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

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the above question is from the Question Bank for Guide 2, FDP (question 5). The answer provided is 7/20. I am confused as to why the answer can be determined. We are not told that no married couples have 0 children; without knowing this proportion, how can we say anything definitive about what proportion of married couples have 2 or 3? I was nearly sure that considering the possibility of '0' was an embedded trick in this problem. Please advise. Is the wording of this problem inappropriately vague? Would we see a problem on the GMAT such as this one which requires an assumption as this one appears to require? Thanks! (sorry if I'm missing something obvious... very late here.)

Hi John: Neither is the question vague nor is any additional information required. Let's go through it step by step:

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

Did you understand?

Yep. Sad thing is it came to me the minute i hit the "post" button. as i had feared, it was too late at night...

thanks for the reply. cogent explanation.

:)

_________________
Tim Sanders
Manhattan GMAT Instructor