I was solving questions from tickbox quiz #6 under algebra foundation (prepswift). The first question is: f(1)=1, f(2)=4, f(3)=9,f(4)=16 and we have to find an compare the value of f(5) with 25.
According to Greg’s solution there isnt enough information to say f(5)=25. I don’t understand why this information is insufficient.
Can you check this please?
https://www.reddit.com/r/GRE/comments/1dfiiw6/prepswift_uant_tickbox_quiz_6_algebra/
Could you please explain the explanation for answer choice D. I checked Reddit but have doubts.
Bear with me- Imagine you are asked to write the nth term or rule for a given sequence, say, 3,5,7,9,… Can we write nth term = 2n+1, n>=1?
If yes, then how? because it satisfies the values of the sequence right? but then you say -
No, we can’t write a rule because we don’t know if the sequence will change say after 6th term or 7th or 8th term. But then we can’t write rules for any sequence at all, for example, any sequences with any rules given are just made up because we don’t know if the sequence will change midway, so those rules are flawed or made by assuming stuff? which makes math itself wrong?
Basically, any pattern-finding questions will become irrelevant because we don’t know if it’ll change midway or after some term.
Now coming back to the question - you say only x^2 fits the rule for the given values and we are not sure whether the f(x) will change abruptly in later stages. One more rule satisfies the sequence: we have increments of 3, 5, 7, 9…so on which also gives f(5) = 25.
Yeah, well all those “pattern finding” questions are kind of ambiguous by nature, but then you just try to go along with what the “author” actually expects from you on those.
For example, if someone asks you what the next number in: 1, 4, 9, 16, ...
then the logical answer would be 25 because this is what you assume the author is presumably looking for. Could you have answered practically anything? Sure, but that’s just trying to be intentionally silly.
For this QC question, however, you’re trying to find a unique function and then retrieve the value of f(5). Why do we need a unique function instead of just being “logical” like above (by choosing the most obvious function like f(x) = x^2) ?
Because you’re given the option to choose “not enough information…” for making the comparison between f(5) with 25.
Owing to that, it is possible that you pick f(x) = x^2 and i pick f(x) = - \frac{x^4}6 + \frac{5x^3}{3} - \frac{29x^2}{6} + \frac{25x}{3} - 4.
We both have functions that meet the designated constraints established in the question, but our values for f(5) don’t coincide and so we can’t make an objective comparison between f(5) and 25.
In fact, f(5) can be anything, as should be evident to you by now.
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