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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
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chetan86
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.
chetan86
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)
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General Discussion
Posts: 75
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
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
Posts: 1,776
chetan86
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
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
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
Posts: 177
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
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
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.
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.
chetan86
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
Current Student
Joined: 20 Oct 2018
Last visit: 07 Jun 2022
Posts: 39
Location: United States
Schools: Johnson '24 (A)
GPA: 3.5
Schools: Johnson '24 (A)
Posts: 39
chetan86
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.
Attachments
CompanyMatrix.png [ 3.3 KiB | Viewed 16738 times ]
Posts: 125
KarishmaB
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.
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