How fast can you answer this scholarship test question (intelligence?) (1 Viewer)

idkkdi

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Beyblader, out of curiosity, was the 40 seconds an actual limit for the question on a online test (ie. timer with lock out) or an allocation based on the total time given for the whole test and the total number of questions?
selective tests/scholarship tests for the GA questions normally average at around this speed. although you could very well spend more time on harder qs.
 

Beyblader

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Beyblader, out of curiosity, was the 40 seconds an actual limit for the question on a online test (ie. timer with lock out) or an allocation based on the total time given for the whole test and the total number of questions?
the test consisted of 60 questions to be completed in 40 minutes so average 40s per question
 

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Applied logical reasoning and a small amount of counting. There's possibly a more elegant method but when time is of an essence, I would usually try to reduce a question (see strategy for first question in this thread) as much as I can by logical reasoning, but will apply quick & dirty if I can see it will get to the solution faster. Only in Olympiad & UNSW comps, would one aim for elegant solutions (I did all forms of comps long before most people in this forum were born and I'm very slow & have forgotten most tricks since my prime).
 
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idkkdi

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Applied logical reasoning and a small amount of counting. There's possibly a more elegant method but when time is of an essence, I would usually try to reduce a question (see strategy for first question in this thread) as much as I can by logical reasoning, but will apply quick & dirty if I can see it will get to the solution faster. Only in Olympiad & UNSW comps, would one aim for elegant solutions (I did all forms of comps long before most people in this thread were born).
n-(n/3 + n/5 - n/3 *1/5) = 95

notice that although n/3, n/5 etc. produce decimal places which may induce error, these errors are basically negligible, and if in doubt, just test the numbers around the n value.
 
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Eagle Mum

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n-(n/3 + n/5 - n/3 *1/5) = 95

notice that the tho n/3, n/5 etc. produce decimal places which may induce error, these errors will become negligible once we convert the fraction to /15.
Yes, but in this case, one knows to round down whatever the decimal place might be.
 
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idkkdi

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Yes, but in this case, one knows to round down.
a faster way may perhaps be
noticing from 1-100, there are 53 numbers. for the 95th number we need another 42.
42/53 is just over 7/9, which means that 42 numbers requires approximately 78.

so 178.

edit: in actuality, 42/53 is around 0.79.
but we notice the first multiple of 3 starts at 102, compared to 3 in the range of 1-100.
so 79-1=78.
 
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Eagle Mum

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A couple of comments about the question itself.

It describes the numbers between 1 and 200 - many would interpret the preposition ‘between’ as a set which is non inclusive of the boundary values, therefore such a question in a competition would be expected to explicitly state whether or not the set of numbers included 1 and 200.

Secondly, stating 200 as the upper boundary of the set is redundant. Most maths questions (as opposed to puzzles) are stated as purely and economically as possible. If the question had been posed as - counting from 1 as the first number, what is the 95th number which is not a multiple of 3 or 5, it would have taken less time to solve (not a big deal in most scenarios but certainly would be significant in selective school tests and the AMC where every second counts as most candidates don’t finish these papers).

IMO, if the question intends to test reading skills and ability to filter the relevant info (ie. inclusion of 200 as the upper limit is a deliberate red herring), then more attention should have been given to grammatical aspects of the question (ie. explicit description of the set), so if it was in an actual scholarship test, it was a poor question. Last year during COVID lockdown, my son had an interesting WFH job, as a quality checker of some Yr 11 & 12 maths practice papers. His employers only asked him to check the answers, but he ended up finding several flaws in the questions in addition to a couple errors in the answers (which the other checkers missed).
 
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