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How to solve a Raven's IQ test
#1

How to solve a Raven's IQ test

PART ONE

The next few posts in this thread are going to be how to approach a Raven's progressive matrix test, a test to measure IQ. As I mentioned in another post, I believe that with most of these tests you can work out the solution if you are able to identify the underlying rules.

I've had to divide the entire write-up into separate parts because the forum does not allow more than 8 attachments per post, so I wasn't able to squeeze all the examples into a single post.

It won't necessarily make you a genius overnight but hopefully after reading this you may have a better idea of how to approach a Raven's test and get a higher IQ score than you would have ordinarily gotten.

If you have no idea what a Raven's test is, go to http://www.iqtest.dk/main.swf and have a look.

For an alternative method to solve Raven's tests, you can go to http://www.jperla.com/blog/post/how-to-ace-an-iq-test, which also has all the answers for the test at the link above.

(What you can also do is just buy the Raven's test books and memorise the answers, if you have $1000 US lying around to buy all the different versions.)

There are 2 reasons why you'd want to do well on a Raven's test:
1) Your potential employer may decide to make you write it as a pre-employment test
2) You may want to get into Mensa or a similar high IQ society for networking purposes. For example, if you are moving from city to city, Mensa can arrange a welcoming at your destination so that at least you know someone in your new city. (WARNING: not all Mensa branches use the Raven test.)

Here's a tip: Always claim to be suffering from the flu when writing a Raven's test. Sickness has been shown to drop your score by a few points on these tests and your examiners may decide to add a few points rather than retesting you when you are 'well.'

So how does a Raven's test look like? Basically it's a 3 x 3 sequence of blocks:

|_|_|_|
|_|_|_|
|_|_|_|

And in these blocks are patterns and shapes and things, and the lower right block is left blank. Based on your assessment of the shapes and patterns, you have to guess what the image will be in the lower right block, based on logical rules you deduce by checking out the other blocks.

To make discussion easier, I'm going to assign a letter to each block, like so:

|A|B|C|
|D|E|F|
|G|H|I|

To deduce the missing pattern (block I) you will have to figure out the underlying logic of the pictures. Generally, a specific logic rule runs in the rows or columns.

So a specific rule may apply to ABC and then DEF (the rows), you then apply the same rule to figure out sequence GHI.

Or the rule may apply to columns, so a rule will exist in ADG and BEH, which you then have to extrapolate to CFI.

The easier puzzles will usually have rules that apply both to columns and rows, so you can choose to look at either to solve the puzzle. Harder puzzles however will either use only rows or only columns, and it will be up to you to quickly decide which one has applicable rules of logic.

On some harder puzzles, crossway rules will apply. CEG will follow a rule that you have to then extrapolate to AEI.

So how do you discover the underlying logic in the puzzle? Actually, Raven's tests use only a few puzzle elements and if you approach the test methodically by checking for each potential puzzle element, you should be able to solve the problem without too much thought going into it.

These are the questions you need to ask to identify the puzzle elements:
1) What are the large shapes involved?
2) What are the small shapes involved?
3) What are the symbols involved?
4) What are the lines doing?
5) What are the colours doing?
6) What are the dots doing?
7) In 3x3 within 3x3 problems: Check if the answers lies in the fact that the columns in each 3 x 3 successive matrix shift one column to the right, and in doing so, the shapes change each time according to a logical rule?
8) Can you stack the boxes on each other?
9) Is there a numerical sequence?

Now let's go through each of these questions in detail one by one. I will use various examples that I culled from the net, but especially the online version at: http://www.iqtest.dk/main.swf While this online version is not actually from the Raven test book, it will give you enough of an idea when faced with the real thing, since many of the online puzzles at that website are just remixed Raven's tests anyway.

What are the large shapes involved?

In general, the third row must always contain the same large shapes as rows 1 and 2, in the same proportion. For easier tests, this usually applies to columns also. For harder tests, it may only apply to rows or only to columns.

Let's start off with a very basic puzzle. Look at this example:
[Image: attachment.jpg13427]   
This one is easy. ABC and DEF both have 3 circles. Therefore GHI must also have 3 circles. Therefore I must be a circle in order to complete the sequence.

Note that ADG and BEH also have 3 circles each. Therefore CFI must also have 3 circles, so I needs to be a circle.

Look at the next one. For now, please ignore the lines, and just look at the circles:
[Image: attachment.jpg13428]   
Ignoring the lines, we still know that in I there has to be a circle, for the same reason as the previous example: if the first two rows have 3 circles, then I has to be a circle to follow the rule.

Next example. Ignore the lines and the small circle. Just look at the large shapes (the triangles):
[Image: attachment.jpg13429]   
Both ABC and DEF have two triangles pointing up and one down. Note that the same rule applies for ADG and BEH. In order for GHI and CFI to match the other two, then I must be a triangle pointing down in order not to break the pattern.

The last example. Ignore the lines and focus just on the shapes for now:
[Image: attachment.jpg13430]   
You'll see that the top two rows and left two columns both contain one square, one triangle and one diamond each. Therefore I must be a square in order not to break the sequence.

My approach to these Raven's test is to always first look at the big shapes (ignoring other elements) and first work out what big shape needs to go into I.

Once the large shape is identified (or if there are no large shapes to work with), the next question to ask is:

What are the small shapes involved?

Much as for large shapes: in general, the third row must always contain the same small shapes as rows 1 and 2, in the same proportion. For easier tests, this usually applies to columns also. For harder tests, it may only apply to rows or only to columns.

Have a look at this example:
[Image: attachment.jpg13499]   
We have a sequence of large shapes with smaller shapes within them. The first rule as taught about is to ask 'What are the large shapes involved?' and to figure which large shape will be in I (in this example it will be the square). The next question is 'What are the small shapes involved?' Looking at ABC and DEF, we get a small dark square and a small dark circle in each row. The columns ADG and BEH follow the same pattern. So in order to continue the sequence, GHI and CFI should both only have one small dark circle and one small dark square. However, these conditions are already satisfied, so actually no small shape is required in I. So the final shape in I is simply a large square with nothing in it.

Let's go back to the triangle example from above (we can ignore the lines for now):
[Image: attachment.jpg13429]   
We already know that in I we should have an upside down large triangle. But should it have a circle in it? Looking at the rows, we see each row has only one circle; furthermore each column also has only one circle. Putting a circle in I would violate this rule of only one circle so there are no small shapes in I, so no small shape is required in I.

As you can see, for large shapes and small shapes the rules tend to be quiet logical.

Now we start moving on to trickier territory:
What are the symbols involved?

Various symbols may be present, like multipliers, plusses, minuses, division symbols, etc.

Their behaviour can be odd, sometimes they act as ‘rules’, altering the behaviour of things around them

Here's an easy enough example to start off with:
[Image: attachment.jpg13545]   
First we can work out that the large shape is a square. Note that the rows and columns are operating with different rules for large shapes. The rows are operating on a 'one-of-each' principle while the columns are 'three-of-a-kind' for large shapes. There are no small shapes, so we can skip that question. The symbols consist of a diamond, a star, and a plus-sign, and follow the inverse rule to the large shapes : the rows are three-of-a-kind, and the columns are one-of-each. In I we get a square with a plus-sign inside of it.

Now let's go on to a puzzle where the symbols start developing weird rules of their own:
[Image: attachment.jpg13566]   
There are shapes here, but they at first seem to be doing their own thing. But actually they are being transformed by the symbols. Symbols often have rules which you have to dissect. Consider ADG. The large square suddenly becomes a smaller square. It appears that a plus-sign causes a shape to decrease in size - in other words, ADG can be read as 'Large square in A is diminished in size by the symbol in D, causing a small square to result in G.'

BEH does not have a plus-sign though, it has a diagonal line. Rather than having an effect on size, it appears to have an effect on orientation, causing objects to revolve by 45 degrees. So BEH can be read as 'S-shaped line in B is forced to revolve by diagonal line in E, resulting in an s-shape that has been nudged 45 degrees in H'. Consider also DEF as 'Plus sign in D is forced to revolve by diagonal line in E, resulting in a plus sign that has been nudged 45 degrees in F'.

Look at ABC, the s-line appears to transform shapes without changing shapes or orientation i.e 'The square in A becomes transformed by the s-shape line in B, resulting in a clover shape in C.'

So let's solve for I now. Based on the observations above, we know that: 1) the plus sign causes the top shape to diminish into a smaller bottom
shape 2) the s-shaped lines cause the shape on the left to transform into something different on the right hand side. 3) diagonal lines change orientation

Following the rules and looking at CFI, the large clover needs to be come diminished into a smaller clover in I; likewise looking at GHI, the small square needs to be transformed into a small clover in I; however both the plus sign in F is skew, and now has diagonal lines, so we can assume the small clover changes in orientation. This gives our answer as a small clover with a slight orientation change i.e. answer 'e'

Once you've sorted out the large shapes, small shapes and symbols, the next question to ask is:
"What are the lines doing?"

TO BE CONTINUED.

Circumstances permitting, I'll try to post Part 2 and Part 3 within the next few days.
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#2

How to solve a Raven's IQ test

Very good. But will this get me laid?
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#3

How to solve a Raven's IQ test

I thought the entire purpose of this test was to measure your ability to figure out these patterns on the fly, ie: your intelligence. Going in with advanced knowledge like this will defeat the entire purpose of the test and give you an inaccurate score.

What is the purpose of gaming an IQ test? To get into Mensa? What's the point?
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#4

How to solve a Raven's IQ test

Yeah, I see no point in studying to an IQ test if the results aren't going to actually represent you IQ.
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#5

How to solve a Raven's IQ test

Mensa game?

Vice-Captain - #TeamWaitAndSee
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#6

How to solve a Raven's IQ test

For the people who've replied to this post:
Some jobs require you to get an IQ test, and the Raven's test is popular. So this might help people who want to get an edge for the interview process.

Otherwise, Mensa does have an international networking wing, and since any network is better than no network, there's no reason not to include it in your networking arsenal if you can get into it. You only need to pass the IQ test once, and even if your membership in Mensa expires you can ask them to check your old records whenever you feel like renewing it.

I doubt that this guide will be useful except for a small minority, but for what it's worth, here it is. Maybe one or two people will find it useful.

Anyway, on to PART TWO:
What do the lines do?
Lines typically delete or add on to one another. Sometimes a line or a part of it will rotate.

Here's a good example of deletion:
[Image: attachment.jpg13659]   
Much like in the above examples from symbols, the blocks in the above sequence work almost like an equation. For ABC, all the lines in A and B which are held in common will be deleted, leaving only the leftover lines to form C. The same rules hold for DEF, ADG, BEH. Therefore both CFI and GHI yield the same result - a short diagonal line in the left hand corner.

In the next puzzle, the lines do something else:
[Image: attachment.jpg13660]   
The lines are rotating, one small segment at a time. First in A, the lower right hand line segment rotates 90 degrees. This forms a new picture which is presented in B. Then the upper left hand segment (i.e. the segment directly opposite) in B rotates 90 degrees to form the picture in C.
Exactly the same rule applies to DEF.

The columns follow a similar rule, except it involves first the lower left segment, then moves on to the opposite line in the upper right segment.

You can solve for I either by looking at the rows or columns, but in either case the answer is the same: it will be 'e.'

So in summary, lines can be used in a number of ways, but for most of the time in Raven's tests they are deleting one another. Often this deletion will work almost like a formula eg (lines in A) - (lines in B) = C
If the lines are not deleting, then most of the time some segment of line is rotating.

Having figured out what the lines are doing, the next step is to ask:
What are the colours doing?

Colours can expand, shrink, or move, or otherwise change according to a logical rule.

Have a look at this example:
[Image: attachment.jpg13661]   
For rows ABC and DEF, a new colour is added to the sequences in a clockwise directions.

For the columns a different rule applies. In ADG and BEH, the colours move in a clockwise direction one segment at a time.

Colours are generally not too much of a challenge in Raven's tests, they are usually added merely to add complexity or as a red herring (an example of colour as a red herring will be shown below). Sometimes colours do follow bizarre rules, but they usually expand/shrink/move, so just decide which one is the most applicable and take it from there.

The next question is:
What are the dots doing?

Dots are the most likely element in Raven's tests to have peculiar random placements in order to confuse the puzzle solver, although there is usually some logic to their movements. However, if you cannot find any underlying logic in their movements, try assuming that the placement is random and see if there is any other logical element behind the dots.

Have a look at this one:
[Image: attachment.jpg13662]   
Looking at the large shapes first (and ignoring the dots), it's clear that we have to have a triangle in I. As for the dots, in ABC we have: an inner dark dot, an inner white dot, and an outer white dot. Same for DEF. The columns follow the same rule. Not that the positioning of the dots is otherwise random and does not follow any logical rule. Since we already have two white dots in GHI and CFI, I must have an inner black dot. The answer for this puzzle will therefore be any triangle with a dark dot in it, therefore it will be 'b'

The next example is a bit more complicated, but shows that dot movement isn't necessarily random:
[Image: attachment.jpg13663]   
Basically the two circles move one square to the right in the next box. If they are at the end of the row, that circle will instead move on to the first square of the next row. After entering a black area, the circles change colour: a white circle will become black, and a black circle will become white. Following the movements with the circles, we find that the answer will end up as 'h'

Follow the above steps, look at each puzzle aspect in isolation and you should be able to solve most Raven problems - most Raven problems are really just combinations of simpler puzzles but you have to be able to look at the individual elements in isolation to see this.

However, there is a particularly brutal class of Raven problem consisting of 3x3 grids within the 3x3 grid, which deserves some discussion in and on its own:
The grids-within-a-grid puzzle

TO BE CONTINUED IN PART THREE
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#7

How to solve a Raven's IQ test

Damn very nice breakdown and explanations TTR. Always good for a man to expand his knowledge/way of thinking. Much appreciated
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#8

How to solve a Raven's IQ test

Great breakdown - when I finish reading and if everything checks out, I'll be glad to rep you. Did you write this all yourself?

Would be very helpful if you have to take IQ tests in the future, if they resemble this at all.
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#9

How to solve a Raven's IQ test

Oh. OOOOHHHH....

Okay. I, uh, I was thinking...

You know...

Ravens.

[Image: Ray-Lewis.jpg]
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#10

How to solve a Raven's IQ test

PART THREE

The grids-within-a-grid puzzle

The problem with these grids-in-a-grid puzzles is that they are often so complex that there can logically be multiple correct answers, and which is the actual correct answer is really up to the whimsy of the tester. This is the point where a Raven's test can become less a measure of intelligence of the test-taker and more of a measure of the tester's predisposition.

I still struggle with these, but based on the few examples I could find on the net, here is a potential rule to try out:
Check if the answers lies in the fact that the columns in each 3 x 3 successive matrix shift one column to the right, and in doing so, the shapes change each time according to a logical rule.

Look at this one:
[Image: attachment.jpg13732]   
Look at A. See that leftmost column that forms cross-triangle-cross? This column shifts one column to the right in B, and also changes shapes to circle-cross-circle, and then shifts columns once more in C and becomes triangle-circle-triangle. If you look at the other columns in all the rows, you'll see that all the columns shift space and change shape in this similar manner, with cross always becoming a circle, a triangle always becoming a cross, and a circle always becoming a triangle. This makes it suddenly easy to find I, which must be 'b', because that is the only option that will allow H to shift columns/change shapes without violating the rule set.

Now have a look at this one:
[Image: attachment.jpg13733]   
In this one the columns shift to the left, rather than to the right, but they also change symbols according to specific rules. For example, the right most column in A shifts to the left in B, with clubs changing to hearts, and hearts to diamonds.

Another thing to check for, if you can't figure out the answer to the puzzle, is to check for this rare puzzle:
Can you stack the boxes on each other?

Have a look here:
[Image: attachment.jpg13734]   
Basically, ABC can be put next to each other to make continuously running lines. DEF can be stacked on top of one another to make continuous lines. Then GHI goes back to having lines next to each other. Note that there is no logical rule for the columns, this is a rows only puzzle.

The last question to ask is:
Is there a numerical sequence?

Some puzzle just follow a 1-2-3 sequence. If you are struggling to see any sequence upon asking the earlier questions, quickly check whether you are not confusing yourself where a simple 1-2-3 relationship exists.
An example:
[Image: attachment.jpg13737]   

Now let's go through a few examples of what I consider to be 'layered' puzzles, where multiple puzzle elements are combined in a way intentionally meant to confuse the puzzle solver.

Example 1:
[Image: attachment.jpg13735]   
So this is a combination of a large shapes test with a lines test, but the trick here is that the side of the shape is used as a line. Each row/column has to have a partial line, a blank line, and a full line. To complete the sequence we need to use answer 'h'

Example 2:
[Image: attachment.jpg13736]   
This actually consists of 2 seperate line puzzles. The inside lines (touching the dot) and the outer lines are two separate components to consider. Inner lines will delete whatever line is held in common, whereas outer lines will only preserve whatever line is held in common.

So for the inner lines: lines in A + lines in B = lines in C, but removing the lines that are held in common.

For the outer lines: lines in C = lines held in common by A and B

Following the same rules for GHI, the answer will be '2'

That's it for my tutorial on how to tackle a Raven's progressive matrix. The key to solving them successfully is to understand all the different tools that Raven used to build the puzzles in the first place, and to dissect the puzzle into it's most basic elements. Practicing the test at http://www.iqtest.dk/main.swf will help you get used to going through the steps.

By understanding how the puzzles are put together and through a bit of practice, I suspect that anyone could do much better than they ordinarily would have done on this particular IQ test.
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#11

How to solve a Raven's IQ test

[url=http://kryten.mm.rpi.edu/COURSES/LOGAIS02/carpenter.pdf]

Five rules can solve all the problems.

1) Constant (e.g., a square in each figure).

2) Quantitative progression (e.g., shapes getting progressively larger).

3) Figure addition or subtraction.

4) Distribution of three values (e.g., square, circle, triangle in each row).

5) Distribution of two values (e.g., square, circle, and blank in each row).
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#12

How to solve a Raven's IQ test

Quote: (08-03-2013 06:09 AM)bachelor tax Wrote:  

I thought the entire purpose of this test was to measure your ability to figure out these patterns on the fly, ie: your intelligence. Going in with advanced knowledge like this will defeat the entire purpose of the test and give you an inaccurate score.

What is the purpose of gaming an IQ test? To get into Mensa? What's the point?
There is a learning curve in basically every activity, so also in doing an IQ test.

You can improve your 'IQ', depending on your capabilities. The brain learns to identify certain patterns and according to these tests this results in a higher 'IQ'.

It's not cheating. It's improving the capabilities of your brain. That's why you shouldn't trust IQ statistics, because you can't compare an Asian guy who studies 12 hours a day with a guy who never went to school. Of course the Asian guy will score better, because he trained his brain.
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#13

How to solve a Raven's IQ test

You could definitely study for this tests...

But a person smart enough to care about IQ scores is able to figure all this rules on the fly in a matter of seconds, while doing the test. So whether you studied or not doesn't make a difference.

I loved doing this kind of tests as a kid, they are a fun puzzle. I convinced my parents to do them 4 times over a period of 10 years.

My scores didn't change over time because I figured these rules during my first test, so there was nothing new to "train" or "learn".

You recognize the patterns the first time, so it already influences the result of your first test.
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#14

How to solve a Raven's IQ test

Quote: (08-07-2013 09:10 AM)Thomas the Rhymer Wrote:  

The problem with these grids-in-a-grid puzzles is that they are often so complex that there can logically be multiple correct answers, and which is the actual correct answer is really up to the whimsy of the tester. This is the point where a Raven's test can become less a measure of intelligence of the test-taker and more of a measure of the tester's predisposition.

This is why I've never liked the Raven IQ Test. It has less to do with finding patterns, than with reading someone else's mind; it's cryptography, not intelligence, and while the former requires the latter, the latter doesn't guarantee an equivalent score in the former.

Quite frankly, stuff like this turns me off. Part of me winds up suspecting that I'm just spinning my wheels, that there is no correct answer and someone's laughing at me for falling for their gag.

It reminds me of a "riddle" I read in a Mensa handbook that was sitting around the army base, back in the day. It was something like: "Susan has all of these seemingly improbable qualities. How is this possible?" After spending half an hour puzzling on it, I gave up and read the answer in the back.

Turns out that Susan was a ghost.

OH WELL DOUBLE DUMB-ASS ON ME! I DIDN'T KNOW WE WERE PULLING THE SUPERNATURAL INTO THIS VERBAL LOGIC GAME!

With other riddles I'd figure out the "correct" answer almost immediately, only to dismiss it as being stupid, and keep searching for something that 'clicked' in a witty and meaningful manner. Take that question where the shapes transform as they move horizontally, from triangle to X to O - I might very well notice that pattern, but dismiss it, because the rule "X on line 1, X on line 2, O on line 3" is a stupid, obtuse rule. It's the sort of thing you'd only put there to mess with people. Chances are, I'm going to keep searching idea space for something that's far more elegant and explanatory - thus wasting my time, and even if I do find a pattern, it winds up being considered "incorrect".

I've done professional IQ testing, and I'm thankful to say it didn't involve any of this duplicitous, cryptographic Raven nonsense. In fact, I'd even go so far as to say that it shows preference for people who are clever at figuring out puzzles, over people who possess a wide-ranging intelligence.

By the way, great write up! If this ever comes up, I'm sure you've helped me bump my score by 15 points. I never realized that the answers were this stupid.
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#15

How to solve a Raven's IQ test

Quote: (08-03-2013 06:09 AM)bachelor tax Wrote:  

I thought the entire purpose of this test was to measure your ability to figure out these patterns on the fly, ie: your intelligence. Going in with advanced knowledge like this will defeat the entire purpose of the test and give you an inaccurate score.

What is the purpose of gaming an IQ test? To get into Mensa? What's the point?

These tests are popular with potential employers. For example, Proctor and Gamble makes applicants take a test that heavily features these questions.
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#16

How to solve a Raven's IQ test

Are there any IQ tests based on philosophy or which heavily incorporate philosophy?

The mathematics & patter recognition tests make sense.
Yet there is more to life than just mathematics & pattern recognition.
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#17

How to solve a Raven's IQ test

I took this test a few months ago (without prepping). I got 132. I took a different test over a decade ago and had a similar score.
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#18

How to solve a Raven's IQ test

Quote: (10-29-2017 04:07 PM)Easy_C Wrote:  

These tests are popular with potential employers. For example, Proctor and Gamble makes applicants take a test that heavily features these questions.

This depends on where you are in the world. In the US, employers tend to avoid this type of test, since group differences in native intelligence can lead to claims of discrimination = legal trouble.
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#19

How to solve a Raven's IQ test

Quote: (10-29-2017 09:14 PM)CynicalContrarian Wrote:  

Are there any IQ tests based on philosophy or which heavily incorporate philosophy?

The mathematics & patter recognition tests make sense.
Yet there is more to life than just mathematics & pattern recognition.

Check out the LSAT.
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#20

How to solve a Raven's IQ test

Quote: (10-29-2017 04:07 PM)Easy_C Wrote:  

Quote: (08-03-2013 06:09 AM)bachelor tax Wrote:  

I thought the entire purpose of this test was to measure your ability to figure out these patterns on the fly, ie: your intelligence. Going in with advanced knowledge like this will defeat the entire purpose of the test and give you an inaccurate score.

What is the purpose of gaming an IQ test? To get into Mensa? What's the point?

These tests are popular with potential employers. For example, Proctor and Gamble makes applicants take a test that heavily features these questions.

Now what's really going to bake your noodle is this.

Most likely to get one of these cubicle drone jobs you will have to have first spent about three or more years of your life at a Suburban Indoctrination Centre learning all manner of theoretical stuff that they promised you would set you up for a career in the job that you're currently applying for.

To get into said Suburban Indoctrination Centre, you had to be presumably more intelligent and responsive to unknown scenarios than a lot of knuckle-draggers and assorted others at one, if not several, different tests, the results of which were all recorded.

And then during the course of those three years, you were subjected to dozens more similar such tests, and they are even kind enough to tell you (unlike an employer) how you actually did on those tests. They even put you in an alphabetic range, A through F. You know this, because you provided the results of those tests in your application for this job.

Your prospective job employer, by administering this test, is basically saying: the entirety of your educational record, from kindergarten through to graduation, is so open to rigging, gaming, and outright fraud by students, teachers, universities, and, finally, governments that we cannot tell anything meaningful about your intelligence from your grades. We have to resort to stupid, once-off, death-or-glory intelligence tests, and, when that fails, to sexism or racism to try and figure out whether you'll actually be able to do this job or not.

It's the sort of insight to make a normal person look back at their lost sixteen years of studying bullshit, look forward at their decades of student debt repayments, and decide to start mounting barricades, waving flags, and burning down government buildings.

Fortunately, because we were brought up by the dumbest generation of narcissists in history, none of this will actually happen.

Remissas, discite, vivet.
God save us from people who mean well. -storm
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