Company X has 50 employees and company Y has 60 employees.

Question

Company X has 50 employees and company Y has 60 employees. Both companies have same number of full time employees, but company Y has 3 more than twice the number of part-time employees that Company X has. How many part-time employees does Company Y have?
(A) 3
(B) 7
(C) 14
(D) 17
(E) 20

(A) 3
(B) 7
(C) 14
(D) 17
(E) 20

adiagr · Accepted Answer

X Y
Total Employees 50 60
Full time Employees F F 
Part Time Employees 50-F 60-F

Given: {2* (50-F)} + 3 = 60- F

100-2F+3 = 60 - F

F = 43

Total employees in Company Y = 60. Therefore pat time employees : 60-43 = 17.

D is the answer.

KarishmaB · Answer

X has 50 employees and Y has 60. Why does Y have 10 extra employees? Because it has 3 more than twice the number of part time employees of company X. 
So the number of 10 extra employees is composed of 3 + 7 ----> 7 must be the number of part time employees company X has.

Number of part time employees company Y has = 3 + 2*7 = 17

Answer (D)

sudhirmadaan · Answer

two ways :- 
in comp X let part time employees = X 
full time = 50-x
in comp Y
(part time number is) 2x+3 + (full time) 50-x = 60 ==> x=7

another quick way is Full time employees are same difference is only because of part time explyee 
2x+3 -x =10 ==> x= 7

OptimusPrepJanielle · Answer

X: 50 employees
Y: 60 employees

Assume the total full time employees with each company = f
part time in X = 50 - f
Part time in Y = 60 - f

Given: Part time in Y = 2(part time in X) + 3
60 - f = 2(50 - f) + 3
60 - f = 103 - 2f
f = 43

Part time employees in Company Y = 60 - 43 = 17

Correct Option: D

law258 · Answer

7x+4y=50
3+2x+y=60

Substitute (1) into (2) --> 3+2(50-y)+y=60
103-y=60
 y=43

Plugging into second equation --> 3+2(7) = 17

matthewsmith_89 · Answer

You could even do process elimination

It can not be A
2x + 3 = 3
x = 0

It can not be B
2x + 3 = 7
x = 2

Full time Y 60 - 7 = 53

Full time X 50 - 2 = 48 X & Y do not coincide.

It can not be C
2x + 3 = 14
The number is not an integer

The answer is D!
2x + 3 = 17
2x = 14
x = 7

Full time Y 60 - 17 = 43

Full time X 50 - 7 = 43

No need to work out E.

The answer is D

fiel9882 · Answer

F = full time employees at both companies since they are the same.
Let x = part time employees at X.
Let y = part time employees at Y.

"Y has 3 more than two times the part time employees as X" is y=2x+3

Y: F+y=60
X: F+x=50

X-Y: (F+y=60) - (F+x=50) = y-x=10

Now, y=2x+3, so: (2x+3)-x=10 -> x=7

Part time employees at Y is y=2x+3, so plug in x to get y=17.

Basshead · Answer

F = full time 
P = Part time

Company X:  P + F = 50

Company Y:  2P + 3 + F = 60

2P + 3 + F - (P + F) = P + 3 = 10 
 P = 7

2P + 3 = 17

Answer is D.

dylanl1218 · Answer

I found that a matrix was the most straight forward way to solve this question:

Utilizing this matrix we can see that A + P = 50, and A + P + P + 3 = 60, so then 50 + P + 3 = 60, and from there P can be easily solved for 7 and 3+2(7) = 17.

sriharsha4444 · Answer

why would the 10 extra employees that Y has be decomposed into 3 + 7 and 7 must be number of part time employees company X has.

bumpbot · Answer

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Company X has 50 employees and company Y has 60 employees.

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Company X has 50 employees and company Y has 60 employees.

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