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Company X had a ratio of 4 full-time employees for every 3 part-time

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Company X had a ratio of 4 full-time employees for every 3 part-time  [#permalink]

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New post 17 Jan 2018, 00:12
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Company X had a ratio of 4 full-time employees for every 3 part-time employees until 2 part-time employees quit. If that brought the current ratio down to 3:2, how many employees does the company now have?

A. 30
B. 40
C. 50
D. 60
E. 70

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Company X had a ratio of 4 full-time employees for every 3 part-time  [#permalink]

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New post 17 Jan 2018, 02:05
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Bunuel wrote:
Company X had a ratio of 4 full-time employees for every 3 part-time employees until 2 part-time employees quit. If that brought the current ratio down to 3:2, how many employees does the company now have?

A. 30
B. 40
C. 50
D. 60
E. 70


The current ratio of the FT : PT = 4:3
where FT - number of full-time employees and PT - number of part-time employees

After two part-time employees leave, the ratio becomes 3:2

\(\frac{4x}{3x-2} = \frac{3}{2} => 8x=9x-6 => x=6\)

Therefore, the total employees that the company has(currently) is \(4x+3x-2 = 7x-2 = 7*6-2 = 40\)(Option B)
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Re: Company X had a ratio of 4 full-time employees for every 3 part-time  [#permalink]

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New post 17 Jan 2018, 06:04
4x/(3x-2) = 3/2
(...)
x=6

Total = 40.

Ans. = B
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Re: Company X had a ratio of 4 full-time employees for every 3 part-time  [#permalink]

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New post 26 Feb 2018, 11:15
Bunuel wrote:
Company X had a ratio of 4 full-time employees for every 3 part-time employees until 2 part-time employees quit. If that brought the current ratio down to 3:2, how many employees does the company now have?

A. 30
B. 40
C. 50
D. 60
E. 70


We know that the ratio of fulltime to part-time employees = 4x : 3x

After 2 part-time employees quit, the ratio is 3:2, so we have:

4x/(3x-2) = 3/2

8x = 3(3x - 2)

8x = 9x - 6

6 = x

Thus, the company now has 4(6) + 3(6) - 2 = 40 total employees.

Answer: B
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Re: Company X had a ratio of 4 full-time employees for every 3 part-time  [#permalink]

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New post 08 Mar 2018, 19:06
Once we know that x = 6, why don't we plug that into the new ratio (3:2)? Confused as to why the new ratio isn't the current number of employees.
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Company X had a ratio of 4 full-time employees for every 3 part-time  [#permalink]

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New post 09 Mar 2018, 20:37
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jsheppa wrote:
Once we know that x = 6, why don't we plug that into the new ratio (3:2)? Confused as to why the new ratio isn't the current number of employees.

jsheppa , the multiplier x = 6 is for the original ratio. That is the ratio that has the mathematical "operation" performed on it.

When we have a ratio whose parts (numerator and/or denominator) change, and that change results in a different ratio, the multiplier is for the original. Its "counting number" of members changed.

Everything that happens (2 people leave, the result is a different part:part ratio) stems from the original ratio.

Thus:
\(\frac{4x}{3x}\)
\(\frac{4x}{(3x-2)}=\frac{3}{2}\)

\(8x = 9x - 6\)
\(x = 6\)

The number of original employees had to be
(4x = 24) + (3x = 18) = 24 + 18 = 42 ORIGINAL minus 2 people who left = 40 NOW

Those 40 are in a 3:2 ratio, but if you used x=6 on that ratio, you would get (3x = 18) and (2x = 12). 18 + 12 = 30.

Hope that helps. :-)
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Re: Company X had a ratio of 4 full-time employees for every 3 part-time  [#permalink]

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New post 27 Apr 2018, 01:38
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I found the answer in a much easier way without doing much math.

You are said that before two employees leave the ratio of employees is 4:3.

This means that the total number of employees before is a multiple of 7.

All you are left to do is to add 2 (which corresponds to the number of employees that left) to each answer choice. The answer choice that is a multiple of 7 must be the right answer

Thus :
A. 30+2 = 32 Not a multiple of 7
B. 40+2 = 42 A Multiple of 7
C. 50+2 = 52 Not a multiple of 7
D. 60+2 = 62 Not a multiple of 7
E. 70+2 = 72 Not a multiple of 7
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Re: Company X had a ratio of 4 full-time employees for every 3 part-time  [#permalink]

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New post 19 Sep 2018, 21:06
f :p
4:3
f:p
3:2
make ratios same
f:p
12:9
f:p
12:8
diff between part time is 1 but diff is 2 so multip factor is 2
12*2 + 8*2
24+16
40
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Re: Company X had a ratio of 4 full-time employees for every 3 part-time  [#permalink]

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New post 19 Sep 2018, 21:48
Bunuel wrote:
Company X had a ratio of 4 full-time employees for every 3 part-time employees until 2 part-time employees quit. If that brought the current ratio down to 3:2, how many employees does the company now have?

A. 30
B. 40
C. 50
D. 60
E. 70


If F is number of full time employees and P is number of Part time employees
F:P = 4:3

i.e. F = 4x
and P = 3x

After two employees quit, P = 3x-2

New F:P = 4x : (3x-2) = 3:2

i.e. 8x = 9x-6
i.e. x = 6

Current number of employees = 4x+3x-2 = 7x - 2 = 7*6 - 2 = 40

Answer:option B
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Re: Company X had a ratio of 4 full-time employees for every 3 part-time  [#permalink]

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New post 19 Sep 2018, 21:51
Bunuel wrote:
Company X had a ratio of 4 full-time employees for every 3 part-time employees until 2 part-time employees quit. If that brought the current ratio down to 3:2, how many employees does the company now have?

A. 30
B. 40
C. 50
D. 60
E. 70


ALTERNATIVELY:

earlier Ratio = 4:3 i.e. Before 2 employees left, Total employees was a multiple of 7

After two employees left the ratio is 3:2 i.e. Answer and final number of employees is a multiple of 5

All options are multiples of 5
But only 40 (out of all options) with addition of 2 (employees left) is a multiple of 7


Hence
Answer: Option B
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Re: Company X had a ratio of 4 full-time employees for every 3 part-time &nbs [#permalink] 19 Sep 2018, 21:51
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