Fractions Problem

[championspunch]

Question: 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?

[GMATGuruNY]

Question: 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) Cannot be determined

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 TWO 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 FOUR OR MORE children = (2/5)20 = 8.
Thus, of the 15 couples who have 2 or more children, the number who do NOT have 4 or more children (in other words, the number WITH EXACTLY TWO OR EXACTLY THREE children) = 15-8 = 7.
Thus:
(couples with 2 or 3 children)/(total couples) = 7/20.

The correct answer is C.

[Anju@Gurome]

Question: 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?

3/4 of all the married couples have more than one children, i.e. either 2 or 3 or more than 3 children.
2/5 of all the married couples have more than 3 children.

Hence, fraction of all the married couples who have 2 or 3 children = (3/4 - 2/5) = (15 - 8)/20 = 7/20

[CSASHISHPANDAY]

Assume there are 100 married couples.
Therefore, 75 of them will have more than one child (as per the stem)----(1)

Also, 2/5 of all married couples have more than 3 children. This translates to: 40 of them have more than 3 children---(2)

Now observe closely and you'll find (2) to be a subset of (1). ie; No. of people having more than 1 child will definitely include number of people having more than 3 children as well.

We are not interested in couples having greater than 3 children. So subtract 40(couples having more than 3 children) from 75(total number of couples having more than 1 child, including couples having more than 3children) and you get 35.( the number of couples having more than 1 but not more than 3 children)
Required Fraction =35/100 =7/20