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Yesterday, the ratio of males to females working at Gigacorp

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

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New post 28 Feb 2017, 09:50
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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

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

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New post Updated on: 30 Apr 2019, 07:44
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GMATPrepNow wrote:
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


Yesterday, the ratio of males to females working at Gigacorp was 2:3
There are many scenarios that meet this condition:
- Gigacorp employs 2 males and 3 females (for a TOTAL of 5 employees)
- Gigacorp employs 4 males and 6 females (for a TOTAL of 10 employees)
- Gigacorp employs 6 males and 9 females (for a TOTAL of 15 employees)
- Gigacorp employs 8 males and 23 females (for a TOTAL of 20 employees)
.
.
.
etc.

Notice that the TOTAL number of employees yesterday is a multiple of 5. This is because our ratio of 2:3 tells us that, for every 5 employees, 2 are males and 3 are females. Since the number of males and females must be POSITIVE INTEGERS, the TOTAL number of employees yesterday must be a multiple of 5

Today, Gigacorp hired an additional 81 employees, and the ratio of males to females is now 6:5
By the same logic, the NEW TOTAL number of employees must be a multiple of 11, since this new information tells us that, for every 11 employees, 6 are males and 5 are females.

So, once we add 81 to yesterday's TOTAL, the NEW TOTAL must be a multiple of 11.

Let's see what happens if there was a TOTAL of 5 employees yesterday.
NEW TOTAL = 5 + 81 = 86.
Since 86 is NOT a multiple of 11, it cannot be the case that there was a TOTAL of 5 employees yesterday.

Let's see what happens if there was a TOTAL of 10 employees yesterday.
NEW TOTAL = 10 + 81 = 91.
Since 91 is NOT a multiple of 11, it cannot be the case that there was a TOTAL of 10 employees yesterday.

Let's see what happens if there was a TOTAL of 15 employees yesterday.
NEW TOTAL = 15 + 81 = 96.
Since 96 is NOT a multiple of 11, it cannot be the case that there was a TOTAL of 15 employees yesterday.

Notice that each NEW TOTAL follows the pattern: 86, 91, 96, 101, etc (the units digit of each number is either 1 or 6.
So, let's continue the pattern until we get to the first multiple of 11
86, 91, 96, 101, 106, 111, 116, 121

BINGO!
When the NEW TOTAL = 121, then the OLD TOTAL = 121 - 81 = 40
So, 40 is the smallest possible number of employees yesterday.
Since the ratio of males to females working at Gigacorp was 2:3 yesterday, we can conclude that there were 16 males and 24 females.

Answer: A

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Originally posted by GMATPrepNow on 28 Feb 2017, 14:52.
Last edited by GMATPrepNow on 30 Apr 2019, 07:44, edited 1 time in total.
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Re: Yesterday, the ratio of males to females working at Gigacorp  [#permalink]

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New post 28 Feb 2017, 13:27
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GMATPrepNow wrote:
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


Hi

Nice question.

\((1) 2x + 3x = N\)

\(5x = N\)

\((2) 6y + 5y = N + 81\)

\(11y = N + 81\)

\((2) - (1)\)
\(11y - 5x = 81\)

\(y_0 = 11, x_0 = 8\)

\(2x = 2*8 = 16\)

Answer A
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Re: Yesterday, the ratio of males to females working at Gigacorp  [#permalink]

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New post 28 Feb 2017, 13:10
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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.
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Yesterday, the ratio of males to females working at Gigacorp  [#permalink]

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New post 17 Sep 2017, 22:25
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GMATPrepNow wrote:
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.

Hence Answer A
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Re: Yesterday, the ratio of males to females working at Gigacorp  [#permalink]

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New post 29 Apr 2019, 22:55
GMATPrepNow wrote:
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
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Re: Yesterday, the ratio of males to females working at Gigacorp  [#permalink]

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New post 30 Apr 2019, 05:29
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
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Re: Yesterday, the ratio of males to females working at Gigacorp  [#permalink]

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New post 30 Apr 2019, 07:52
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doomedcat wrote:
GMATPrepNow wrote:
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
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Re: Yesterday, the ratio of males to females working at Gigacorp  [#permalink]

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New post 30 Apr 2019, 09:21
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GMATPrepNow wrote:
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
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Yesterday, the ratio of males to females working at Gigacorp  [#permalink]

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New post 30 Apr 2019, 15:04
GMATPrepNow wrote:
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.
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Yesterday, the ratio of males to females working at Gigacorp   [#permalink] 30 Apr 2019, 15:04
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