A retail store has 60 employeesfull-time salespeople (FT sales), part

Question

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A retail store has 60 employees—full-time salespeople (FT sales), part-time salespeople (PT sales), and managers—in the proportions shown by the graph. Each full-time salesperson and each manager works the same number of hours per week; each part-time salesperson works exactly half that many hours per week.

The store wants the ratio of the total number of hours worked per week by full-time salespeople to the total number of hours worked by part-time salespeople to be 2:3 and wants to achieve this ratio without changing the number of managers or the number of hours each manager works per week.

Based on the information provided, select the option from each drop-down menu that creates the most accurate statement.

To achieve the desired ratio, the store could  GRAPH_1_PLACEHOLDER  the number of full-time salespeople and  GRAPH_2_PLACEHOLDER  the number of part-time salespeople.

ID: 700246

egmat · Accepted Answer

This GI Pie chart question exemplifies the importance of organizing information in a table so that we do not get confused about which factor can be changed and which factor cannot be changed according to the conditions specified in the question.

Next, this question also showcases how to utilize answer choices to arrive at the answer. Through data processing, we get one equation in two variables and we need to find the answers to both these variables. Thus, for such questions, we need to use the answer choices. But for that as well, there are two approaches:
1. Plugging the choices one by one
2. Drawing inferences from the equation and then doing smart analysis with the choices

Watch the video solution to see the detailed solution. While plugging choices one by one may appear to be the faster way, in the long run as you develop your skill of drawing inferences, you will realize that it is faster to solve the question by drawing inferences and then doing smart analysis of the choices. So, invest the time in building this skill during your preparation mode.

https://www.youtube.com/watch?v=Sjkz29q1DxM

KarishmaB · Answer

Of the 60 employees, 30% are FT (= 18) and 60% are PT (= 36)
FT are half in number but work twice the hours of PT so their ratio of total number of hours worked is 1:1.

We want to make it 2:3 by adding or reducing the number of FT and PT only. Since the ratio has to be reduced, we must need to decrease the number of FT and/or increase the number of PT. Keep an eye on the available options.

Say each PT works x hrs and each FT works 2x hrs.

Ratio of total number of hours worked =  \frac{2}{3} = \frac{(18 - ?)*2x}{(36+?)*x}=\frac{(18 - ?)*2}{(36+?)}

Denominator should be 3 times (18 - ?).
If we reduce 18 by 2, we get 16 but denominator cannot be made 48 (no option of adding 12 PTs)
If we reduce 18 by 4, we get 14 and denominator can be made 42 by adding 6 PTs. This works.

Decrease FTs by 4 and increase PTs by 6. ANSWER

The question uses the application of concepts of ratios and percentages. Check them here: https://youtu.be/5ODENGG5dvc 
 https://youtu.be/HxnsYI1Rws8

chetan2u · Answer

ckavya2691 , refer your query on the question

There are 60 employees. Manager - 6; FT - 18 and PT - 36
Let each PT work for x hours, so FT will work for 2x hours.

The ratio = 18*2x:36*x = 1:1

However, this has to be changed to 2:3 by changing the number of employees.
Clearly, number of hours worked increases for PT / decreases for FT, so their PT has to be increased / FTcould be increased/decreased depending on the increase in PT.

Increase in PT:
2: 38, so number of hours = 38x....Ratio  38x*\frac{2}{3}:38x .....NUmber of hours for FT is not an integer and options are in integer.
4: 40, so number of hours = 40x....Ratio  40x*\frac{2}{3}:40x .....NUmber of hours for FT is not an integer and options are in integer.
6: 42, So number of hours = 42x....Ratio  42x*\frac{2}{3}:42x = 28x:42x = 14*2x:42*x .....Thus, increase by 6, 36 to 42, and a simultaneous decrease of 18-14 or 4 would give a ratio 2:3.

Solution
A. Decrease by 4
B. Increase by 6

Bisleri · Answer

As per the Question - "and wants to achieve this ratio without changing the number of managers or the number of hours each manager works per week"

Therefore, the Decrease in the number of FTs should be equal to the increase in no of PTs.

On solving, Decrease and Increase come to 4.5 Each, which is not possible

IMO All options are wrong

chetan2u · Answer

The question nowhere mentions that the number of employees has to be constant.

It says that the number of hours manager works should not change, and number of hours for FT and PT is related to the number of hours manager works.
You can only change the number of FT and PT to get the ratio.

Oppenheimer1945 · Answer

ft=18 (2h hrs)
pt=36 (h hrs)

2/3=2(18+x)/(36+y)

(18+x)/(36+y)=1/3

as 18/36 is 1/2 >1/3

lets reduce Num in steps. red by 2 should have denom of 42 (inc by 6)

ruis · Answer

Official answer: https://gmatclub.com/forum/download/file.php?id=81820 Does anyone have a different approach to this question? other than the already discussed or the official? GMAT-Club-Forum-qfrjtvdv.png

chetan2u · Answer

ruis , another logical approach would be

The ratio of working hours that we want FT:PT to be is 2:3
As PT works half time, we require half the number of FT to do same work. Thus, converting the ratio to number of FT people : number of PT people = 2/2 : 3 or 1:3

Knowing this, we now know that earlier ratio of 30%:60% or 1:2 has to be brought down to 1:3.
Clearly FT has to be reduced and PT increased.

Initially, FT people = 30% of 60 or 18 and 60% of 60 or 36
Decrease: by(2,4,6) means (18-2,18-4,18-6) or (16,14,12)…..(I)
Increase: by(2,4,6) means (36+2,36+4,36+6) or (38,40,42)…..(II)

Now find a number in I and II that give you a ratio 1:3 => 14:42 is the answer

ruis · Answer

Are there similar questions (PS, DI or DS) to practice where we go from initial an ratio to a different final ratio?  Bunuel

colfer · Answer

https://gmatclub.com/forum/download/file.php?id=82024 GMAT-Club-Forum-kznx5q1x.png

playthegame · Answer

Official Explanation

Apply
Let a represent the change in the number of FT employees, each of whom works x hours per week, and let b represent the change in the number of PT employees, each of whom works ​x over 2​ hours per week. Since 30% of the 60 employees are FT, 18 employees are FT. Since 60% of the 60 employees are PT, 36 employees are PT. The ratio ​total number of hours worked by FT employees over total number of hours worked by PT employees​ needs to be 2:3. It follows that

​open paren 18 plus a close paren times x over open paren 36 plus b close paren times open paren x over 2 close paren​

= 
​two thirds​

3(18 + a)(x)

= 
2(36 + b) ​open paren x over 2 close paren​

54 + 3a

= 
36 + b

18

= 
b − 3a

a

= 
​the fraction with numerator 18 minus b and denominator negative 3​

In order for a to be an integer, 18 − b must be divisible by 3, from which it follows that b must be divisible by 3. The only number given in the answer choices that is divisible by 3 is 6 so b = 6 and a = ​the fraction with numerator 18 minus 6 and denominator negative 3​ = −4.

RO1: Apply
Since a = −4, the number of FT employees must be decreased by 4.

The correct answer is decrease by 4.

RO2: Apply
Since b = 6, the number of PT employees must be increased by 6.

The correct answer is increase by 6.

Gemmie · Answer

2x: number of hours that a FT person works per week
x: number of hours that a PT person works per week

a: change in number of FT persons
b: change in number of PT persons

From the pie chart => PT = 36; FT = 18

\frac{(18 + a) * 2x}{(36 + b) * x} = \frac{2}{3}

=>  \frac{18 + a}{36+b} = \frac{1}{3}

=> 54 + 3a = 36 + b
=> 18 + 3a = b
=> 3 (6 + a) = b
=> b is divisible by 3
=> b is either 6 or -6

If b = 6 => 6 + a = 2 => a = -4
If b = -6 => 6 + a = -2 => a = -8

Therefore, a = -4 and b = 6

To achieve the desired ratio, the store could   the number of full-time salespeople and   the number of part-time salespeople.

PeachSnapple1 · Answer

Took me a second try because I had assumed the total number of employees stays unchanged.

pappal · Answer

FT 
 PT 
 M 
 
  employees 
 18 
 36 
 6 
 
  hrs. worked per week 
 2x 
 x 
 2x 
 
  total man hours 
 36x 
 36x 
 12x

desired ratio=>FT man hrs./PT man hrs.=2/3 (which currently is 1:1), condition without disturbing managers or their work hrs. per week
lets examine the options step wise:  for certain we have to have decrease in option1 and increase in option2 
if FT no. reduces by 2 then total man hrs.=32x, to get the desired ratio we have to increase PT no.to (32x/2)*3=48 i.e. 12 increase which is not given in the option 2.  DISCARD 
if FT no. reduces by 4 then total man hrs.=28x, to get the desired ratio we have to increase PT no.to (28x/2)*3=42 i.e. 6 increase given in option 2  RIGHT CHOICE 
so correct answer is  4,6

A retail store has 60 employeesfull-time salespeople (FT sales), part

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	FT	PT	M
employees	18	36	6
hrs. worked per week	2x	x	2x
total man hours	36x	36x	12x

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A retail store has 60 employeesfull-time salespeople (FT sales), part

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