At a certain organisation, the number of male members went up by 12%

Question

At a certain organisation, the number of male members went up by 12% in the year 2001 from year 2000, and the number of females members went down by 6% in the same time period. If the total membership at the organisation went up by 1.2% from the year 2000 to 2001, what was the ratio of male members to female members in the year 2000?

a.1:2
b.1:3
c.2:3
d.3:2
e.2:1

a.1:2
b.1:3
c.2:3
d.3:2
e.2:1

mikemcgarry · Accepted Answer

Dear Turkish, I'm happy to help! This is a really great problem! What is the source? Let M and F equal the numbers of male & female employees in 2000. We are looking for M/F. I will use multipliers for the percent increases. See this blog: https://magoosh.com/gmat/2012/understand ... -the-gmat/ men increase by 12% ==> 1.12M = males in 2001 women decrease by 6% ==> 0.94F = women in 2001 total employees increase by 1.2% ==> 1.012*(M + F) = total number of employees in 2001 Obviously (males in 2001) + (females in 2001) = total number of employees in 2001 1.12M + 0.94F = 1.012*(M + F) 1.12M + 0.94F = 1.012M + 1.012F 1.12M - 1.012M = 1.012F - 0.94F 0.108M = 0.072F M/F = (0.072)/(0.108) = 72/108 = 2/3 Answer = (C) Does all this make sense? Mike :-)

PrepTap · Answer

Let's say the no. of male and female members were m and f respectively in 2000.

Total increase in members from 2000 to 2001 =
0.012 (m+f) 
is also equal to
0.12m - 0.06f

0.012m + 0.012f = 0.12m - 0.06f
0.072f = 0.108m
 \frac{m}{f} = \frac{0.072}{0.108} = \frac{2}{3}

C is the correct answer here.

EMPOWERgmatRichC · Answer

Hi Turkish,

This ratio-based question can be solved in a number of different ways; you can take an Algebraic approach or you can use a combination of TESTing VALUES and the TESTing THE ANSWERS.

We're given a few facts about the make-up of an organization from 2000 to 2001
1) The number of male members INCREASED by 12%
2) The number of female members DECREASED by 6%
3) The overall membership INCREASED by 1.2%

We're asked for the ratio of male members to female members in the year 2000.

To start, I'm going to prove something about the ratio in the year 2000....

IF....we had an equal number of male members and female members, the membership increase would have been GREATER than 1.2%.....Here's proof:

IF.....in 2000
Males = 100 
Females = 100
Total = 200

in 2001
Males = 112
Females = 94
Total = 206

The total increase from year to year would be 6/200 = 3%

Since we're told that the total increase was 1.2%, that means that there had to be MORE women than men in 2000 (which would end in a % change that would be less than 3%) - probably not that many more women, but enough to bring down the percent. Eliminate answers D and E.

From the remaining 3 answers, we can TEST VALUES, using the ratios in the answers to select our VALUES. From the 3 options, we have....

Answer A: Females is DOUBLE the number of males
Answer B: Females is TRIPLE the number of males
Answer C: Females is 50% more than the number of males

Answer C involves the smallest difference, so I'm going to start there...

IF.....in 2000
Males = 200 
Females = 300
Total = 500

in 2001
Males = 224
Females = 282
Total = 506

The total increase from year to year would be 6/500 = 1.2%

This is an exact MATCH for what we were told, so we have the correct answer.

Final Answer:  C

GMAT assassins aren't born, they're made,
Rich

Russ19 · Answer

men increase by 12% ==> 1.12M = males in 2001
women decrease by 6% ==> 0.94F = women in 2001
total employees increase by  1.2%  ==>  1.012  *(M + F) = total number of employees in 2001

Obviously
(males in 2001) + (females in 2001) = total number of employees in 2001
1.12M + 0.94F = 1.012*(M + F)
1.12M + 0.94F = 1.012M + 1.012F
1.12M - 1.012M = 1.012F - 0.94F
0.108M = 0.072F
M/F = (0.072)/(0.108) = 72/108 = 2/3

Answer =  (C)

Hi
Could anyone please show the calculation that how 1.2% colored above becomes 1.012? Thanks for your help in advance!

EMPOWERgmatRichC · Answer

Hi sjuniv32,

Converting relatively small percentages to decimals can sometimes "look" weird, so it might help to start with larger examples and work down to the smaller ones.

For example:
-if we raise X by 50%, then we end up with X + .5X = 1.5X
-if we raise X by 10%, then we end up with X + .1X = 1.1X
-if we raise X by 5%, then we end up with X + .05X = 1.05X
-if we raise X by 1%, then we end up with X + .01X = 1.01X

In the specific example you're referring to, we're raising a number by 1.2%....
-if we raise X by 1.2%, then we end up with X + .012X = 1.012X
 
GMAT assassins aren't born, they're made,
Rich

ivycation2024 · Answer

How come this is a hard question? shouldn't this be considered ~555+?

Bunuel · Answer

The difficulty level of a question on the site, after sufficient attempts, is determined automatically based on various parameters collected from users' attempts via timer, such as the percentage of correct answers and the time taken to answer the question. So, this is an 655-705 Level level question based on our statistics. https://gmatclub.com/forum/download/file.php?id=86541 GMAT-Club-Forum-lfsy2thq.png

At a certain organisation, the number of male members went up by 12%

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At a certain organisation, the number of male members went up by 12%

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