Can you solve this ? Zagreb UNI humanities entrance exam

[Jana]

Zagreb University has demanding entrance exam required if you want to enroll to study humanities. Thing is, despite humanities orientations, potential students have to pass IQ test, with additional matematicss, logics and even physics questions. This caused lot of controversy in Croatia because humanities students don't need such skills......nevertheless, in addition to standard matura-leaving nation wide exams, they have to pass special entrance exam. I posted few questions here, and challenge you to solve them. Average time allowed per question is 1.5 minute, and calculators are not allowed:

1. Long line of numbers is formed by writing down number 2009 exactly 2009 times. Total sum of all odd numbers in that line, that are followed by an even number are .....?

2. In pool with balls, there are 24 blue balls, 56 green balls and 39 yellow balls. If we take one ball from the pool, which is the possibility for it to be yellow ?

3. From 30 high school graduates, 8 applied for architecture, 20 for humanities, and 30 for medicine. How much candidates did apply for at least one course ? And the most that applied one course ?

4. 100 tourists arrived by boat. Among them 10 do not speak neither German nor French. 75 speaks German, and 83 speak French. How much tourists speak both languages ?

5. Car travels by speed of 90 km per hour to the east for 3 minutes, and than turns to the north and drives for another 100 minutes. In the end he travelled 234.5 kn/h total. What speed did he have when he turned north ?

6. Using 3/4 of her average speed, Sonja arived in town 20 minutes later than usual. How much tim Sonja needs to arrive in town using her average speed ?

7. There are both pigs and chickens on the farm. Totl sum of animals is 80, and total sum of legs is 220. How much chicken there is ?

8. Dance troup does their every new training in 3/5 of time they did they last training in. For how much time they do their fourth training, if they did their first practice in 2 hours and 5 mns ?

9. Group of people started to swimm regulary. When they had first practice, they menaged to swimm one olympic lenght of the pool. Every next day they menaged to swimm one olympic lenght more than they did in previous day. How much they menaged to swimm in one day on average, if they went swimming whole week, including weekend ?

10. Man needs to cross the river by boat with one goat, one wolf and one pack of vegetables. But, he needs to cross the river only with wolf, or only with goat, or only with vegetables. In mans presence, wolf wont eat the goat and got wont eat the vegetables. What is the smallest number of crossings man needs to make
not to leave goat, wolf and vegetables unsupervised ? They all need to cross the river in one piece. Every crossing is couned as one, including the crossing he makes back to the starting shore. Calculate.


These are average questions from maths part only. I'm wondering do you find them easy of difficult and does humanities collages in your country require similar skills on ther entrance exams ?

Cheers, try solve it. I can write correct answers later.

[Duke]

e našla si crkvu di ćeš boga molit :D

[Damião de Góis]

So what do Math students have to solve? The analysis of Dorian Gray?

[Ivan Kramskoï]

I have been thinking a bit about those.
Some are quite easy if you have some basics mathematical knowledge like the 7 (system of 2 equations with two unknown).
Some like the 4. is pure logic and do not need any mathematical knowledge.
Anyway very interesting stuff.

[Duke]

1=18072
2=30,5%
3=30; 2
4=68
5=86,7 km/h
6=80 min? :P
7=50 chickens
8=27 min
9=4 pools average
10=7 times


Kids these days...

[Jana]

e našla si crkvu di ćeš boga molit :D
Ae :D


So what do Math students have to solve? The analysis of Dorian Gray?
Croatia, where paradox happen :D


I have been thinking a bit about those.
Some are quite easy if you have some basics mathematical knowledge like the 7 (system of 2 equations with two unknown).
Some like the 4. is pure logic and do not need any mathematical knowledge.
Anyway very interesting stuff.
Good observation. Most of it is basic maths, but there is little time and for many it's problematic becuse maths is not their strong side. Absolutely useless exam, there was a girl who was national champion in Italian, with 100% solved test, who couldn't enroll in UNI because she failed this test. She had to go study in another city.....
This is good example how our educaional system is old-fashioned, and more or less, non-practical.



1=18072
2=30,5%
3=30; 2
4=68
5=86,7 km/h
6=80 min?
7=50 chickens
8=27 min
9=4 pools average
10=7 times

Kids these days...

You would pass, it's actually very good score:)
1. correct 2. close enough, 0.327/32 % 3. least 2, most 10 4. correct 5. 138 km/h 6. 60 minutes :p
7. correct 8. correct 9. correct 10. correct

[Duke]

Ae :D


Croatia, where paradox happen :D


Good observation. Most of it is basic maths, but there is little time and for many it's problematic becuse maths is not their strong side. Absolutely useless exam, there was a girl who was national champion in Italian, with 100% solved test, who couldn't enroll in UNI because she failed this test. She had to go study in another city.....
This is good example how our educaional system is old-fashioned, and more or less, non-practical.



You would pass, it's actually very good score:)
1. correct 2. close enough, 0.327/32 % 3. least 2, most 10 4. correct 5. 138 km/h 6. 60 minutes :p
7. correct 8. correct 9. correct 10. correct

Maybe some of your questions are not translated good, i had some trouble dicipering some of them, but i am interested how did you get 32% on second, and not 30,5%, and in 5th question that answer is impossible, 138km/h to travel 144km, in 100 minutes??? that speed would be closer for 60 mins travel time, or am i wrong here :P

[щрбл]

The questions are pretty easy.. you get only 1,5 minute per question though, so I don't know. :)

[Duke]

The questions are pretty easy.. you get only 1,5 minute per question though, so I don't know. :)

i haven't touched math for years, youth that is preparing for collage should not have problem

[щрбл]

i haven't touched math for years, youth that is preparing for collage should not have problem

Well, I didn't understand all of the questions too...
For example, 2009200920092009...etc, the number of odd numbers followed by an even number is 2009, right?
Or is it 20092009... etc, followed by 2.
Or maybe 200920092009...etc, followed by 2.

Or maybe, it's the sum of all of these which would make 2009+2009+2009/2+2009/3+...

It's confusing. xD

[Minesweeper]

The questions are solvable but I don't understand, they have this instead of history, sociology, etc?

[Duke]

Well, I didn't understand all of the questions too...
For example, 2009200920092009...etc, the number of odd numbers followed by an even number is 2009, right?
Or is it 20092009... etc, followed by 2.
Or maybe 200920092009...etc, followed by 2.

Or maybe, it's the sum of all of these which would make 2009+2009+2009/2+2009/3+...

It's confusing. xD

its 9*2008, because in last sequence there is no even number

[щрбл]

its 9*2008, because in last sequence there is no even number
yep, of course if you consider that one number = one digit, because 2009 is an odd number too, so is 20092009, 200920092009 and so on. :D
The question is weird!

[Duke]

yep, of course if you consider that one number = one digit, because 2009 is an odd number too, so is 20092009, 200920092009 and so on. :D
The question is weird!

its not weird, you need to add every 9 that has 2 after it, its easiest question of the 10

there are 2009 9 in total, but last one doesn't have 2 after it so its 9 times 2008

[щрбл]

its not weird, you need to add every 9 that has 2 after it, its easiest question of the 10

there are 2009 9 in total, but last one doesn't have 2 after it so its 9 times 2008

Ok, the question is not weird but imprecise, it should have been about the sum of odd digits, not the sum of odd numbers. I would have spent all my time trying to calculate something that can't be calculated by hand. :)

[Duke]

Ok, the question is not weird but imprecise, it should have been about the sum of odd digits, not the sum of odd numbers. I would have spent all my time trying to calculate something that can't be calculated by hand. :)

problem is google translate, but your logic still fails, if you thought on literary on number and not a digit, then whole sequence is 1 odd number, and that doesn't make sense, right? :D

[Jana]

problem is google translate, but your logic still fails, if you thought on literary on number and not a digit, then whole sequence is 1 odd number, and that doesn't make sense, right? :D

I haven't used google translate, I translated it myself. Sorry for imprecision.
Will write down explanation for two questions you asked about, just wait.

@Minesweeper: yes, they have this test of ''intelecltual capabilities'' instead of history, sociology etc knowlege ;)
Although you have to write specific subjects on matura-for example psychology for psychology course , etc.

[Jana]

Maybe some of your questions are not translated good, i had some trouble dicipering some of them, but i am interested how did you get 32% on second, and not 30,5%, and in 5th question that answer is impossible, 138km/h to travel 144km, in 100 minutes??? that speed would be closer for 60 mins travel time, or am i wrong here :P

Question no. 5:
I FORGOT TO WRITE CARS TRAVELS 3 MNS TO THE EAST, f--k. Sorry:picard1:

v1/speed - 90 km/h
t1/time - 3 mns
t2 - 100 mns
s/speed - 234.5 km/h
.....
s1=v1xt1=90 km/h.......x=0.05h=4.5 km....means he drove 4.5 km from point A to point B.
s2=234.5-4.5=230 km......v2=s2/t2=230km/100 mns=230km/100x1/60h = 138 km/h.

Of course you couldn't solve it when I forgot to write down entire thing. LOL

[Duke]

Question no. 5:
I FORGOT TO WRITE CARS TRAVELS 3 MNS TO THE EAST, f--k. Sorry:picard1:

v1/speed - 90 km/h
t1/time - 3 mns
t2 - 100 mns
s/speed - 234.5 km/h
.....
s1=v1xt1=90 km/h.......x=0.05h=4.5 km....means he drove 4.5 km from point A to point B.
s2=234.5-4.5=230 km......v2=s2/t2=230km/100 mns=230km/100x1/60h = 138 km/h.

Of course you couldn't solve it when I forgot to write down entire thing. LOL

well that makes whole lot difference, i took into account while reading it that it drove 1 hour for 90km before turning, which then left me 144km taken in 100 minutes :P

also this one is bit confusing as written
From 30 high school graduates, 8 applied for architecture, 20 for humanities, and 30 for medicine. How much candidates did apply for at least one course ? And the most that applied one course ?


because as written, all 30 took at least 1 course, i got the minimum right

[Jana]

Question no.2:

P/probability= 39/ 24 + 56 + 39....P=39/119= 0.327=32.77 %

[Duke]

Question no.2:

P/probability= 39/ 24 + 56 + 39....P=39/119= 0.327=32.77 %

yea i did the math wrong there, i went 119/39, and that seemed about right to me

it was late :P

as an excuse i dint touch math in a decade

[Jana]

well that makes whole lot difference, i took into account while reading it that it drove 1 hour for 90km before turning, which then left me 144km taken in 100 minutes :P

also this one is bit confusing as written
From 30 high school graduates, 8 applied for architecture, 20 for humanities, and 30 for medicine. How much candidates did apply for at least one course ? And the most that applied one course ?


because as written, all 30 took at least 1 course, i got the minimum right

Ovako piše: koliko ih je najmanje prijavilo jedan studij? A najviše?
The solution: 30-(20 + 8)=2
30-20=10

This one is complicated to explain....You solved them great Duke, sepecially after a decade :cool: I haven't touched maths in 5 yrs, and find them difficult to do in such short time without calculator. Anway, some brain challenge is always good.

:P