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Married Couples Problem

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Manager
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Married Couples Problem [#permalink] New post 17 Feb 2010, 16:25
00:00
A
B
C
D
E

Difficulty:

(N/A)

Question Stats:

75% (01:44) correct 25% (00:00) wrong based on 11 sessions
3/4 of all married couples have more than one child. 2/5 of all married couples have more than 3 children. What fraction of all married couples have 2 or 3 children?


A. 1/5
B.1/4
C. 7/20
D. 3/5
E. It cannot be determined from the given information.

[Reveal] Spoiler:
C


Source: MGMAT.

I'm debating this answer. I understand how they derive it when you make the assumption that ALL married couples have kids but the fact that it DOES NOT explicitly say what fraction of couples have no kids we do not have sufficient to information to conclusively answer the question asked. Am I missing something?
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Senior Manager
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Re: Married Couples Problem [#permalink] New post 17 Feb 2010, 16:33
Currency wrote:
3/4 of all married couples have more than one child. 2/5 of all married couples have more than 3 children. What fraction of all married couples have 2 or 3 children?


A. 1/5
B.1/4
C. 7/20
D. 3/5
E. It cannot be determined from the given information.

[Reveal] Spoiler:
C


Source: MGMAT.

I'm debating this answer. I understand how they derive it when you make the assumption that ALL married couples have kids but the fact that it DOES NOT explicitly say what fraction of couples have no kids we do not have sufficient to information to conclusively answer the question asked. Am I missing something?


I guess its right, lets take step by step, Lets assume there are 100 couple in total

now according to the question stem 3/4 of all married couples have more than one child
i.e 75 couples have more than one child and rest of them (25 couples have either one or none )

second part of the question says 2/5 of all married couples have more than 3 children
i.e 40 couples have 3 + children.

Question asks us to calculate couple with either or 2 or 3 children.

now we know 25 couples have either one or none children and 35 ( 75-40) have either 2 or 3 children

Hence 35/100 = 7/20 is the answer.

To add on to it we explicitly dont have to calculate how many couples have 0 kids we just need the number of couples who have 2 or 3 kids which can be calculated as shown above.

I hope that helps.
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Re: Married Couples Problem [#permalink] New post 17 Feb 2010, 16:35
Currency wrote:
3/4 of all married couples have more than one child. 2/5 of all married couples have more than 3 children. What fraction of all married couples have 2 or 3 children?


A. 1/5
B.1/4
C. 7/20
D. 3/5
E. It cannot be determined from the given information.

[Reveal] Spoiler:
C


Source: MGMAT.

I'm debating this answer. I understand how they derive it when you make the assumption that ALL married couples have kids but the fact that it DOES NOT explicitly say what fraction of couples have no kids we do not have sufficient to information to conclusively answer the question asked. Am I missing something?


Plug in simple numbers. Take 100 couples for example.

3/4 of 100 couples have more than one child = 75 couples.
2/5 of 100 couples have more than 3 kids = 40 couples.
This implies that 40 couples are a subset of 75 couples and the complement of 75 couples within those 100 couples, which equals 25 couples have either one or no kids at all.
We need to find couples that have 2 or 3 kids, so essentially, it is 75 - 40 = 35. Fraction will be 35/100 = 7/20.
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Re: Married Couples Problem [#permalink] New post 17 Feb 2010, 17:48
C

100 Married couples.

1 or more = 75
4 or more = 40
2 or 3 = 75-40 = 35

35/100 = 7/20
Manager
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Re: Married Couples Problem [#permalink] New post 17 Feb 2010, 18:42
Thanks fellas. I see the solution now. Makes sense when you grind it out.

One of my trouble spots is not fully grinding out a problem when I believe it to be unsolvable after reading thru the question. I get this more on DS questions.

In any event, thanks for the help!
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Round 1: 05/12/10 handling-a-grenade-thesituation-s-official-debrief-94181.html

Round 2: 07/10/10 - This time it's personal.

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Re: Married Couples Problem [#permalink] New post 18 Feb 2010, 07:39
Couples with two or three children = 3/4 - 2/5 = 7/20 hence C.
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Re: Married Couples Problem [#permalink] New post 18 Feb 2010, 19:19
Currency wrote:
Thanks fellas. I see the solution now. Makes sense when you grind it out.

One of my trouble spots is not fully grinding out a problem when I believe it to be unsolvable after reading thru the question. I get this more on DS questions.

In any event, thanks for the help!


By practicing, you will be able to think thru logically while reading the question. Also, just reading the questions on the forums and solving helps a lot!
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Re: Married Couples Problem [#permalink] New post 18 Feb 2010, 21:29
bangalorian2000 wrote:
Couples with two or three children = 3/4 - 2/5 = 7/20 hence C.


NICE AND EASY! I LIKE IT!
Re: Married Couples Problem   [#permalink] 18 Feb 2010, 21:29
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