Last visit was: 17 May 2024, 16:46 It is currently 17 May 2024, 16:46

Close

GRE Prep 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 GRE 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.

Close

Request Expert Reply

Confirm Cancel
Retired Moderator
Joined: 07 Jan 2018
Posts: 739
Own Kudos [?]: 1376 [3]
Given Kudos: 93
Send PM
Retired Moderator
Joined: 07 Jan 2018
Posts: 739
Own Kudos [?]: 1376 [2]
Given Kudos: 93
Send PM
avatar
Manager
Manager
Joined: 02 Dec 2018
Posts: 74
Own Kudos [?]: 31 [2]
Given Kudos: 0
Send PM
User avatar
Manager
Manager
Joined: 01 Nov 2018
Posts: 87
Own Kudos [?]: 140 [0]
Given Kudos: 0
Send PM
Re: In a research and development department [#permalink]
Expert Reply
How about this
Women with PHD =Wp
Women without PHD is Wp+10
That means total women is Wp+Wp+10=2Wp+10
Men with PHD=M/3
Total Men is M

Men+Women=44
M+2Wp+10=44

M=34-2Wp, so we have a substitution for Women to men
Then lets look at the PHD's
M/3 + Wp = 14
(34-2Wp)/3+ Wp = 14

(34-2wp +3Wp)/3= 14
34+Wp=42
Wp=8
Wp+10=18
Total women = 2Wp+10= 26

The choice is C
Retired Moderator
Joined: 10 Apr 2015
Posts: 6218
Own Kudos [?]: 11734 [0]
Given Kudos: 136
Send PM
Re: In a research and development department [#permalink]
1
amorphous wrote:
In a research and development department, 14 workers have a PhD, and 30 workers don't have a PhD degree. In the department, the number of women that do not have a PhD degree is 10 greater than the number of women who do have a PhD. If a third of the men working in the department have a PhD degree, then how many women work in the department?

A) 16
B) 18
C) 26
D) 28
E) 32


Let's use the Double Matrix Method.
This technique can be used for most questions featuring a population in which each member has two characteristics associated with it (aka overlapping sets questions)..

Here, we have a population of workers, and the two characteristics are:
- has a PhD or doesn't have a PhD
- woman or man

In a research and development department, 14 workers have a PhD, and 30 workers don't have a PhD degree.
So there are 44 workers in TOTAL.
Our diagram looks like this:
Image



In the department, the number of women that do not have a PhD degree is 10 greater than the number of women who do have a PhD.
Let x = the number of women who DO have a PhD degree is 10 greater
So, x+10 = the number of women who do NOT have a PhD degree is 10 greater
We can add this information to the diagram to get:
Image



A third of the men working in the department have a PhD degree
Let y = the total number of men working in the department
So, y/3 = the number of men WITH a PhD degree
And 2y/3 = the number of men WITHOUT a PhD degree
We get: Image



How many women work in the department?
On the left-side column, we see that: x + y/3 = 14
Multiply both sides by 3 to get: 3x + y = 42

On the right-side column, we see that: (x + 10) + 2y/3 = 30
Simplify to get: x + 2y/3 = 20
Multiply both sides by 3 to get: 3x + 2y = 60

We have:
3x + 2y = 60
3x + y = 42

Subtract the bottom equation from the top equation to get: y = 18
This means there are 18 MEN in the department.
Since there are 44 workers in total, the remaining 26 workers are WOMEN

Answer: C

This question type is VERY COMMON on the GRE, so be sure to master the technique.

To learn more about the Double Matrix Method, watch this video:
User avatar
GRE Prep Club Legend
GRE Prep Club Legend
Joined: 07 Jan 2021
Posts: 4501
Own Kudos [?]: 68 [0]
Given Kudos: 0
Send PM
Re: In a research and development department [#permalink]
Hello from the GRE Prep Club BumpBot!

Thanks to another GRE Prep Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
Prep Club for GRE Bot
[#permalink]
Moderators:
Moderator
1085 posts
GRE Instructor
218 posts

Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne