If 30 percent of the members of a certain organization are

3/10 (30%) of the members are women and 3/8 of the members are married men. Let the total numbers of members is 80 (the LCM of 10 and 8). Then there are:

3/10*80 = 24 women;
80 - 24 = 56 men;

3/8*80 = 30 married men;
56 - 30 = 26 unmarried men.

So, only option III is true.

Answer: D.
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I. The number of women in the organization is greater than the number of married men in the organization.
# percentage of women in organization = 30% and percentage of married men in organization= 3/8 = 37.5%. Not True

II. The number of women in the organization is greater than the number of unmarried men in the organization.
# percentage of women in organization = 30% and percentage of married men in organization= 70-37.5 = 32.5%. Not True
III. The number of married men in the organization is greater than the number of unmarried men in the organization.
# percentage of married men in organization = 32.5% and percentage of married men in organization= 37.5%. True

Ans: D

In the solution above aren't we assuming that the club doesn't not have other members like children?

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hi akamkhalia,
if not specified otherwise, they will be part of the unmarried/married groups
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-----------------Men----------Women------Total

Married---------3/8x--------------------------

Unmarried-----13/40x------------------------

Total----------7/10x---------3/10x-----------x

St.1. 3/8>3/10, so WRONG

St.2. 7/10-3/8=13/40>3/10, WRONG

St.3. 3/8>13/40, RIGHT


D

this is rathe difficult

one of mistake for non native, who think they are good at math is study of hard questions. never study too hard question. ignore some very hard questions in gmatprep . on the test, you can be wrong at two questions of 37 questions to get maximum score of 51.

Let total strength of the office be 800 .
Women = 240
Men= 560

Married Men = 300
Not married men = 260

Answer D .
Please see attached image.

Bunuel: Thanks for the solution. Even I did this by picking numbers. But, how do we be sure that the numbers that we have picked on will help us rule out all of the possible conditions mentioned in (I), (II), and (III). Unless and until we get a "No" in each case, we might feel that we have missed a case. How do we ensure that we have not missed a case and can mark the answer with certainity when taking an example in this question.
Thanks.

I. If there are 80 total members: woman = 3/10*80 = 24 and man = 3/8*80 = 30. False
II. Same logic, except now you're comparing same 30% of women vs 5/8 men. Can be false again if total of 80 is used.
III. 3/10 woman and 3/8 married man => 24/80 woman and 30/80 man, you have 26/80 unaccounted for. Even if all 26/80 are unmarried man, you still have 30>26. So must be true.

D.

Let’s say the total number of members is 800. Since 30% of the members are women, there are 800(0.3) = 240 women and 800 - 240 = 560 men in the organization. Moreover, 3/8 of the members are married men; therefore, there are 800(3/8) = 300 married men and 560 - 300 = 260 unmarried men in the organization. Let’s go over each Roman numeral in light of these figures:

Roman numeral I: The number of women in the organization is greater than the number of married men in the organization.

Since we found the number of women to be 240 and the number of married men to be 300, we see that Roman numeral I is false.

Roman Numeral II: The number of women in the organization is greater than the number of unmarried men in the organization.

Since we found the number of women to be 240 and the number of unmarried man to be 260, we see that Roman numeral II is false.

Roman Numeral III: The number of married men in the organization is greater than the number of unmarried men in the organization.

We have found that there are 300 married men and 260 unmarried men in the organization; therefore, Roman numeral III is true.

Alternate solution:

Since 30% of the members are women, it must mean 70% of the member are men. Since 3/8 of the members are married men and 3/8 = 37.5%, 37.5% of the members are married men, and thus 70% - 37.5% = 32.5% of the members must be unmarried men.

So, women = 30%, married men = 37.5%, and unmarried men = 32.5%.

Looking at the statements given in the Roman numerals, we see that only III is true.

Answer: D
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I got the answer by picking numbers, but the number for the total number of people that i picked was 24. I got this my seeing the 30% and the 8 and somehow figured that 24 would be a good number (3*8). While i did get this correct, I want to know if went about picking the numbers incorrectly?

Thanks!

24 might not be the best number to choose.

3/10 (30%) of the members are women and 3/8 of the members are married men. We should choose a number for which both 3/10 and 3/8 would be an integer. So, it's better to choose for the total numbers of members 80, which is the LCM of 10 and 8.

For more on picking numbers check the links below:
Backsolving on GMAT Math
How to Plug in Numbers on GMAT Math Questions
Why Approximate?
GMAT Math Strategies — Estimation, Rounding and other Shortcuts
The Power of Estimation for GMAT Quant
The 4 Math Strategies Everyone Must Master, Part 1 (1. Test Cases and 2. Choose Smart Numbers.)
The 4 Math Strategies Everyone Must Master, part 2 (3. Work Backwards and 4. Estimate)
Intelligent Guessing on GMAT
How to Avoid Tedious Calculations on the Quantitative Section of the GMAT
GMAT Tip of the Week: No Calculator? No Problem.
The Importance of Sorting Answer Choices on the GMAT
Identifying the Correct Answer on GMAT Quant Questions
How to Manage Unmanageable Numbers on the GMAT
Should You Double Check Your Answer Choices on the GMAT?
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Hi All,

This question can be solved by TESTing VALUES, but we're given enough information in the prompt to set this up as a simple comparison of percentages:

We're told that...
30% of the member are WOMEN (this accounts for ALL women in the group)
37.5% of the members are MARRIED MEN

30% + 37.5% = 67.5%, which leaves....

32.5% are UNMARRIED MEN

Now that we have the exact percentages, we can assess the three Roman Numerals to determine which ones are true. With the percentages, that work won't take long...

Final Answer:

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

why cant you just work with the fractions only?

So what I did:

women= 3/10 men=7/10

married men= 3/8 unmarried men= 5/8

I. false (3/10)<(3/8)

ii. false (24/80) < (30/80)

iii. false (3/8)<(5/8)

what did i do wrong?

Hi Ish1996,

To start, you might find it easier to convert the given fractions into percentages:

We're told that...
30% of the member are WOMEN (this accounts for ALL women in the group)
37.5% of the members are MARRIED MEN

Totaling up those 2 groups, we have:
30% + 37.5% = 67.5%

This means that the remaining 100% - 67.5% = 32.5% are UNMARRIED MEN. Thus, Roman Numeral III is actually true. Your error was based on the idea that 5/8 of the people in the group were unmarried men - but that's NOT correct (since some members of the group are clearly women).

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

Must remember:

1/8 = 12.5%
1/4 = 25%
1/2 = 50%

We know 30% are women and 37.5% are married men. We have 33.5% unaccounted for.

The only statement that must be true is the 3rd statement: 33.5% < 37.5%.

Answer is D.
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can anyone explain let suppose 80 is total member
m+w=80
3/8of m we will take why 80???

Hi SHYAM23,

You can absolutely TEST VALUES to answer this question, but it's worth noting that you have to keep track of 3 groups of people:
-Women
-Married Men
-Unmarried Men

We would want to start off with a multiple of 8 (since we are told that 3/8 of the members are MARRIED men), so the number 80 is a good choice for the TOTAL number of people:

Total = 80 people
Women (.3)(80) = 24 Women
Married Men = (3/8)(80) = 30 Married Men
Unmarried Men = 80 - 24 - 30 = 80 - 54 = 26 Unmarried Men

With these 3 numbers, which of the three statements is true? It's also worth noting that since we have a ratio of women:married men:unmarried men, we can use ANY number for the TOTAL and the correct answer will not change.

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

what about genders other than binary one ?

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