Sets ?

[prachi18oct]

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 the married couples have 2 or 3 children?
A)1/5
B)1/4
C)7/20
D)3/5
E)3/22

[GMATGuruNY]

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 the married couples have 2 or 3 children?
A)1/5
B)1/4
C)7/20
D)3/5
E)3/22

Let the total number of married couples = the LCM of 4 and 5 = 20.

Since 3/4 of all married couples have more than one child, the number of married couples with 2 OR MORE children = (3/4)(20) = 15.
Since 2/5 of all married couples have more than 3 children, the number of married couples with 4 OR MORE children = (2/5)(20) = 8.
Thus:
The number of married couples with 2 OR 3 CHILDREN = (total number with 2 or more) - (total number with 4 or more) = 15-8 = 7.

Resulting probability:
P(2 or 3 children) = 7/20.

The correct answer is C.

[theCEO]

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 the married couples have 2 or 3 children?
A)1/5
B)1/4
C)7/20
D)3/5
E)3/22

3/4 of married couples have 2,3,4,5...... children [1]
2/5 of married couples have 4,5...... children [2]

If we subtract these 2 equation we get the fraction og married couples that have 2 or 3 children
3/4 - 2/5 of married couples have 2 or 3 children
15/20 - 8/20 of married couples have 2 or 3 children
7/20 of married couples have 2 or 3 children
ans = c

[Matt@VeritasPrep]

We want (More Than One) - (More Than 3), so (3/4)x - (2/5)x = (7/20)x, and we're done!