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 Your Progress
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.
Thank you for using the timer!
We noticed you are actually not timing your practice. Click the START button first next time you use the timer.
There are many benefits to timing your practice, including:
Does GMAT RC seem like an uphill battle? e-GMAT is conducting a free webinar to help you learn reading strategies that can enable you to solve 700+ level RC questions with at least 90% accuracy in less than 10 days. Sat., Oct 19th at 7 am PDT
Yesterday, the ratio of males to females working at Gigacorp
[#permalink]
Show Tags
28 Feb 2017, 09:50
7
Top Contributor
29
00:00
A
B
C
D
E
Difficulty:
95% (hard)
Question Stats:
46% (02:49) correct 54% (02:53) wrong based on 184 sessions
HideShow timer Statistics
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?
Yesterday, the ratio of males to females working at Gigacorp
[#permalink]
Show Tags
Updated on: 30 Apr 2019, 07:44
7
Top Contributor
5
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.
Re: Yesterday, the ratio of males to females working at Gigacorp
[#permalink]
Show Tags
28 Feb 2017, 13:27
5
2
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?
Re: Yesterday, the ratio of males to females working at Gigacorp
[#permalink]
Show Tags
28 Feb 2017, 13:10
3
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.
Yesterday, the ratio of males to females working at Gigacorp
[#permalink]
Show Tags
17 Sep 2017, 22:25
1
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
_________________
If you like the post, show appreciation by pressing Kudos button
Re: Yesterday, the ratio of males to females working at Gigacorp
[#permalink]
Show Tags
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 _________________
If this post helped you learn something pls give kudos
Re: Yesterday, the ratio of males to females working at Gigacorp
[#permalink]
Show Tags
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
Re: Yesterday, the ratio of males to females working at Gigacorp
[#permalink]
Show Tags
30 Apr 2019, 07:52
Top Contributor
1
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.
Re: Yesterday, the ratio of males to females working at Gigacorp
[#permalink]
Show Tags
30 Apr 2019, 09:21
1
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 _________________
Thanks and Regards
Abhishek....
PLEASE FOLLOW THE RULES FOR POSTING IN QA AND VA FORUM AND USE SEARCH FUNCTION BEFORE POSTING NEW QUESTIONS
Yesterday, the ratio of males to females working at Gigacorp
[#permalink]
Show Tags
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.