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The secret questions only the top 2% of young mathematicians can answer

Einstein

Think you’re good at maths? Results to the OECD’s ‘Programme for International Student Assessment’ (PISA) are out today and have been causing upset in Western democracies like the US and the UK, whose 15 year olds have scored badly by international standards.

The questions in PISA tests are segmented by difficulty, with level 6 questions being the hardest. Students answering level 6 questions must be able to, ‘conceptualise, generalise, and utilise information based on their investigations and modelling of complex problem situations,’ according to the OECD’s own website.  In the U.K. and the U.S. only 3% and 2% of 15-year-old students respectively achieve level 6.

Fancy your chances? Unfortunately, the OECD’s PISA questions are a highly guarded secret, with only one level 6 sample question provided on the OECD site. However, we’ve scoured the internet and found a further three listed on various government pages. These are below.

If you think you have the answers please enter them in the comment box at the bottom of this page. We’ll add the correct responses tomorrow.

QUESTION A: HELEN THE CYCLIST

Pisa test question 1

 

 

Pisa test question 1a

 

ANSWER: 28

 

QUESTION B: A CARPENTER HAS SOME TIMBER….

Pisa level 6 2

ANSWER: “Design A, Yes; Design B, No; Design C, Yes; Design D, Yes.”

QUESTION C: THERE HAS BEEN A HUGE INCREASE IN ROBBERIES…

Pisa 6 3

Answer:  ‘The inappropriate cut in the y-axis indicates quite a large increase in the number of robberies, but the absolute difference between the number of robberies in 1998  and 1999 is far from dramatic.’ In percentage terms the increase was only around 2%.

QUESTION D: NUMBER CUBES

Pisa level 6 4

ANSWER: No, yes, yes, no.

Comments (74)

Comments
  1. A: 28

    B: Yes/No/Yes/Yes

    C: Not reasonable. It is only about 2% increase but the graph seems like a 100% increase due to adjusted y-axis.

    D: No/Yes/Yes/No

  2. 28 km/h

    A Yes
    B No
    C Yes
    D Yes

    No, increase only 8/508 or around 1.6% not huge

    I No
    II Yes
    III Yes
    IV No

  3. A: 28km/h

    B:a Yes
    b No
    c Yes
    d Yes

    C: No, only 1.4% increase

    D: I No
    II Yes
    III Yes
    IV No

  4. A: 28km/h
    B:Design A & D
    C: If only this graph is given: No, I do not consider the reporter’s interpretation of the graph to be reasonable. (no further explanation needed)
    D: Cube II and III

    MarctheMathMagician Reply
     
  5. 1) 28k.hr

    2) a-no, b-yes, c-no, d-yes

    3) NO. Robberies increased by 10 in one year on a abse of 505. That is a 2% increase probabaly less than the population growth. Certainly not an “huge” increase

    4) I-no, II-yes. III-yes, IV-no

  6. Question 1: the average speed is 28km/h
    Question 2: A C D
    question 3
    Question 4: II and III

  7. 28kmh
    b no, acd yes
    no
    nyyn

  8. A/ 28km/h
    B/ YNYY
    C/Not reasonable..
    D/NYYN

  9. 1) 28km/h
    2) ACD – Yes, B – No
    3) No. Only a (approx) 1.5% increase. (516-508)/508
    4) 2,3 follows rule.

  10. 2-3% get these questions right, no wonder we are doing so badly in these rankings. I blame the teachers.

  11. * 28 km/h trip speed average *assuming* that Susan turned around for home immediately upon her arrival at the river (7 km in 15 mins scales up by x4 to 28 km in 60 min).
    * YNYY (case B requires 20+24/sqrt(3) ~= 33.856m of timber assuming parallelogram has interior angles of 60 and 120 degrees, simple trigonometry) N.B. for (a) and (c) imagine breaking the polygon at the vertices and sliding the horizontal/vertical line elements outwards to the perimeter of the bounding box in which case it will identically resemble (d).
    * ~1.5% increase in 1Y is hardly huge. Unless it had been 507-509 robberies per year for each of the past twenty years in which case 516 is a several standard deviation event relative to the prior.
    * NYYN as (a) has a 6 and a 2 diametrically opposite, (d) has a 6 and a 4 diametrically opposite. □

  12. a)28 b) y,n,y,y c) no, small pct changed d) ii, iii, iv

  13. @AllCommenters – Last time I checked, you were all bankers/uni students and not 15 year olds. If you guys went to a target school, you can probably answer all these questions. Or if you work at a damn bank. There is the added advantage of the freaking answers being written in the post!

    PS: For some adult level math fun, check out Heard on the Street by Tim Crack

  14. The problem with education systems in Werstern democarices is that they are run by left wing socialists. They focus on trying to make the dumb kids average, instead of making average kids smarter, and they neglect the smart kids.

  15. You guys better check banking-guides.com, then you all would have answered correctly to such easy 0815 questions.

  16. I don’t see the relevance. Does efc cater to 15 yo kids? It seems I’m on the wrong website.
    @Desi: you’d think so, wouldn’t you? Although, from my limited experience in banks, I am beginning to think 15 year olds would do better.

  17. These questions are not difficult. I am amazed that they consider only a few % of people can answer these. I was doing more complex problems than these when I started Year 8.
    If the statement in the article above that states such a small amount of 15yr old can answer these, the future of our world really is in trouble.

  18. “The problem with education systems in Werstern democarices is that they are run by left wing socialists. They focus on trying to make the dumb kids average, instead of making average kids smarter, and they neglect the smart kids.” I could not have said it better!!!

  19. Stupidly simple questions. How can any young ‘mathematician’ fail these? Or is someone joking?

  20. Big news: the American and British schooling system fails at preparing its pupils in solving simple math problems.
    That’s just too sad.

  21. As “anonymous ” says, these are very simple questions which most 12 or 13 year old should be able to answer without any trouble – certainly when I went to school in the 1950’s’.

  22. So, if British younguns are duncing out on these types of problems, does that mean I’m a shoe-in for a British job? I’m willing to relocate, and learn some manners.

  23. Easy questions. Very basic junior high school mathematics. The problem is that nobody teaches that any more. It is not hard if you are taught how, but very difficult if nobody teaches you. Questions B & D are simply spatial arrangement tests – not mathematics at all. Question A is the only real mathematics question and Question C is an opinion based on the relativity between two numbers.

  24. I find it really hard to believe two points about the above story, i) that such a small percentage of students can answer these correctly and ii) that these are actually the hardest level of questions posed. If this really is where students are currently at then the world is in a whole lot of trouble. These questions are not simple all simple calculations that can be “typed” into a computer, you need to understand the entire question and be able to sort the relevant from irrelevant data which very few computers are going to be able to do for you.

  25. The headline for the article is misleading, ie the 15 yo students are not mathematicians, they are just studying maths as part of their curriculum. The questions are very easy, and the picture of Einstein set me up for disappointment. Unbelievable to me that only 2% or 3% of students got them right, assuming the above questions are representative of the degree of difficulty.

  26. Most of you have calculated the average speed for the trip, but didn’t calculate the speed to the river…, and speed back…(as per question) meaning the average speed to the river which was 26.6666km/hr, and 30km back, the average of these two legs were actually 28.33333km/hr… the second part of the question is 28km which most of you answered correct BUT INCORRECT!!! HAHAHAH

  27. Sorry Asian Nerd but you are wrong. The average speed is exactly 28 km/h. You cannot simply add the 2 speeds together and divide by 2 because she spent more time travelling at the slower speed. The correct solution is ((26.666 * 9) + (30 * 6)) / 2 This equates to (240+180)/2 which equals 28. Which is exactly the same answer that you get if you take the total distance travelled divided by the time taken.

    Using your logic, if I spend 59 minutes going 999 km/h and 1 minute going 1 km/h then my average speed is 500 km/h. I don’t think so.

  28. 7klm in 12 minutes = 35klm per hour

  29. 9mins = 4 kms
    1min = 4/9 Kms
    60mins = 4/9*60 = 26.666

    6mins = 3Kms
    1min = 3/6Kms
    60mins = 3/6*60 = 30

    average speed Km/h = (26.666+30)/2 = 28.333 Answer

  30. These questions are very easy if they were for 15 year olds. And the convoluted answers of some are a joke. For example, Problem A. If she rode 7 kms in 15 minutes, then times 7 by 4 to get 28 kph. It’s not rocket science. Obviously with Problem B, as B is not a right-angled figure, you know straight away that the two “hypotenuse” will be longer, and ergo, there’s not enough timber.

  31. A) Average speed = 28 km/Hr
    B) Yes, No, Yes, Yes
    C) No. The graph is a classic example of data manipulation or “statistical fraud”. The graph is correct, but the contraction of the y-axis leads to a misleading representation of the information. Graph axis contraction has legitimate uses; but not where statistical comparison is a key feature.
    D) No, Yes, Yes, No

    COMMENT: In answer to Kevin (25/1/14), ‘All socialists are by traditional definition “left wing” ‘. Some socialists are “extremely” left wing in their opinions. Others are more moderate.

    My observations during time spent in a Western University, in its Education faculty, were that the majority of the teaching staff were Marxist in their political orientation. This was reflected in their rhetoric, agenda, indoctrination of students during lectures and workshops and personal ideologies. Everything was politicised and made to suit their agendas.
    Nor is this any accident. It is a very deliberate process. It has the effect of real political manipulation and influence over the minds of a certain percentage of emerging young professionals. It has in view the gradual manipulation and control of society toward conformity to a set of ideas. This also is nothing new. Idealogues at least as far back as Plato, have sought to control the public psyche of nations to conform to their personal philosophies, opinions and agendas (See, “The Republic”, by Plato).
    I recall a federal politician in Austarlia labelling certain university lecturers as “Idealogues”. I would have say that this description is in my experience very apt, and accurate.
    Adieu

  32. Why are people giving answers the questions when the answers are below every question?

  33. @ Polymath. What has this got to do with the article? Are ideOlogues only left-wing? I had to re-read Kevin’s comments. What a load of nonsense that also has nothing to do with this article. Actually most universities in the west are run for the benefit of corporations, to provide them with a future supply of compliant employees. Extreme socialists are generally called Communists. “It has in view the gradual manipulation and control of society toward conformity to a set of ideas”, is one comment I agree with. I think this might be what motivated Ed Snowden to dob in the NSA to America’s “Allies”. Saw Chris Boyce interviewed last night, and he was motivated by the same beliefs. America is becoming a police state. Just look at how many “intelligence” agencies you have. I read today online, that 25% of Americans don’t know the Earth orbits the sun. Must be that Commie education system you have!!

  34. The problem with the education system is that the system used to centered around the male brain model (spartal memory). Now the education system is based on the female brain model which is better at remembering. Just because you can remember something does not mean that it is understood. I remember E=MC^2 but I do not fully understand it.
    And can be dangerous as memory is always relied on, not looking up the latest solution. To maximise human potential we need to educate the sexes differently. Which can be modeled on existing infrastructure. We as a people need to get away from the lazy thinking of one size fits all. It does not and never did.

  35. Einstein wasn’t a mathematician. He was a physicist.

    That’s a fairly basic mistake to make.

  36. Congratulations! you people have answered the questions when the answers are under the questions, good work, noobs

  37. I remember getting the dice question right when I was 7, but in any case this question focuses on logical thinking and not maths abilities (unless you consider the ability to simply count to seven as maths).

    The veggie patch and cycilist type of questions were regulars in my math class back in primary school, the teachers regularly threw these in to keep the kids entertained and interested, so they’re happy to dive into much more elaborate and difficult problems that take more time to figure out.

    The statistical question is just common sense though, anyone can solve that if they just take 20 sec to think it over…

    Note to self: send kids to weekend schools where they get challenged as they should.

  38. Everyone seems to be doing the maths the hard way. She rode a total of 15 km in 15 minutes, an average of 28 km/hr. It doesn’t matter if the second leg was a return trip or not, simply distance travelled divided by time taken.

  39. To those people asking why people were posting their answers, maybe you need to bursh up on your reading skills “If you think you have the answers please enter them in the comment box at the bottom of this page. We’ll add the correct responses tomorrow.”

    Given this article was originally posted on the 3rd December 2013 the answers have been up there for almost 3 months.

  40. Question A = 28kph

    Question B = a,c,d

    Question C = 508 divided by 516 = 0.985% (answer 2%) you all need a western style education!

    Question D no yes yes no

  41. Even a chimp could answer these absurdly simple puzzles.

  42. My maths is rusty but these are really easy questions that just require some common sense. Now that is probably what is lacking amongst the majority of the population.

  43. Black Magic: A Physicist is usually good and strong in Mathematics too!

  44. Fred: I resent your racist comment. Be educated, please!

  45. QA yes quizzes rely on “common sense” but also assumptions…in the technical sense if adequate is given to get the right answers or resolve there is no right answer…. maybe some kids cant answer because ‘they know too much” and the questions are dumb..!!

    QA.,
    Wouldn’t the accurate answer it be none? . If you cut the timber the cut displacement ( sawdust) will shorten the lengths of timber..? ( recall I gave the same answer in a school test and the teacher “belittled” me for my stupid answer.. lucky he never become a carpenter imagine the number of pieces of timber he would have cut “short one end”!!

    QB
    The bicycle journey… but did she stop on the way..? and was the stoppage deemed part of the “trip ” does the word “: trip ” imply to include stationary time?
    one internet searched “trip” definition..trip1 [trip] Show IPA
    noun
    1.
    a journey or voyage: to win a trip to Paris.
    2.
    a journey, voyage, or run made by a boat, train, bus, or the like, between two points: It’s a short trip from Baltimore to Philadelphia.
    3.
    round trip ( defs 1, 2 ) .
    4.
    a single journey or course of travel taken as part of one’s duty, work, etc.: his daily trip to the bank.
    5.
    a stumble; misstep.

    Another definition…you can go on a “trip” with Lsd…….. I wonder what the average speed is there..

    NO wonder im confused about the questions.. or am I just tripping ? lol

    QC.
    The robbery question I argue you need to see a graph for 1997 and 2010
    to be sure of a balanced answer.
    If 1997 robberies and the years before where the same as 1998 and after 2009 robberies were the same ………… then 1998 -1999 while the per cent vs numbers in crease is small…. but if the years before and after are the same numbers ……… I suggest its huge increase because all other years there was no movement or increase..!

    QD….Dices -ie which way are we folding the dices.. One way I come up up with an answer that no fold shows the dice opposite face as seven.. it come up blank every time on every opposite face!

    Man for detail.. Reply
     
  46. I think “top 2%” might be a USA perspective – these questions could probably be answered by the top 10-20% of maths students in any other developed country.

  47. These are terribly written questions!

    Question A) Speedometers don’t display the distance travelled, odometers do

    Question B) Shapes A, C & D have perimeters of 32m, however it is possible none of the designs can be built. Even if the 32m of timber is a single length, or the lengths happen to be sized such that their is little waste, some lenght will still be lost in the construction (eg. sawing, making joins).

    Question C) Is the increase from 508 to 516 (approx 1.6%) large? Why is the provided answer so poor:
    * It describes the cut as “inappropriate” without justification
    * It attributes the cut as “indicating” a large increase, when the cut itself does no such thing
    * It says that the absolute difference is “far from dramatic” it doesn’t actually state whether the reporter’s statement was reasonable as was asked, it just gives an alternative interpretation (which does not necessarily conflict with the reporter’s statement)

    Question D) Due to the lack of tabs, none of these templates can be cut, folded and glued as is to make a cube where the opposite faces sum to 7, assuming cutting along the perimeter only; without the unstated assumption that one only cuts out the perimeter, then all of the templates can produce cubes where opposite sides sum to 7, one only has to rearrange the faces…

  48. OK, I will admit to being conned by this article. The alluring headline immediately triggered my competitive response: I was excited to know I got all the questions right: and for a moment I assumed I was as clever as the top 2% of young mathematicians. On reflection I can see I ,and all other readers have been set up by a combination of a sensational headline, limited research, and flawed methodology.
    My positive vibes were pleasant while they lasted.

    Old School Conservative Reply
     
  49. Gee, I thought 15 year olds should be acing these questions. As for the timber garden border, making a hypothetical question out of it isn’t really necessary. On average every cut made there is a loss of between two and three millimetres so only the rectangle will come close. C will lose 40-60mm in cutting. But this adds a practical problem to an every day basic aspect of building which is carried out by 16 y/o apprentices. If children are becoming more obese and less adept to solving simple problems then what are they doing and why are my taxes involved?

  50. I Think the world would be better off if 15 year olds were taught something more relevant to modern day life.

  51. I think only the least intelligent 2% people will get them wrong

  52. There’s a MUCH easier way to calculate the speed she’s doing.
    Total of 7km over 15 minutes. 15 x 4 = 60 minutes, which is an hour.
    Therefore:
    7km x 4 = 28km over the hour.

  53. anonymous said, “Most universities in the west are run for the benefit of corporations, to provide them with a future supply of compliant employees.”

    That is a blatant lie. Most universities in the West are run by governments and are packed to the rafters with communist lecturers. It’s been like that for many decades. It began during the Cold War, when the Soviet Union infiltrated Western universities, wharves, unions, newspapers and Hollywood with communist agents. Those agents were bankrolled by Russia to promote the communist cause, expand and recruit more communists. They did an excellent job. Today most unions, schools, Hollywood directors, and wharves are infested with communists.

  54. These simple questions can be answered by any clear thinking individual. They barely require any education.

  55. Asian Nerd is actually very incorrect. He simply averaged the speeds of a longer and a shorter route without considering that the cyclist had lower speed for longer (over a longer distance).

    The first trip was done in 0.15 hour, the second trip in 0.1 hour. The total of 7 kilometres took 0.25 hours. the speed is calculated: 7 divided y 0.25 equals 28 km per hour.

  56. Qa. 28.35km

    Qb. a.yes b.no c.yes d.yes

    Qc. 1.57%

    Qd. I. no II.yes III.yes IV.no

  57. T x D = S S x D =T S x T= D which ever way you put it the answer for D, T, or S will be the same

  58. Answers: A) 28 km/h
    B) Design A: yes Design B: yes Design C: yes Design D: yes
    C) No there was not a huge increase (only 8 robberies up 516 – 508 = 8)
    D) shape 1 yes shape II yes Shape III yes Shape IV yes

  59. These are tests of simple thinking not mathematics. These are skills that are hard to teach if they can be taught at all. What it shows is that society does not value or encourage thinking. The bigger question is “WHY does society not value thinking”? This is where conspiracy theories could abound. ( For example it is the football hero or the cheerleader that is respected at school not the nerd, The filmstar or wealthy tycoon, not the engineer and so on )

  60. thank you aussie educational system, for all your misgivings you taught us well! these questions suck

  61. There is an error in the image of the two die in question 28. In one the numbers 1,2 and 3 are clockwise around a corner and in the other it is in the opposite dirction. This means that one dice is the mirror image of the other, provided they follow the rule that the opposite sides always add to seven.

  62. The questions are not difficult, however, from some of the answers and comments given a result of 2%-3% might be about right !!

    I like the comment about the two dice – very perceptive. I wonder how Einstein would have worded these questions to weed out the sawdust, the mathematicians, the socialists, the communists and all those trips.

  63. are u sure only top 2% of young mathematicians can answer this
    because they are simple.

  64. this is quite amazing in that it took no more than 30 seconds to answer and I am a little preoccupied. When I was seven, I calculated the maximum population possible on planet earth, using the following assumptions; a family of four , two parents and two children; (zero population growth) can survive on one acre ,approx 2440metres squared, and using the three field system, dating back to the middle ages; in which that 1 acre is divided into four equal segments, and 1 of those segments is left fallow; that is planted with beans, a nitrogen fixer and not consumed by man nor beast, and that the total arable land ( that land that is available to plant crops that yield enough food to support those four occupants- still zero population growth) equated to 100 billion people. I understand the total arable acres has significantly decreased since 1975, maybe those kids can re-calculate the modern equivalent using the same assumptions; all the best for humans, with love from martin

  65. Dude, I am in grade 9 and this is very easy, even a student in grade 6 in hong kong can do it correctly

  66. I was no good at arithmetic, but got all the answers – so easy! Unimaginable that only 2-3% of 15 yr olds got it right?! Probably because of the Western feminist post-modern curiculum which does not require maths as compulsory – and where 2+2 now equals anything you want to create it to be – after all, your own cognitive perception and subjective feelings are what matter, there being no objective truth anymore.

  67. The students have been encourged to think outside the box for a long time. Since these questions are inside the box, it is not surprising that most of them could not answer them properly. Well they might have given answers, which were out the box and therefore should be correct if not judged in a conventional inside-the-box way.

  68. wow I spent a really long time on problem A. I know mathematically its a damn simple question, but I just couldn’t work it out. It took me ages and ages. First cab off the rank, I knew the formula for speed was distance multiplied by time. But it was asking for the speed in kilometers per hour. Yeah ok, no problem, I’m good with that. I then couldn’t work out how many hours 9 minutes are. Finally cam to the conclusion, 9 minutes is 60 minutes divided by 9 hours. So it was 60/9 times 4 (kilometers). Which gives you 26.66666 reccuring (how do you put the dot above the six?) kilometers per hour. Hurrah! I’m getting somewhere. Next equation. 60 minutes divided by 9 minutes times 3 kilometers. And that equals 30 kilometers per hour. Now the average speed. 26.6 reccuring kph plus 30 kph divided by two equals 28.3333 reccuring kilometers per hour! Hurrayyy! I worked it out.

    And jiminy cricket! I think I ran out of the coal that was powering the “furnace” that is my brain while trying to solve this problem. But anyhoo I had a lot of fun doing it. Frustrating at times, sure. But hey. Like I said at he start of my report, its a pretty darn simple mathematical equation (at least, for someone who can do maths).

    Ok, so for the other questions I got:
    Q2: a) yes b) couldn’t really prove it. Don’t know the formula for calculating areas of (are they paralelagrams?) the logical part of me wanted to say no c) yes d) yes

    Q3) I said no, unless you count an increase from 508 to 515 as huge.

    Q4) was quite literally a piece of cake (chocolate mud cake) I got;
    a) no
    b) yes
    c) yes
    d) no

    Anyway so those are my results. Call me an idiot if you want, I don’t care :-)

  69. daniel, reading your solution to the first one – no. Same mistake as Asian Nerd above, explained by Fred:

    “The average speed is exactly 28 km/h. You cannot simply add the 2 speeds together and divide by 2 because she spent more time travelling at the slower speed. The correct solution is ((26.666 * 9) + (30 * 6)) / 2 This equates to (240+180)/2 which equals 28. Which is exactly the same answer that you get if you take the total distance travelled divided by the time taken.

    Using your logic, if I spend 59 minutes going 999 km/h and 1 minute going 1 km/h then my average speed is 500 km/h. I don’t think so.”

  70. I have seen some people having a hard time on understand the questions , so I would like to share my insight on the question (but it might not be right , it’s just how I view it)

    QA) Average speed for “trip to the river” and “back” , so just add up the time of and km =)

    QB) Actually , I don’t really understand the mathematical part of this question , but the design B is a rhombus , so the actual width is not given (might be possible , might not be , i guess) =)

    QD) There is something wrong with the drawing of the two dices , if you observe carefully , you will notice that either dice has the wrong faces.

    luciusinspiration Reply
     
  71. It is amazing, how if there is anything not on cue with our school kids or more to the point our teenager population, we blame the teachers. So, ‘NotAmused’ I’m afraid you’re not quite correct, the amount of energy, hours and dedication that teachers put into attempting to educate the children of today can be said as unsurpassed by most other occupations. Remember the old adage about “it takes a community to raise a child”, it couldn’t be more true in this case. Parents, teachers, congregation and other community members are all responsible to raising a well disciplined and focused child. If people have to rely on teachers to do all the work then perhaps they shouldn’t have children. We as parents are as much responsible as anyone else. Now with that aside, the public should be aware the teachers are governed by the education authorities of each state. The education departments are forever implementing new strategies to engage the students based on the latest research, however if you think about it, although there is more to learn in terms of technology, the basics haven’t changed so why should the teaching strategies? As an engineer, one of the first things that we were ever taught was “if it’s not broken don’t try to fix it,” and I’m sure any clear minded individual could align that with the so called advances in pedagogical strategies.

    Conspiring Cynic Reply
     
  72. I am a 15 year old. From Australia. And I could answer all of those questions, most of them correct….and I’m not even considered to be a really mathsy person.

  73. To the many posting answers here and to those quibbling about the qurestions: You are both math failures and annoying morons. Deal with it.

  74. I’m 16, and I answered all those questions fine. I can see why people may have to think but they are not that hard.

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