above two: 11.5c+19m = 13c+13m 6m = 1.5c c=4m 4m+m=20 m=4 c=16 This year, 'n' clerks were promoted to manager c= 16+4-n m=4+n (20-n)11.5+(4+n)19 = (20-n+4+n)14 230-11.5n+76+19n=336 7.5n = 336-306 = 30 n=4 Answer is B Senior PS Moderator Joined: 26 Feb 2016 Posts: 3341 Location: India GPA: 3.12 Re: A retail store employs only clerks and managers and the clerks earn$1  [#permalink]

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18 May 2017, 11:46
a+b=20(where a is number of clerks and b the number of manager)
Also 11.5a+19b=13*20=260

Solving for both the equations(19a+19b=380,11.5a+19b=260) and substracting, we will get 7.5a=120 or a=16)

Now since 4 new clerks were added and few members were promotes, we have 20-x clerks now and 4+x managers.

Also given that
11.5(20-x) + 19(4+x) = 24*14
230 + 76 + 7.5x = 336
7.5x = 30 or x=4(Option B)

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04 Jun 2017, 02:44
2
Here's the shortcut to do this question in 30 seconds!
Solution - think of this problem as an expenditure problem! there were 20 employees, $13.00 avg salary - Total expenditure is$260
4 employees are added, total employees now is 24, $14.00 avg. salary - Total expenditure is$336
Extra expenditure is $76 for the 4 clerks that are added, it's$46, remaining amount is $30 ($76-$46) and this$30 is expenditure for promotions. each promotion cost $7.5 ($19-$11.5), so divide 30 by$7.5 - you can 4. 4 clerks were promoted! Hope you will find it easier and faster!
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Re: A retail store employs only clerks and managers and the clerks earn $1 [#permalink] ### Show Tags 04 Apr 2019, 18:15 Bunuel 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 We can let x = the number of clerks in the store before any new hires or promotions. Thus, 20 - x = the number of managers, and we can create the equation: (11.5x + 19(20 - x))/20 = 13 11.5x + 380 - 19x = 260 -7.5x = -120 x = 16 Therefore, there were 16 clerks and 4 managers before any new hires or promotions, and there were 24 employees after the personnel changes. Now let’s let n = the number of clerks who were promoted to manager. Since there are 4 new clerks who were hired, we can create the equation for the income of the employees: (11.5(16 + 4 - n) + 19(4 + n))/24 = 14 230 - 11.5n + 76 + 19n = 336 7.5n = 30 n = 4 Answer: B _________________ # Scott Woodbury-Stewart Founder and CEO Scott@TargetTestPrep.com 122 Reviews 5-star rated online GMAT quant self study course See why Target Test Prep is the top rated GMAT quant course on GMAT Club. Read Our Reviews If you find one of my posts helpful, please take a moment to click on the "Kudos" button. Re: A retail store employs only clerks and managers and the clerks earn$1   [#permalink] 04 Apr 2019, 18:15
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