In a research and development department, 14 workers have a PhD, and 3

Question

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

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

u1983 · Answer

Lets assume ; 
Women PhD = x & Thus Women Non-PhD = x+10
And Men PhD = y & Thus men Non-PhD = 2y

According to the Q stem :
(1) x+y=14
(2) x+10+2y=30 or x+2y=20 
Now (2)-(1) ==> y=6
hence x=8
Thus x+x+10= 2*8+10=26 Hence  option C .

EgmatQuantExpert · Answer

Solution

Given:  
• In a R&D department, 
 o 14 workers have a PhD, 30 workers don’t have a PhD
o Number of women who don’t have a PhD is 10 more than number of women who have a PhD
o A third of all working men have a PhD

To find:  
• The total number of women working in the department

Approach and Working:   
• Let’s assume the number of women with a PhD degree is x
 o Therefore, the number of women without a PhD degree is (x + 10) 
• Also, let’s assume the total number of men is y
 o Hence, the number of men with a PhD degree =  \frac{y}{3} 
o And, the number of men without a PhD degree =  \frac{2y}{3}

Now we know that 14 workers have a PhD degree and 30 workers don’t have a PhD degree
• Therefore, we can write,
 x +  \frac{y}{3}  = 14 and x + 10 +  \frac{2y}{3}  = 30 
Solving both the equations, we get x = 8 and y = 18

• Therefore, the total number of women working in the department = x + x + 10 = 2x + 10 = 2 * 8 +10 = 26

Hence, the correct answer is option C.

Answer: C

raj2812 · Answer

SOLUTION: LET NUMBER OF WOMEN WITH PHD DEGREE BE = X AND LET TOTAL NUMBER OF MEN BE = Y ------------------------PHD-------------NO-PHD-------------TOTAL MALE-----------------1/3*Y-------------2/3*Y----------------Y FEMALE ----------------X----------------X+10--------------2X+10 TOTAL-----------------14----------------30-----------------44 Now, from above table we can get two equations and solve them. Y/3 + X = 14------------EQUATION 1 = Y + 3X = 42 2Y/3 + (X+10) = 30---------EQUATION 2 = 2Y + 3X = 60 SOLVING BOTH WE GET: Y = 18 AND X = 8. TOTAL NO OF WOMEN = 2X+10 = 2*8 + 10 = 26 ANSWER C

JeffTargetTestPrep · Answer

We see that we have a total of 14 + 30 = 44 people working in the department.

We can create the equation in which m = the number of men and w = number of women, so:

m + w = 44

w = 44 - m

We can let p = number of women with a PhD, and thus p + 10 = number of women without a PhD.

So 2p + 10 = w

Substituting, we have:

2p + 10 = 44 - m

m = 34 - 2p

Using the number of people who have a PhD, we can create the equation:

1/3m + p = 14

Substituting, we have:

(1/3)(34 - 2p) + p = 14

Multiplying by 3, we have:

34 - 2p + 3p = 42

p = 8

We see that 8 women have a PhD; thus, 18 women do not have a PhD, and 8 + 18 = 26 women work in the department.

Answer: C

BrentGMATPrepNow · Answer

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: https://i.imgur.com/HtVyCaR.png 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: https://i.imgur.com/NKY1Nsb.png 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: https://i.imgur.com/Ny4eNwW.png 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 GMAT, so be sure to master the technique. To learn more about the Double Matrix Method, watch this video: https://www.youtube.com/watch?v=jK-tiBrrf04 EXTRA PRACTICE QUESTION https://www.youtube.com/watch?v=DsbPUSH_Wu4 More questions to practice with: EASY: https://gmatclub.com/forum/of-the-120-p ... 15386.html MEDIUM: https://gmatclub.com/forum/in-a-certain ... 21716.html HARD: https://gmatclub.com/forum/a-group-of-2 ... 24888.html KILLER: https://gmatclub.com/forum/a-certain-hi ... 32899.html

effatara · Answer

Total number of workers: 14+30=44
Let the number of Women with PhD be 'x'. Then, the number of Women w/out PhD is (x+10) and total number of Women is (2x+10). Then, total number of Men is 44-(2x+10)=34-2x and number of Men with PhD is (34-2x)/3.

Number of Men and Women with PhD is   which is equal to 14 because it is given that the total number of workers with PhD is 14.
[x + (34 -2x)/3 = 14....> x=8
Total number of women in the department = 2x +10 = 2*8 + 10 = 26. ANS: C

SukanyaRoy · Answer

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

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

C is the answer

Let women with phd=x and women with no phd=x+10
Total women=2x+10
Total people=44
So total men=44-(2x+10)=34-2x
Men with phd=1/3*(34-2x) and men with no phd=20-x

Equating 1/3*(34-2x)+(20-x)=34-2x
X=8

So total women =2x+10
2*8+10=26……..(c)

Thanks!!

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In a research and development department, 14 workers have a PhD, and 3

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