Tick box quiz #14, Q9

GRE Quant Problem Solving
1

In a town of 100, every family has a son, a daughter, both or none. 80 households have a son and 40 households have a daughter.

Quantity A: The number of households with both a son and a daughter

Quantity B: 20

In the question above, the answer is D) the relationship cannot be determined. However, the way the question is worded it seems like there are households that have neither son nor daughter, so this cannot be 0. Lets say only 1 household has neither, then the maximum no. households with both son and daughter would be 19. So wouldnt Quantity B always be bigger?

2

Do you know formal logic? You can consider “every family has… or none” logically identical to “every number in \{2,4,6,8,10\} is even or odd”. Even if all the families have at least a daughter or a son, the statement “every family has a son, a daughter, both or none” is still true, just as in the set example where none of the elements are odd. There is no requirement that a family with none must exist.

Also, even under the assumption that at least one household has no children (None > 0), you should still have A as your answer not B

1 Like
3

Makes sense, thank you!