NEW HERE? LEARN MORE
closeclose
Last visit was: 11 May 2024, 14:12 It is currently 11 May 2024, 14:12
Decision Tracker
My Rewards
New posts
New comers' posts

Close
GMAT Club Daily Prep
Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track
Your Progress

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History
Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.
Go to My Error Log Learn more
Close
Request Expert Reply
Confirm Cancel

In a certain store, the ratio of part-time workers to full-time worker

SORT BY:
Date
Kudos
Tags:
Find Similar Topics 
Show Tags
Hide Tags
User avatar
L
vikasp99
Senior Manager
Senior Manager
Joined: 02 Jan 2017
Posts: 271
Own Kudos [?]: 1478 [10]
Given Kudos: 235
Location: Canada
Send PM
In a certain store, the ratio of part-time workers to full-time worker [#permalink] New post   14 Mar 2017, 03:27
10
Bookmarks
00:00
A
B
C
D
E

Difficulty:

15% (low)

Question Stats:

83% (01:42) correct 17% (02:31) wrong based on 211 sessions
Hide Show timer Statistics
In a certain store, the ratio of part-time workers to full-time workers is 2 to 5. If 4 part-time workers were hired, then the ratio would be 3 to 5. How many workers does the store have?

(A) 11

(B) 12

(C) 21

(D) 28

(E) 35
ShowHide Answer
Official Answer
D
Most Helpful Reply
User avatar
L
BrentGMATPrepNow
GMAT Club Legend
GMAT Club Legend
Joined: 12 Sep 2015
Posts: 6817
Own Kudos [?]: 30145 [2]
Given Kudos: 799
Location: Canada
Send PM
Re: In a certain store, the ratio of part-time workers to full-time worker [#permalink] New post   13 Nov 2019, 08:37
1
Kudos
1
Bookmarks
Expert Reply
Top Contributor
vikasp99 wrote:
In a certain store, the ratio of part-time workers to full-time workers is 2 to 5. If 4 part-time workers were hired, then the ratio would be 3 to 5. How many workers does the store have?

(A) 11
(B) 12
(C) 21
(D) 28
(E) 35


We can also use two variables (although 1 variable is typically faster)

The ratio of part-time workers to full-time workers is 2 to 5\
Let P = number of Part-time workers
Let F = number of Full-time workers
We can write: P/F = 2/5
Cross multiply to get: 5P = 2F


If 4 part-time workers were hired, then the ratio would be 3 to 5.
This would mean there are no P+4 part-time workers
Also, there are still F full-time workers
We can write: (P+4)/F = 3/5
Cross multiply to get: 5(P + 4) = 3F
Expand to get: 5P + 20 = 3F
Replace 5P with 2F to get: 2F + 20 = 3F
Solve to get F = 20
So, there are presently 20 full-time employees

How many workers does the store have?
Since F = 20, we can use the equation 5P = 2F to help find the value of P
Replace F with 20 to get: 5P = 2(20)
Simplify: 5P = 40
Solve to get: P = 8

TOTAL number of workers = F + P = 20 + 8 = 28

Answer: D

Cheers,
Brent
General Discussion
User avatar
L
EMPOWERgmatRichC
GMAT Club Legend
GMAT Club Legend
Joined: 19 Dec 2014
Status:GMAT Assassin/Co-Founder
Affiliations: EMPOWERgmat
Posts: 21843
Own Kudos [?]: 11681 [3]
Given Kudos: 450
Location: United States (CA)
GMAT 1: 800 Q51 V49
GRE 1: Q170 V170
Send PM
Re: In a certain store, the ratio of part-time workers to full-time worker [#permalink] New post   28 Nov 2017, 13:36
1
Kudos
1
Bookmarks
Expert Reply
Hi All,

We're told that the ratio of part-time workers to full-time workers is 2 to 5. This means that:

1) The number part-time workers MUST be a multiple of 2
2) The number of full-time workers MUST be a multiple of 5
3) The total number of workers must be a multiple of 7

We're also told that IF 4 part-time workers were hired, then the ratio of part-time workers to full-time workers would be 3 to 5. We're asked for the TOTAL number of workers there are NOW (meaning before 4 part-time workers are hired).

This question can be solved in a number of different ways. Since the total number of workers is a multiple of 7 - and the answers are numbers - we can TEST THE ANSWERS. To start, we can eliminate Answers A and B (since they're NOT multiples of 7).

Let's TEST Answer D: 28 total workers

IF.... there are 28 total workers
8 are part-time and 20 are full-time
Adding 4 more part-time workers would give us....
12 part-time and 20 full-time
12:20 = 3:5
This is an exact match for what we were told, so this MUST be the answer!

Final Answer:
Show Spoiler
D


GMAT assassins aren't born, they're made,
Rich
User avatar
B
lmuenzel
Intern
Intern
Joined: 09 Jan 2017
Posts: 17
Own Kudos [?]: 83 [2]
Given Kudos: 7
Location: Germany
Concentration: International Business, General Management
GPA: 3.7
Send PM
Re: In a certain store, the ratio of part-time workers to full-time worker [#permalink] New post   14 Mar 2017, 08:50
1
Bookmarks
My Approach
2x+5x=7x

\(\frac{2}{5}\)

+4 part time => \(\frac{3}{5}\)

1x=4

(2*4) + (5*4) = 28
User avatar
L
Bunuel
Math Expert
Joined: 02 Sep 2009
Posts: 93161
Own Kudos [?]: 622947 [1]
Given Kudos: 81832
Send PM
CAT Tests Forum Quiz Mode
Re: In a certain store, the ratio of part-time workers to full-time worker [#permalink] New post   25 Feb 2024, 07:35
1
Kudos
Expert Reply
 
Lowpoint wrote:
In a certain store, the ratio of part-time workers to full-time workers is 2 to 5. If 4 part-time workers were hired, then the ratio would be 3 to 5. How many workers does the store have?

(A) 11

(B) 12

(C) 21

(D) 28

(E) 35

Doubt: Why are we multiplying x = 4 with 2/5 instead of 3/5? Because it says the new ratio is 3/5? So shouldn't we multiply x with 3/5 and won't it become 32 workers at store?


I understand the confusion. The stem states that the ratio IS 2 to 5, and then it presents a hypothetical scenario, stating that IF 4 part-time workers were hired, then the ratio would become 3 to 5. Therefore, in reality, these 4 employees are not hired, and when calculating the number of employees, we should use the 2 to 5 ratio.­

Hope it helps.
User avatar
L
generis
Senior SC Moderator
Joined: 22 May 2016
Posts: 5330
Own Kudos [?]: 35543 [0]
Given Kudos: 9464
Send PM
CAT Tests
In a certain store, the ratio of part-time workers to full-time worker [#permalink] New post   28 Nov 2017, 14:05
Expert Reply
vikasp99 wrote:
In a certain store, the ratio of part-time workers to full-time workers is 2 to 5. If 4 part-time workers were hired, then the ratio would be 3 to 5. How many workers does the store have?

(A) 11

(B) 12

(C) 21

(D) 28

(E) 35

Another approach: set up the original ratio with x, add the number given, set it equal to the new ratio, and multiplier x gives you the original actual numbers.

The ratio of part-time workers to full-time workers is 2 to 5

\(\frac{Part-time}{Full-time}=\frac{2x}{5x}\)

If 4 part-time workers were hired, then the ratio would be 3 to 5:

\(\frac{2x + 4}{5x}=\frac{3}{5}\)

\(5(2x + 4) = 3(5x)\)
\(10x + 20 = 15x\)
\(20 = 5x\)
\(x = 4\)

x is the multiplier for the original ratio

How many workers (TOTAL)?
Part-time = 2x = (2)(4) = 8
Full-time = 5x = (5)(4)= 20

20 + 8 = 28

Answer D
User avatar
L
ScottTargetTestPrep
Target Test Prep Representative
Joined: 14 Oct 2015
Status:Founder & CEO
Affiliations: Target Test Prep
Posts: 18841
Own Kudos [?]: 22194 [0]
Given Kudos: 285
Location: United States (CA)
Send PM
Re: In a certain store, the ratio of part-time workers to full-time worker [#permalink] New post   17 Nov 2019, 20:17
Expert Reply
vikasp99 wrote:
In a certain store, the ratio of part-time workers to full-time workers is 2 to 5. If 4 part-time workers were hired, then the ratio would be 3 to 5. How many workers does the store have?

(A) 11

(B) 12

(C) 21

(D) 28

(E) 35



We can let the number of part-time and full-time workers be 2x and 5x, respectively. We can create the equation:

(2x + 4)/(5x) = 3/5

5(2x + 4) = 3(5x)

10x + 20 = 15x

20 = 5x

4 = x

So there are 2(4) = 8 part-time workers and 5(4) = 20 full-time workers, and therefore, there are 28 workers in the store.

Answer: D
User avatar
B
Lowpoint
Intern
Intern
Joined: 25 Dec 2023
Posts: 15
Own Kudos [?]: 1 [0]
Given Kudos: 130
Location: India
Send PM
Forum Quiz Mode
Re: In a certain store, the ratio of part-time workers to full-time worker [#permalink] New post   24 Feb 2024, 20:10
Doubt: Why are we multiplying x = 4 with 2/5 instead of 3/5? Because it says the new ratio is 3/5? So shouldn't we multiply x with 3/5 and won't it become 32 workers at store?
GMAT Club Bot
gmatclubot
Re: In a certain store, the ratio of part-time workers to full-time worker [#permalink]
24 Feb 2024, 20:10
Moderators:
Bunuel
Math Expert
93161 posts
yashikaaggarwal
Senior Moderator - Masters Forum
3137 posts

Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne
Main navigation
GMAT Resources
Partners
MBA Resources
www.gmac.com|www.mba.com | | GMAT Club Rules | Terms and Conditions