I thought this was a pretty weird question, I'm not gonna lie.
First of all let's sort out the formalities:
Question Type: Identify the FlawArgument core:
friends/family frequently know what another friend/family member is thinking (too frequently to be a coincidence)
---thus-->
telepathy is possible between people with close psychic ties
So, what's the trouble with this argument?
First of all, let's remind ourselves what 'telepathy' means. It's the idea that, for example, I think of the number '42' and wordlessly transmit that idea into your mind.
We can expect from LSAT's conservative world view that it is not going to be a big fan of endorsing something as magic and unscientific as telepathy.
So how
else would we explain why good friends and family members often know what another is thinking?
How did you mom know that you were going to go watch Sportscenter after breakfast? Did you have the thought, "I'm gonna go watch Sportscenter" and then implant it in her brain? Or did she just know what you were thinking from having lived with you and observed your behaviors?
How did you best friend know that when you heard the words 'catnip' and 'evergreen' so close to each other that you were going to start thinking about Katniss Everdeen from 'Hunger Games'. Telepathy? Or is it just that your best friend is ALSO a huge 'Hunger Games' fan and has watched the movies / read the books with you?
It is an INCREDIBLY common LSAT argument template to see:
- premise: [some phenomenon]
- conclusion: [some explanation for the phenomenon]
- correct answer: [some alternative explanation for the phenom]
But, it was definitely harder (for me, at least) to decode that that's what was going down here.
In retrospect, it seems clear that the 2nd sentence is a phenomenon that needs some explanation, because 'coincidence' won't cut it. The 1st sentence is author providing HER explanation: telepathy.
LSAT wants us to consider the less exotic alternative that good friends and family members frequently know what we're thinking simply because they're good friends and family members ... i.e. they've spent a LOT of time around us and/or they have similar biology/psychology due to common genetics.
(A) You nailed why it's wrong. The conclusion doesn't extrapolate from a smaller set of data to a larger one. The conclusion only claims that telepathy is possible, and to prove something is possible you only need one example.
If I found a 4th grader who understood quantum physics, I can fairly conclude that "it's possible for 4th graders to understand quantum physics". It doesn't matter if the 4th grader I found has an incredibly weird, rare set of circumstances leading to her precocious understanding. It's not a sampling flaw unless I'm generalizing to a bigger group, saying something like "quantum physics should be taught as early as 4th grade".
(B) Correct answer ... definitely weird that the answer choice implies that we should have already considered this 'obvious' alternative rather than suggesting what the heck they're referring to.

(C) I think I've only seen this type of answer be correct once, ever. The premise is not an appeal to emotion, so this can't match up. An appeal to emotion is something like "I know my son violated his probation and thus deserves jail time, but he should be allowed to stay out of jail, since picturing him in a prison cell breaks my heart."
(D) 'presumes' and 'takes for granted' just mean
Necessary Assumption. Probably the most common recurring trap answer in Flaw questions is to pair these up with some extreme claim. This one says that the author must assume that people NEVER know what a stranger is thinking. Eliminate.
The author is arguing that telepathy is possible among people with close ties. You can't infer from that that the author believes that telepathy is NOT possible among people WITHOUT close ties. Classic LSAT false opposite.
(E) This describes the formal flaw known as Circular Reasoning. The various common phrasings for it are:
- assumes what it sets out to prove
- presupposes what it seeks to establish
- the conclusion is a restatement of the the premise
These are almost NEVER correct answers. Like 97% of the time you see a Circular Reasoning answer choice, it will be wrong.
Nevertheless, I was more tempted by this one than usual. It DID seem like the author was so set on the truth of 'telepathy' that she was judging her family/friends' behavior with that preconceived idea.
But ... before you ever pick a Circular Reasoning answer choice, see if the conclusion and premise really do just say the same thing.
The premise here is just saying that friends/family so frequently know what one is thinking that it can't be a mere coincidence.
We can accept that idea without NEEDING to believe in telepathy. As discussed before, in relation to (B), we can accept the premise and simply explain it by appealing to the common experience / genetics of close friends and family.
A genuine example of (E) would be "Chocolate is by far the best flavor of ice cream. After all, if you considered every ice cream flavor in existence, you would find all of them inferior to chocolate."
Hope this helps.