A class has twice as many boys as girls . the students in the class stand in one line , with a girl at the front of the line . which of the following must be true?
Let's go through the answers
(A) the last person in line is a girl
That doesn't have to be true, because if there were 1 girl and
2 boys, that one girl would be first in line, not last.
(B) the last person in line is a boy
That doesn't have to be true, because if there were 2 girls and
4 boys, they could be lined up like this
6th (last) 5th 4th 3rd 2nd 1st
G B B B B G
(C) there are more girls than boys in the class
That can't be true because it contradicts the fact that there
are twice as many boys as girls.
(D) there are at least two girls standing next to each other
That certainly isn't necessarily true by the example used above:
6th (last) 5th 4th 3rd 2nd 1st
G B B B B G
(E) there are at least two boys standing next to each other
Indeed (E) is the correct choice, not just because we have ruled
out all the others (which is a good reason!) but also because
except in the case of 2 boys and 1 girl, there aren't enough
girls to be able to put one girl between every pair of boys.
And in the case where there are 2 boys and 1 girl, that one
girl must be at the front of the line, putting the two boys
standing next to each other.
In fact the only reason that the requirement of "a girl at the front
of the line" is necessary is because of the one case where there are
2 boys and only 1 girl. E is automatically true in every other case
even without that requirement.
Edwin
