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

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

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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

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

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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

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.

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

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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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

Answer:
[Reveal] Spoiler:
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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New post 28 Oct 2016, 19:22
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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

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

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

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New post 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?

please help!

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

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New post 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?

please help!



3 more men is hypothetical scenario: "If 3 more men were hired, this ratio would increase to 8:9..."
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Please read this: Ultimate GMAT Quantitative Megathread | All You Need for Quant | PLEASE READ AND FOLLOW: 12 Rules for Posting!!!

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Collection of Questions:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


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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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