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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
Posts: 144
In a certain company, the ratio of male to female employees is 7:8...  [#permalink]

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24 Jul 2016, 01:04
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35% (medium)

Question Stats:

68% (01:37) correct 32% (01:47) wrong based on 289 sessions

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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.
Math Expert
Joined: 02 Sep 2009
Posts: 52231
Re: In a certain company, the ratio of male to female employees is 7:8...  [#permalink]

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24 Jul 2016, 01:15
4
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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Re: In a certain company, the ratio of male to female employees is 7:8...  [#permalink]

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28 Oct 2016, 10:35
[7x+3]/8x=8/9
63x+27=64x
x=27

7(27)=189
CEO
Joined: 11 Sep 2015
Posts: 3331
Re: In a certain company, the ratio of male to female employees is 7:8...  [#permalink]

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28 Oct 2016, 15:51
1
Top Contributor
1
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.
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.

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

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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, 18:22
1
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

still D!

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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, 03:00
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
Joined: 30 Apr 2013
Posts: 78
Re: In a certain company, the ratio of male to female employees is 7:8...  [#permalink]

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18 Aug 2017, 05:32
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?

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Joined: 02 Sep 2009
Posts: 52231
Re: In a certain company, the ratio of male to female employees is 7:8...  [#permalink]

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18 Aug 2017, 05:54
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]

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14 Apr 2018, 08:45
(7x+3)/(8x)=8/9. Solve to get x = 27. That gives the number of men as 189. Hence option D
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Re: In a certain company, the ratio of male to female employees is 7:8...  [#permalink]

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03 Jun 2018, 05:07
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.

Just 2 cents :
Question could have been more clearer if it were mentioned , how many male were there originally?
Just of now question is just a little ambiguous as to whether the male employees after the change or before the change is being asked for.
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Joined: 07 Dec 2014
Posts: 1151
Re: In a certain company, the ratio of male to female employees is 7:8...  [#permalink]

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03 Jun 2018, 16:30
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 substitution:
m/f=7/8
f=8m/7
substituting,
(m+3)/(8m/7)=8/9
m=189
D
Re: In a certain company, the ratio of male to female employees is 7:8... &nbs [#permalink] 03 Jun 2018, 16:30
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