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# In a certain company, the ratio of male to female employees is 7:8...

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Manager
Joined: 24 May 2016
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In a certain company, the ratio of male to female employees is 7:8... [#permalink]

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24 Jul 2016, 02:04
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45% (medium)

Question Stats:

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In a certain company, the ratio of male to female employees is 7:8. If 3 more men were hired, this ratio would increase to 8:9. How many male employees are there in the company?

A) 6
B) 21
C) 27
D) 189
E) 192

Could you someone please explain what is the fastest way of solving this problem?

Thank you.
[Reveal] Spoiler: OA

Kudos [?]: 133 [0], given: 33

Math Expert
Joined: 02 Sep 2009
Posts: 41892

Kudos [?]: 129158 [1], given: 12194

Re: In a certain company, the ratio of male to female employees is 7:8... [#permalink]

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24 Jul 2016, 02:15
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Expert's post
EBITDA wrote:
In a certain company, the ratio of male to female employees is 7:8. If 3 more men were hired, this ratio would increase to 8:9. How many male employees are there in the company?

A) 6
B) 21
C) 27
D) 189
E) 192

Could you someone please explain what is the fastest way of solving this problem?

Thank you.

The ratio of male to female employees is 7:8 $$\frac{Male}{Female} = \frac{7x}{8x}$$;

If 3 more men were hired, this ratio would increase to 8:9: $$\frac{Male'}{Female'} = \frac{7x+3}{8x}=\frac{8}{9}$$;

$$\frac{7x+3}{8x}=\frac{8}{9}$$ --> x = 27.

How many male employees are there in the company --> male = 7x = 7*27 = 189.

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Kudos [?]: 129158 [1], given: 12194

Senior Manager
Status: DONE!
Joined: 05 Sep 2016
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Kudos [?]: 23 [0], given: 283

Re: In a certain company, the ratio of male to female employees is 7:8... [#permalink]

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28 Oct 2016, 11:35
[7x+3]/8x=8/9
63x+27=64x
x=27

7(27)=189

Kudos [?]: 23 [0], given: 283

SVP
Joined: 12 Sep 2015
Posts: 1798

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Re: In a certain company, the ratio of male to female employees is 7:8... [#permalink]

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28 Oct 2016, 16:51
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EBITDA wrote:
In a certain company, the ratio of male to female employees is 7:8. If 3 more men were hired, this ratio would increase to 8:9. How many male employees are there in the company?

A) 6
B) 21
C) 27
D) 189
E) 192

Here's a quick solution....

PRESENTLY, the ratio of male to female employees is 7:8
So, there could be 7 males and 8 females
or 14 males and 16 females
21 males and 24 females
etc.

Notice that the PRESENT number of males must be a multiple of 7.
Check the answer choices....
A, C and E are NOT multiples of 7, so we can eliminate them.
This leaves us with answer choices B and D.

If 3 more men were hired, this ratio would increase to 8:9
So, if we add 3 to our two remaining answer choices, the result must be a multiple of 8
B) 21 + 3 = 24. 24 IS a multiple of 8. So keep it
D) 189 + 3 = 192. 192 IS a multiple of 8. So keep it

So, we're forced to check ONE of the answer choices. If it works, then that's the correct answer. If it doesn't work, then the OTHER answer is correct.
Let's check answer choice B.

B) If there are 21 males, then there are 24 females (simplifies to a 7:8 ratio).
When we add 3 males, we get 24 males and 24 females. This simplifies to a 1:1 ratio, but we want an 8:9 ratio.
ELIMINATE B

[Reveal] Spoiler:
D

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Brent Hanneson – Founder of gmatprepnow.com

Kudos [?]: 2467 [1], given: 357

SVP
Joined: 12 Sep 2015
Posts: 1798

Kudos [?]: 2467 [1], given: 357

Re: In a certain company, the ratio of male to female employees is 7:8... [#permalink]

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28 Oct 2016, 19:22
1
KUDOS
Expert's post
Top Contributor
EBITDA wrote:
In a certain company, the ratio of male to female employees is 7:8. If 3 more men were hired, this ratio would increase to 8:9. How many male employees are there in the company?

A) 6
B) 21
C) 27
D) 189
E) 192

Could you someone please explain what is the fastest way of solving this problem?

Thank you.

Another approach is to use TWO variables.
Let M = present number of males
Let F = present number of females

The ratio of male to female employees is 7:8
So, M/F = 7/8
Cross multiply to get 7F = 8M

If 3 more men were hired, this ratio would increase to 8:9
So, (M+3)/F = 8/9
Cross multiply to get 9(M+3) = 8F
Expand: 9M + 27 = 8F

We now have a system of two equations and two variables:
7F = 8M
9M + 27 = 8F

Solve to get: M = 189 and F = 216

[Reveal] Spoiler:
still D!

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_________________

Brent Hanneson – Founder of gmatprepnow.com

Kudos [?]: 2467 [1], given: 357

Math Forum Moderator
Status: QA & VA Forum Moderator
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GPA: 3.5
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In a certain company, the ratio of male to female employees is 7:8... [#permalink]

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29 Oct 2016, 04:00
EBITDA wrote:
In a certain company, the ratio of male to female employees is 7:8. If 3 more men were hired, this ratio would increase to 8:9. How many male employees are there in the company?

A) 6
B) 21
C) 27
D) 189
E) 192

Could you someone please explain what is the fastest way of solving this problem?

Thank you.

$$\frac{Male}{Female} = \frac{7}{8}$$ after adding 3 more men $$\frac{Male}{Female} = \frac{8}{9}$$

Check the options -

1. The correct answer choice will be divisible by 7 ( Only B & D are possible )
2. The correct answer choice +3 will be divisible by 8 ( Only B & D are possible )

Now , check any one option , lets say (B) -

$$\frac{Male}{Female} = \frac{21}{24}$$

After adding 3 more men $$\frac{Male}{Female} = \frac{24}{24}$$ = 1 ( Hence not possible )

Check Option (D) -

$$\frac{Male}{Female} = \frac{189}{216}$$

After adding 3 more men $$\frac{Male}{Female} = \frac{192}{216}$$ = 8:9

Hope this helps...

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Manager
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Re: In a certain company, the ratio of male to female employees is 7:8... [#permalink]

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18 Aug 2017, 06:32
Am bit confused - Why are we multiplying with the original ratio to get the ans i.e 27*7 ? why not with 8 since after increasing by 3 since new ratio would be 8/9?

Kudos [?]: [0], given: 6

Math Expert
Joined: 02 Sep 2009
Posts: 41892

Kudos [?]: 129158 [0], given: 12194

Re: In a certain company, the ratio of male to female employees is 7:8... [#permalink]

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18 Aug 2017, 06:54
santro789 wrote:
Am bit confused - Why are we multiplying with the original ratio to get the ans i.e 27*7 ? why not with 8 since after increasing by 3 since new ratio would be 8/9?

3 more men is hypothetical scenario: "If 3 more men were hired, this ratio would increase to 8:9..."
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Re: In a certain company, the ratio of male to female employees is 7:8...   [#permalink] 18 Aug 2017, 06:54
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# In a certain company, the ratio of male to female employees is 7:8...

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