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At Gallicum Enterprises, all employees are in one of three categories:

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Director
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At Gallicum Enterprises, all employees are in one of three categories: [#permalink]

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New post 31 May 2018, 05:27
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Question Stats:

80% (01:27) correct 20% (01:45) wrong based on 44 sessions

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At Gallicum Enterprises, all employees are in one of three categories: J, K, or L. The ratio of the numbers of employees in J to K to L has been 1:3:5 for some time. Last month, 20 new J employees were hired, and no employees left. If the new ratio of J to K is now 1:2 with these new J employees, what is the new total number of employees at Gallicum Enterprises?

A. 180
B. 240
C. 260
D. 320
E. 380

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At Gallicum Enterprises, all employees are in one of three categories: [#permalink]

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New post 31 May 2018, 05:58
aragonn wrote:
At Gallicum Enterprises, all employees are in one of three categories: J, K, or L. The ratio of the numbers of employees in J to K to L has been 1:3:5 for some time. Last month, 20 new J employees were hired, and no employees left. If the new ratio of J to K is now 1:2 with these new J employees, what is the new total number of employees at Gallicum Enterprises?

A. 180
B. 240
C. 260
D. 320
E. 380


Initial number of \(J\), \(K\) and \(L\) employees is \(x\), \(3x\) and \(5x\) respectively.
New number of \(J\), \(K\) and \(L\) employees is \(x+20\), \(3x\) and \(5x\) respectively.

Question stem says that \(\frac{x+20}{3x}=\frac{1}{2}\). So, \(x=40\).

New total number of employees is \(x+3x+5x+20=9*40+20=380\).

Answer: E
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Re: At Gallicum Enterprises, all employees are in one of three categories: [#permalink]

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New post 31 May 2018, 06:09
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aragonn wrote:
At Gallicum Enterprises, all employees are in one of three categories: J, K, or L. The ratio of the numbers of employees in J to K to L has been 1:3:5 for some time. Last month, 20 new J employees were hired, and no employees left. If the new ratio of J to K is now 1:2 with these new J employees, what is the new total number of employees at Gallicum Enterprises?

A. 180
B. 240
C. 260
D. 320
E. 380


If we reduce each of the answer options by 20 employees who have joined
last month, the number of employees must be divisible by 1+3+5 = 9

Testing answer options
A. 180 - 20 = \(\frac{160}{9}\) = Not an integer
B. 240 - 20 = \(\frac{220}{9}\) = Not an integer
C. 260 - 20 = \(\frac{240}{9}\) = Not an integer
D. 320 - 20 = \(\frac{300}{9}\) = Not an integer

E. 380 - 20 = \(\frac{360}{9}\) = Integer (Option E)
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Re: At Gallicum Enterprises, all employees are in one of three categories: [#permalink]

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New post 31 May 2018, 06:18
pushpitkc wrote:
If we reduce each of the answer options by 20 employees who have joined
last month, the number of employees must be divisible by 1+3+5 = 9

Testing answer options
A. 180 - 20 = \(\frac{160}{9}\) = Not an integer
B. 240 - 20 = \(\frac{220}{9}\) = Not an integer
C. 260 - 20 = \(\frac{240}{9}\) = Not an integer
D. 320 - 20 = \(\frac{300}{9}\) = Not an integer

E. 380 - 20 = \(\frac{360}{9}\) = Integer (Option E)


Interesting answer, I haven't thought about this one. good learning for sure.
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At Gallicum Enterprises, all employees are in one of three categories: [#permalink]

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New post 31 May 2018, 11:15
This one is a Reverse Plugging In question.

We can see that the parts J, K and L add up to 9. Thus, the initial total number of employees should be divisible by 9.

Subtract the amount of newcomers (20) from the answer choices and get the following numbers: 160, 220, 240, 300, 360. Clearly, only 360 is divisible by 9 out of these 5 numbers.

Just to be sure, it may be wise to check the option. If there are 360 total employees, then there are \(\frac{1}{9}*360 = 40\) employees working for J. Consequently, \(40* 3 = 120\) and \(40 * 5 = 200\) employees working for K and L respectively.

If we add 20 employees to the J division, the number of employees in J is 60. Hence the new ration of J to K is indeed 1:2, because 60:120 is 1:2. Thus, E is the correct answer.
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Re: At Gallicum Enterprises, all employees are in one of three categories: [#permalink]

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New post 01 Jun 2018, 11:19
aragonn wrote:
At Gallicum Enterprises, all employees are in one of three categories: J, K, or L. The ratio of the numbers of employees in J to K to L has been 1:3:5 for some time. Last month, 20 new J employees were hired, and no employees left. If the new ratio of J to K is now 1:2 with these new J employees, what is the new total number of employees at Gallicum Enterprises?

A. 180
B. 240
C. 260
D. 320
E. 380


We have the ratio of:

J : K : L = x : 3x : 5x, and so the original total number of employees is x + 3x + 5x = 9x.

Last month, 20 new J employees were hired, and no employees left, and the new ratio of J to K is 1:2 with these new J employees:

(x + 20)/3x = 1/2

2(x + 20) = 3x

2x + 40 = 3x

x = 40

The original number of employees was 9x = 9(40) = 360. So the new number of employees is 360 + 20 = 380,

Answer: E
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Re: At Gallicum Enterprises, all employees are in one of three categories:   [#permalink] 01 Jun 2018, 11:19
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