A retail store employs only clerks and managers and the clerks earn $1

Question

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

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

Tapesh03 · Accepted Answer

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!

sleepynut · Answer

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

quantumliner · Answer

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

pushpitkc · Answer

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)

Sent from my LG-H818 using  GMAT Club Forum mobile app

nainy05 · Answer

Hi  Bunuel  ,
Though I reached the answer, it took more than two minutes. Is there any shortcut that I might have missed?

--
Regards.

ScottTargetTestPrep · Answer

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

Akshaynandurkar · Answer

Lets assume there are x clerks last year. so total no of managers would be 20-x
and average pay is 13$
that means 11.5x + 19(20-x) = 13 x 20
solving this we get x = 16 
therefore clerks last year = 16 and managers = 4
now 4 employees are added as clerks so total employees becomes 24 (important)
assume y no of clerks are promoted to managers
so distribution of clerks and managers becomes = 20-y and 4+y respectively and average is 14$
so we get,
11.5(20-y)+19(4+y) = 14 x 24 (24 not 20, remember 4 employees are added)
solving this we get y = 4

ravi1522 · Answer

Hello ,
You can use alligation also

11.50 19

13
6 1.5

so you will get ration as 4:1 and we have 20 employees =clerk 16 and manager 4

11.50 19

14
5 2.5

ration is 2:1 so now we have 24 employees so clerk will 16 and manager will be 8 
Hence 4 clerk have been promoted

Answer is 4

Thank you

A retail store employs only clerks and managers and the clerks earn $1

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A retail store employs only clerks and managers and the clerks earn $1

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