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

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Math Expert
Joined: 02 Sep 2009
Posts: 46167
Company X had a ratio of 4 full-time employees for every 3 part-time [#permalink]

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17 Jan 2018, 00:12
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Difficulty:

35% (medium)

Question Stats:

69% (01:30) correct 31% (01:27) wrong based on 157 sessions

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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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17 Jan 2018, 02:05
1
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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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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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.

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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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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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09 Mar 2018, 20:37
1
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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27 Apr 2018, 01:38
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
Re: Company X had a ratio of 4 full-time employees for every 3 part-time   [#permalink] 27 Apr 2018, 01:38
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