Problem Solving

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Problem Solving

by mbaonly » Fri Jul 06, 2012 6:22 pm
If 30 percent of the members of a certain organization are women and 3/8 of the members of the organization are married men, which of the following statements concerning the membership must be true?

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

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

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


a. None
b. I only
c. II only
d. III only
e. I and III
Last edited by mbaonly on Fri Jul 06, 2012 6:28 pm, edited 1 time in total.

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by mbaonly » Fri Jul 06, 2012 6:22 pm
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by Jim@StratusPrep » Sun Jul 08, 2012 3:36 pm
Let's say there are 1000 people

300 are then women (.3 x 1000)
375 are married men (3/8 * 1000)
325 must then be unmarried men (1000- 675)

Only statement III is true.

D
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by mcdesty » Sat Jul 19, 2014 9:33 pm
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by Jeff@TargetTestPrep » Mon Jan 08, 2018 4:50 pm
mbaonly wrote:If 30 percent of the members of a certain organization are women and 3/8 of the members of the organization are married men, which of the following statements concerning the membership must be true?

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

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

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

a. None
b. I only
c. II only
d. III only
e. I and III
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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