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3/4 of all married couples have more than one child. 2/5 of all marrie

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Bunuel
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3/4 of all married couples have more than one child. 2/5 of all marrie [#permalink] New post   20 Feb 2020, 06:25
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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.
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C
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BrentGMATPrepNow
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Re: 3/4 of all married couples have more than one child. 2/5 of all marrie [#permalink] New post   20 Feb 2020, 07:18
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Bunuel 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.


GIVEN: 3/4 of all married couples have more than one child
In other words, 3/4 of all married couples have 2 or 3 or 4 or 5 or 6 or ...(etc) children

GIVEN: 2/5 of all married couples have more than 3 children
In other words, 2/5 of all married couples have 4 or 5 or 6 or ...(etc) children

Notice that the married couples who have 4 or 5 or 6 or ...(etc) children are included among the married couples who have 2 or 3 or 4 or 5 or 6 or ...(etc)

So, we know that (number of couples with 2 or 3 or 4 or 5 or 6 or ...(etc) kids) - (number of couples with 4 or 5 or 6 or ...(etc) kids) = number of couples with 2 or 3 kids.

So, the fraction of married couples with 2 or 3 kids = 3/4 - 2/5 = 15/20 - 8/20 = 7/20

Answer: C

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Re: 3/4 of all married couples have more than one child. 2/5 of all marrie [#permalink] New post   20 Feb 2020, 07:22
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3/4 have more than one child: >1 is 2,3,4,5, etc.
2/5 have more than three childeren: >3 is 4,5,6, etc.

Because we have overlap between the two (exactly between 2 and 3 children), we can determine the fraction of couples that have 2 or 3 children:
=3/4-2/5
=15/20-8/20
=7/20

C
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3/4 of all married couples have more than one child. 2/5 of all marrie [#permalink] New post   Updated on: 04 Apr 2020, 19:12
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Bunuel 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.


Let there be 100 couples

75 couples have more than 1 child -> 25 have less than or equal to 1 child
40 have more than 3 child -> 60 have less than or equal to 60 child (which includes 25 couples who have less than or equal to 1 child)

Therefore couples who have 2 or 3 child = couples less than or equal to 3 - couples less than or equal to 1 child = 60-25 = 35 couples have 2 or 3 children

35/100 = 7/20 = Answer - C

Originally posted by shameekv1989 on 20 Feb 2020, 07:55.
Last edited by shameekv1989 on 04 Apr 2020, 19:12, edited 1 time in total.
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Re: 3/4 of all married couples have more than one child. 2/5 of all marrie [#permalink] New post   20 Feb 2020, 08:35
Bunuel 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.


total children = 20
so 3/4 of all married couples have more than one child = 3/4*20 ; 15
and 2/5 of all married couples have more than 3 children = 2/4*20 ; 8
so married couples have 2 or 3 children ; 15-8 ; 7
7/20
IMO C
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Re: 3/4 of all married couples have more than one child. 2/5 of all marrie [#permalink] New post   10 Jul 2023, 07:20
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Re: 3/4 of all married couples have more than one child. 2/5 of all marrie [#permalink]
10 Jul 2023, 07:20
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