I recently wrote a government entrance exam, and I encountered some questions I was unsure about. I'm pretty sure I know the answers, but I want to make sure my logic is correct. Since you're not allowed to take the exam questions with you after the test, I only remember the options that I had narrowed it down to (there were 4 options on each question though).

Question 1:

If Jane submits her application for university before May 1, there is a 75% chance she will be accepted. Jane is accepted to university.

Which of the following is the best response?

a) With a probability of 0.75, Jane submitted her application before May 1.
b) The probability that Jane submitted her application before May 1 is unknown.

Question 2:

Given the series: 30, 124, 30, -64, ___

Which of the following completes the series?

a) -30
b) 30
c) -158

My thought is, if the chance of acceptance if submitted on or after May 1 wasn't also specified, then the answer is b.

Imagine if the odds of being accepted if you submit your application on or after May 1st is 0%, then the odds that she submitted her application before May 1st is 100% since it was accepted.

Imagine if the odds of being accepted if you submit your application on or after May 1st is 100%. Then, you would have the following:

Given 4 submissions before May 1st, 3 would be accepted. Given 4 submissions after May 1st, 4 would be accepted. Since it was specified that the application was accepted, there are 7 applications accepted, 3 of which were submitted before May 1st, so the odds would be 3/7.

So the answer seems to be b given the information you provided.

The given sequence is +94, -94, -94, ?

That being the case, it seems like -30 can be thrown out as an option since it doesn't follow the pattern of +/- 94 from the previous number. So then the question is does the sequence continue with another -94 or change back to a +94.

I'd like to visualize this as a sequence of y values of a sin wave f(x)=94*sin(x)+30, and we're seeing results from f(0), f(90), f(180), f(270), and the ? is then f(360)=30, so I'd go with b.

1. b). We can't say a) unless we assume .75 chance of getting accepted though a later submission.. edit: oops its asking for probability of submitting not acceptance..

2. b) /30 + 94, 30 - 94, 30 + 94, 30 - 94/ We can assume a completed pattern or we can assume a incomplete pattern. Neither answer is more likely, but if we assume that its 50/50 for the pattern to be complete - than b) is infinitely more likely

This. Basically rules out answer a)

The term "series" as taught in calculus books means something entirely different than how the question uses the term series, so the first assumption that must be made is that the test designer made an innocent error. OP didn't specify if this is some top secret NSA aerospace engineering spy satellite personnel exam so the assumption of test designer error is valid here on 2p2.

I can show a few sequences where 30 would be the correct answer but only top two seem justifiable for purpose of the exam:

30, 124, 30, -64, (repeat these same 4 terms forever)

30, 124, 30, -64, 30, f(124), 30, f(-64), 30, f(f(124)), 30, f(f(-64))

where f(x) could be a simple function like 2x therefore f(124) = 248

-The reason we know that the value of a sequence element DOES NOT depend only on the previous sequence element is because the 4th term doesn't equal the 2nd term yet the 1st term does equal the 3rd term

-We must assume the numbers aren't random (i.e. there is at least one plausible pattern) this is kinda self-evident but YOLO...

Answer C is plausible if we assume that our number moves 94 in the direction of its previous move unless it becomes triple digit, in which case it will then move 94 into the opposite direction and continue moving 94 in the continued direction until it reaches another "trigger" and reverses

if C & A were the only 2 choices I'd pick C as the best answer

Justaspectator made an excellent point when he asked, "So then the question is does the sequence continue with another -94 or change back to a +94."

For this reason, we see that when the sequence hits the 2nd term it immediately "panics" and changes direction to move the opposite direction as soon as possible.

We see no evidence that the sequence changes direction or panics when becoming a negative number. We have only seen the sequence's reaction to becoming a 3-digit number. Since our sequence has obviously been "free to decrease" twice in a row, there's no inherent reason it can't be "free to decrease trice in a row" therefore since we have 1 clue that triple-digit number makes the sequence change direction, we cannot ignore that clue and that's the most "telling" clue we have (in addition to the fact that the first and 3rd term are both 30 which justaspectator satisfactorily restated in the quote I attributed to him)

Also, if I weren't given ANY answer choices, I'd be keenly aware that the decrease is linear (decreases by the same amount) between the 2nd, 3rd, and 4th elements. If I weren't given ANY answer choices, I'd waste many hours thinking why "30" is the first term but luckily we have ultimately just 2 plausible answer choices of -158 or +30

If mega society (or john cena) were arbitrator I'd risk $50 to win $2 that C is correct answer.

I prefer to visualize it as a sequence that moves (in increments of 94) in a continuous direction if the previous number is double digit and reverses direction if the previous number is triple digit.

(i.e. after a triple digit positive number is reached, the sequence subtracts 94 however many times is necessary to reach a triple digit negative number, then will repeat until becoming a triple digit positive number again, and repeating)

My visualization is simpler and describes the same pattern without nearly as much complexity as you have summoned. (parsimony principle)

Since 94*sin(90)+30=114, f(x)=94*sin(x)+30 doesn't work well.


What would you expect if the sequence was 0,94,0,-94,____?

Zero, right? So adding 30 to each term takes us back to the original sequence and then b)30 seems to be the best answer.

Use degrees, not radians.

I'm curious why you see a sine wave based on these 4 numbers? The pattern you posited also fails to incorporate relevance to the starting number 30 and the increment size 94.

You're just normalizing everything to N, N+X, N, N-X because that lets you see a sine wave pattern but this dismisses the significance of the starting value (30) and the increment (94)

The numbers 30 & 94 are specifically chosen by the test-writer and your pattern dismisses these two values because you just normalized everything to a simple sine wave, true?

When not encumbered, you should always try to include as much of the information they give you. (especially when they give you only 4 elements) I score high on these types of sequence problems on iq tests, fwiw.

Seems you answered your own question.

As do I. And I stand by my answer, as I'm sure you do yours.

Sometimes the dress is both blue and gold.

Thanks for the reply! I'm only attached to my answer until someone chimes in with new insights. Additionally, I made a couple extra assumptions given the context OP has provided to us regarding imprecise phrasing of the sequence question. Either way, fun little puzzle—I enjoyed it.

It would have been nice to see the exact question and answers as written. And your answer is clever.

If this were a required exam for citizenship into the country into which I was born I would have to login to fb and change my status to refugee (assuming the oceans get wifi).

edit:
The only insight I can give is on question 2 (and I'm grunching here, fwiw). The correct answer to this question, imo, is 30--and this is independent of what the 'real correct answer' is. What I mean is in this situation, the correct answer is not the answer that makes the given question true but the answer that gives you the best chance of being accepted. You don't want to stand out in any way, and you definitely dont want to level yourself. If I were taking this exam I would think "the vast majority of people taking this exam will say 30, so I will say 30" even if I knew '-30' was the correct answer from a mathematical pov. Keep in mind that my answer depends on the assumption that the people writing governmental entrance exams are not in the set of those people that did >= undergraduate level math.