Good Girls And Bad Boys (4)

Suppose the older one is a girl. Then it will be true that she has a younger sister. But as a girl, her younger sister is also supposed to be truthful which supposedly validates the statement "We are of opposite genders". This contradicts with what we know that both are girls.

This means the older one is a boy. So it is unsure that he has a younger sister, meaning he has a younger brother. His younger brother is also a liar which makes the idea that they are of opposite genders false. Which is indeed the case since both are boys.

here's the 4 possibilities

1) 2 sisters: so the youngest girl is liar, which is not true

2) older brother, younger sister: the older boy is telling the truth, which isn't true

3) older sister: younger brother: the older girl is lair, the younger boy is telling the truth, which isn't true

4) 2 brothers: both boys is liar, this is the only possible one

The younger child's statement proves that the older child is a boy. If it were a girl, then the younger child wouldn't say they were of the opposite gender. We can consider the two cases separately - if they are both girls, the younger girl would tell the truth and say they're the same gender. If the older is a girl and the younger one is a boy, he would lie and say they're the same gender. Hence, we can rule those two cases out, and the older one must be a boy.

However, I have to point out that it's not specified that the two children are siblings, nor that the older child is referring to the younger one. We know the older child is a boy, meaning he does not have a younger sister. So, the younger child is not his sister, but it could be some other girl (who would correctly say they're different genders). Or it could be a boy, who would lie and say they're different genders. So, there are two possible cases...

This question was a little difficult for me because the way it was written didn't reveal if they were even related or not, which would/could affect the answer. When I looked at the answer choices, I was able to deduce that they were obviously related, though.

Anyhow, to solve this one, just take the list of answers and cross them out in your head by the contradictions they have until you meet one without one.

Case 1: Older sister, younger brother The sister says that she has a younger brother. Assuming that's true, then the younger brother is lying, which means they are not of opposite genders, which is a contradiction. So, that's out.

Case 2: Older brother, younger sister If the older one is lying, then he doesn't have a younger sister, which means that the younger one is lying (because they wouldn't be opposite genders), which is a contradiction.

Case 3: Two sisters If the older one is telling the truth, then the younger one is lying, which is a contradiction.

Case 4: Two brothers If the older one is lying, then he doesn't have a younger sister. If the younger one is lying, then they are not of the opposite sex. There is no contradiction; therefore, this is your answer.

Anytime somebody denied to be associated with another person / party in a bigger group, then we can be sure that the other person is a liar even when that someone who did the whole denial might do so deceptively, too. From this, we know that the older brother is lying with his "I have a younger sister" speech. They must be a pair of two brothers.