Last visit was: 11 Sep 2024, 23:28 It is currently 11 Sep 2024, 23:28
Toolkit
GMAT Club Daily Prep
Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History
Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.

# Yesterday, the ratio of males to females working at Gigacorp

SORT BY:
Tags:
Show Tags
Hide Tags
GMAT Club Legend
Joined: 12 Sep 2015
Posts: 6803
Own Kudos [?]: 31274 [55]
Given Kudos: 799
GMAT Club Legend
Joined: 12 Sep 2015
Posts: 6803
Own Kudos [?]: 31274 [17]
Given Kudos: 799
Senior Manager
Joined: 13 Oct 2016
Posts: 299
Own Kudos [?]: 791 [7]
Given Kudos: 40
GPA: 3.98
General Discussion
Intern
Joined: 06 Feb 2015
Posts: 1
Own Kudos [?]: 5 [5]
Given Kudos: 2
Re: Yesterday, the ratio of males to females working at Gigacorp [#permalink]
3
Kudos
2
Bookmarks
The answer should be a multiple of 2 as the ratio of male to female originally was 2:3 . Now eliminate ans choice 39. Remaining 16,24,40 and 42.

A. If we choose 16 as 2x , then 3x will be 24 and the total will be (16+24) 40. Adding 81 employees gives total of 121 employees. we know that the new ratio is 5:6. There fore 5x + 6x = 11x. This tells us,the answer has to be divided by 11. Clearly 121 is divisible by 11.
Perform same logic for other options 24, 40 and 42. The end result is not divisible by 11. So going for Option A 16.

There must by easy way to solve this. But this came in handy as we have the options listed out.
Manager
Joined: 28 May 2017
Posts: 223
Own Kudos [?]: 737 [1]
Given Kudos: 12
Concentration: Finance, General Management
Yesterday, the ratio of males to females working at Gigacorp [#permalink]
1
Kudos
GMATPrepNow
Yesterday, the ratio of males to females working at Gigacorp was 2:3. Today, Gigacorp hired an additional 81 employees, and the ratio of males to females is now 6:5 (no employees left or were fired). What is the least number of males that could have been working at Gigacorp yesterday?

A) 16
B) 24
C) 39
D) 40
E) 42

*Kudos for all correct solutions

Logical Approach for this NICE question -

Original Ratio of Male to Female = 2x:3x
Total Original Population = 5x

After adding 81 employee New Ratio of Male to Female = 6y:5y
Total New Population = 11y

We May Write -
5x + 81 = 11y
Above equation conveys that LHS must be DIVISIBLE by 11
5x + 4+ 77 = 11y

After Reducing
5x + 4 = 11y

Value of 2x is given in the options. Just Plug the value of x in above equation to get the answer.

Only option A would FIT.

Manager
Joined: 24 Jun 2013
Posts: 120
Own Kudos [?]: 334 [1]
Given Kudos: 124
Location: India
Schools: ISB '20 GMBA '20
GMAT 1: 680 Q47 V36
Re: Yesterday, the ratio of males to females working at Gigacorp [#permalink]
1
Bookmarks
GMATPrepNow
Yesterday, the ratio of males to females working at Gigacorp was 2:3. Today, Gigacorp hired an additional 81 employees, and the ratio of males to females is now 6:5 (no employees left or were fired). What is the least number of males that could have been working at Gigacorp yesterday?

A) 16
B) 24
C) 39
D) 40
E) 42

*Kudos for all correct solutions

Pls help m stuck on how to solve this problem

let initial ratio $$\frac{Male}{Female}$$ = $$\frac{2x}{3x}$$
now let y males were hired of the 81 employees , then females = 81-y

new ratio $$\frac{(2x+y)}{(3x+(81-y)}$$ = $$\frac{6}{5}$$

which comes down to y=$$\frac{(8x+486)}{11}$$

i am lost here, what to do next; x has to INT den min value to y should be the ans
Intern
Joined: 08 Jan 2019
Posts: 40
Own Kudos [?]: 40 [0]
Given Kudos: 3
Re: Yesterday, the ratio of males to females working at Gigacorp [#permalink]
Hi

there are multiple ways of solving a maths problem especially with Ratio - 1 variable 2 variable 3 variable etc. Though I agree with the above logic I am trying to find a hole in my logic - feel free to post it out to me please...
The first post of gmat prep CEO actually tried the 1 variable approach albeit picking numbers.

M/F = 2x/3x Total is 5x
Now add 81 so 5x + 81
Ratio turns to 6x/5x - total 11x

5x+81 = 11x implies 6x = 81
Initial male is 2x so 2x = 81/3 = 27

So the least from the choices given has to be 39?

2nd way: start from the answers and back calculate and try to arrive at answers
16 - x=2
24 - x=12
39 - x= 19.5
40 - x=20
42 -x= 21

Now the irony is as soon as I read the question, I did some mental calculations and without putting any pen to paper I arrived at the answer intuitively at 39. But obviously the answer is not 39 so then start doubting yourself, do multiple complicated x y variables and reach at another answer 16.
Request here is to find and discuss the two ways of thinking in ratio - using 1 variable vs multiple variables vs back calculating

Similar question solved with 1 variable
https://gmatclub.com/forum/the-ratio-of ... fl=similar
GMAT Club Legend
Joined: 12 Sep 2015
Posts: 6803
Own Kudos [?]: 31274 [1]
Given Kudos: 799
Re: Yesterday, the ratio of males to females working at Gigacorp [#permalink]
1
Bookmarks
Top Contributor
doomedcat
GMATPrepNow
Yesterday, the ratio of males to females working at Gigacorp was 2:3. Today, Gigacorp hired an additional 81 employees, and the ratio of males to females is now 6:5 (no employees left or were fired). What is the least number of males that could have been working at Gigacorp yesterday?

A) 16
B) 24
C) 39
D) 40
E) 42

*Kudos for all correct solutions

Pls help m stuck on how to solve this problem

let initial ratio $$\frac{Male}{Female}$$ = $$\frac{2x}{3x}$$
now let y males were hired of the 81 employees , then females = 81-y

new ratio $$\frac{(2x+y)}{(3x+(81-y)}$$ = $$\frac{6}{5}$$

which comes down to y=$$\frac{(8x+486)}{11}$$

i am lost here, what to do next; x has to INT den min value to y should be the ans

Once you have y=$$\frac{(8x+486)}{11}$$, you need to find the smallest value of x such that y=$$\frac{(8x+486)}{11}$$ is an integer.

Cheers,
Brent
Board of Directors
Joined: 11 Jun 2011
Status:QA & VA Forum Moderator
Posts: 6046
Own Kudos [?]: 4819 [1]
Given Kudos: 463
Location: India
GPA: 3.5
WE:Business Development (Commercial Banking)
Re: Yesterday, the ratio of males to females working at Gigacorp [#permalink]
1
Kudos
GMATPrepNow
Yesterday, the ratio of males to females working at Gigacorp was 2:3. Today, Gigacorp hired an additional 81 employees, and the ratio of males to females is now 6:5 (no employees left or were fired). What is the least number of males that could have been working at Gigacorp yesterday?

A) 16
B) 24
C) 39
D) 40
E) 42

*Kudos for all correct solutions

$$(2x + 3x ) + 81 = ( 6y + 5y)$$

Or, $$5x + 81 = 11y$$

Or, $$x = \frac{11y - 81}{5}$$ {We are intentionally finding a solution for x for ease of calculation. as any no will be divisible by 5 only when the last digit is 0 Or 5 }

Now, The least possible value of y to make RHS divisible by 5 is 11, as $$121 - 81 = 40$$ (Which is completely divisible by 5)

Now, $$x = 8$$ , So the no of males yesterday is 16 , Answer must be (A) 16
Intern
Joined: 21 Oct 2018
Posts: 3
Own Kudos [?]: 1 [0]
Given Kudos: 42
Yesterday, the ratio of males to females working at Gigacorp [#permalink]
GMATPrepNow
Yesterday, the ratio of males to females working at Gigacorp was 2:3. Today, Gigacorp hired an additional 81 employees, and the ratio of males to females is now 6:5 (no employees left or were fired). What is the least number of males that could have been working at Gigacorp yesterday?

A) 16
B) 24
C) 39
D) 40
E) 42

*Kudos for all correct solutions

Although this is a 700 level question, it surprisingly simple if we are able to see the question in a different perspective. I'm not sure if this method works or it was just luck.

Since we are asked what the LEAST number of males are, I started with the least number in the answer choice.

2:3 ratio = 5X
2X = 16 (From answer choice)
X= 8
5X = 40

+81 Employees = 121

6:5 Ratio = 11X
11X = 121
X= 11

16 works, and since it is the smallest number in the answer choice, (A) is correct.
UNC Kenan Flagler Moderator
Joined: 18 Jul 2015
Posts: 237
Own Kudos [?]: 263 [0]
Given Kudos: 120
GMAT 1: 530 Q43 V20
WE:Analyst (Consumer Products)
Re: Yesterday, the ratio of males to females working at Gigacorp [#permalink]
GMATPrepNow
Yesterday, the ratio of males to females working at Gigacorp was 2:3. Today, Gigacorp hired an additional 81 employees, and the ratio of males to females is now 6:5 (no employees left or were fired). What is the least number of males that could have been working at Gigacorp yesterday?

A) 16
B) 24
C) 39
D) 40
E) 42

*Kudos for all correct solutions

Sharing an approach to solve this backwards from answer choices. In questions pertaining to least/smallest, always start from the least/smallest answer choice. In this question lets start with A i.e. $$16$$
We are told that the ratio of male to female was $$2:3$$ yesterday, hence if there were $$16$$ males then:
$$2x = 16$$
$$x = 8$$

Using $$x=8$$, the number of females would be $$3x = 3*8 = 24$$
Total employees yesterday = males + females = $$16 + 24 = 40$$

Today, $$81$$ new employees were hired hence total would be $$40 + 81 = 121$$ and the new ratio given to us is $$6:5$$. Using this ratio the total employees would be $$11x$$.
$$11x = 121$$
$$x = 11$$

We do not need to solve other options as the first option worked for us. In case you do try to solve then you will realize that the total employees today will not be divisible by $$11$$ in case of the other answer choices.

Ans. A
VP
Joined: 15 Dec 2016
Posts: 1318
Own Kudos [?]: 232 [0]
Given Kudos: 188
Re: Yesterday, the ratio of males to females working at Gigacorp [#permalink]
Experts -- chetan2u Bunuel Gladiator59 generis

I have a specific question on this one

If

Original Ratio of Male to Female = 2x:3x
Total Original Population = 5x

After adding 81 employee New Ratio of Male to Female = 6y:5y
Total New Population = 11y

I get that 5x + 81 = 11 y

Question :
I always thought x and y do not have to be integers

Logic : 5x has to be an integer == thus x can still be a fraction ...like x can be 4.8 (as 4.8 x 5 = integer) or 4.6 (as 4.6 x 5 = integer) or 4.2 (as 4.2 x 5 = integer)

Similarly, Y does not have to be an integer

== y can be a fraction like ....like y can be 5/11 (as 5/11 x 11 = integer) or 20/11 (as 20/11 x 11 = integer) or 4.2 (as 26/11 x 11 = integer)
UNC Kenan Flagler Moderator
Joined: 18 Jul 2015
Posts: 237
Own Kudos [?]: 263 [0]
Given Kudos: 120
GMAT 1: 530 Q43 V20
WE:Analyst (Consumer Products)
Re: Yesterday, the ratio of males to females working at Gigacorp [#permalink]
jabhatta@umail.iu.edu
Experts -- chetan2u Bunuel Gladiator59 generis

I have a specific question on this one

If

Original Ratio of Male to Female = 2x:3x
Total Original Population = 5x

After adding 81 employee New Ratio of Male to Female = 6y:5y
Total New Population = 11y

I get that 5x + 81 = 11 y

Question :
I always thought x and y do not have to be integers

Logic : 5x has to be an integer == thus x can still be a fraction ...like x can be 4.8 (as 4.8 x 5 = integer) or 4.6 (as 4.6 x 5 = integer) or 4.2 (as 4.2 x 5 = integer)

Similarly, Y does not have to be an integer

== y can be a fraction like ....like y can be 5/11 (as 5/11 x 11 = integer) or 20/11 (as 20/11 x 11 = integer) or 4.2 (as 26/11 x 11 = integer)

Hi,

We are discussing about men and women here. Imagine, can men and women be fractions in real life? Can there be 4.8 men, No right. The same rule applies in GMAT Quant as well. In questions pertaining to humans and animals we will always consider the quantities to be integers.

Hope this helps.

Warm Regards,
Pritishd
Non-Human User
Joined: 09 Sep 2013
Posts: 34817
Own Kudos [?]: 877 [0]
Given Kudos: 0
Re: Yesterday, the ratio of males to females working at Gigacorp [#permalink]
Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
Re: Yesterday, the ratio of males to females working at Gigacorp [#permalink]
Moderator:
Math Expert
95451 posts