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If 30% percent of the members of the organisation

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If 30% percent of the members of the organisation

by Needgmat » Tue Sep 06, 2016 8:06 am
If 30% percent of the members of the organisation are women and 3/8 of the members of the organisation are married men, which of the following statements concerning the membership must be true?

a) The number of women in the organisation is greater than the number of married men in the organisation.

b) The number of women in the organisation is greater than the number of unmarried men in the organisation.

c) The number of married men in the organisation is greater than the number of unmarried men in the organisation.

A) None

B) a only

C) b only

D) c only

E) a and c only

OAD

Please explain [/spoiler]
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by GMATGuruNY » Tue Sep 06, 2016 8:33 am
Needgmat wrote:If 30% percent of the members of the organisation are women and 3/8 of the members of the organisation are married men, which of the following statements concerning the membership must be true?

a) The number of women in the organisation is greater than the number of married men in the organisation.

b) The number of women in the organisation is greater than the number of unmarried men in the organisation.

c) The number of married men in the organisation is greater than the number of unmarried men in the organisation.

A) None

B) a only

C) b only

D) c only

E) a and c only
Test the SMALLEST POSSIBLE CASE.
Since 30% = 3/10 and 3/8 of the members are married men, the total number of members must be divisible by 10 and 8.

Let the total number of members = the LCM of 10 and 8 = 40.
Since 30% percent of the members are women, the total number of women = (30/100)(40) = 12, implying that the total number of men = 40-12 = 28.
Since 3/8 of the members are married men, the total number of married men = (3/8)(40) = 15, implying that the total number of unmarried men = (total men) - (married men) = 28-15 = 13.

Resulting ratios:
(total number of women)/(total number of married men) = 12/15 = 4/5.
(total number of women)/(total number of unmarried men) = 12/13.
(total number of married men)/(total number of unmarried men) = 15/13.

The resulting ratios indicate that only Statement C must be true.

The correct answer is D.
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by cubicle_bound_misfit » Tue Sep 06, 2016 8:48 am
@GMATGuruNY

why we can't do simple percentage without doing LCM. Please let me know.

If we take 100 people in the organization

Women # = 30
Married Man # = 3/8 of 100 = 37.5
Unmarried Man # = 100 - 30 - 37.5 = 32.5

and it becomes clear.
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by [email protected] » Tue Sep 06, 2016 10:05 am
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: D

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by Cthulu » Wed Sep 07, 2016 6:39 pm
We can use 100 as total number of people in the organization but we see a fraction 3/8 down the question. So better if we use an easier number like 80.

Total Member : 80
Number of women : 30% of 80 = 24
Married Men : (3/8)*80 = 30
Unmarried Men : 80 - 24 -30 = 26

Now running through the options only D satisfies the numbers above.
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