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.

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.