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Unfair Mensa test

In July of 1991 I applied to join Mensa, which is the organization whose only entrance requirement is a few bucks (oh, and an IQ in the top 2% of the population).  If you've wandered around other parts of this site (accessible by clicking any of the links above) you will not be surprised to learn that based on my preliminary test score I was rejected.

To quote from their rejection letter, dated November 15, 1991,

Dear [me]:

Your unsupervised practice test has been scored, with the following results:

Cattell A                I.Q. 135         Percentile 93

These results should be looked on as an indication and not an exact number, as most experts in testing feel that a home test is not as reliable as one given under standardized, supervised conditions.  However, on the basis of of this preliminary test score, we do not recommend that you take the supervised test.
. . .
S/Simi Turchin
Testing and Admissions Dept


My problem is that I think the test was unfair, and if I had gotten every one right that I was wrongly scored wrong on, maybe I'd be a genius after all, and maybe you would too if you'd tried.  In the form of an edited letter I wrote on October 26, 1991, here's why I think that, and I want you tell me where I went wrong.


Dear Sir or Madam:

. . . Anyway, here are my specific complaints about The Cattell Intelligence Tests, Second Edition, Revised, Group and Individual, Scale III: Form A, with a date of 6/90 in the lower left-hand corner of the first page (copyright 1966, 1974 Mensa).

     The test is written by a Britisher, presumably for a British-speaking readership, yet I am a purebred American, which I do not think should count against me.  Certainly in your Synonyms and Opposites tests, and arguably in your Analogies test and others as well, the sometimes not-too-subtle differences between British English and American English can become significant, and since these tests specifically focus on vocabulary, you risk counting some of my answers wrong that might otherwise be right (and vice versa!).

     The instructions you provided are both imprecise and, in some cases, contradictory.   For example,


INSTRUCTIONS.  Look at these five words:

Dog,  elephant,  sparrow,  cow,   lion

They are all names of animals except 'sparrow,' so 'sparrow' is underlined.  In the test you must underline in each row the word or phrase that does not belong to the same class as the other four -- that is, pick out the word or phrase most unlike the others in meaning and underline it.

in the sample answer on page 3 you plainly imply that sparrows are not animals.  Needless to say, sparrows are indeed animals.  They aren't mammals, if that's what you're thinking, but they certainly are animals, just as sharks and toads and rattlesnakes and gnats are.  What are we candidates to think when it appears that the test writer is ignorant of such basic facts as that a sparrow is an animal?

[Update of June 1, 2012: A correspondent points out that another reasonable answer is that unlike the other four, the word cow (c.f. bull) usually means the female of the species, whether it be kine or elephants or whales or moose.]

As another example, the instructions for Test 6 (Inferences) specifically state as follows:

"Below each of [the problems] will be found four or five words, sentences, or numbers which make answers to the problems concerned."

Yet problem #7 and problem #12 both contain not four or five but six possible answers.   Now I would agree that this error should not discombafulobefudulate a candidate with any reasonable expectation of achieving Mensa-hood, but it still strikes me as a questionable sort of thing to run across.  It would have been easy enough for you to get it right.

Worse than that, though, is this problem, in the sentence immediately following the one quoted above:

"In each case choose the one that makes the best answer. . . ." [emphasis mine].

Now, this makes it quite clear that the testee is to mark only one answer (to "put a cross in the square standing at the right-hand end of it," as the distinctly non-American phrasing puts it, although earlier the instructions specifically also tell us to use a check mark), yet the instructions for a problem in that test state

"Indicate more than one [adjustment to the rifle sights] if more than one satisfy the required conditions" [emphasis mine];

and problem #12 is unconditionally contradictory of the general instructions for Test 6:

"Place a cross against the two sums of money that he entered up wrongly" [emphasis mine].

Gosh, dear Sir or Madam, when the instructions that are presumably so important to a candidate's ability to score accurately are so obviously contradictory, you should not be surprised when testees begin to suspect that the instructions may be ignored.  Was this your intention?  Is this sort of thing -- figuring out that the printed instructions must be disobeyed -- actually a secret part of the test?


     Problem #2 in Test 6 admits of more than one perfectly correct answer, which should not be the case.


2.  A man bought a horse for 20 and gave in payment a cheque for 30.  The horsedealer persuaded a shopkeeper to change the cheque for him, and the buyer, having received his 10 change, rode off on the horse and was not seen again.  Later the cheque was found to be valueless, and the horsedealer had to refund the shopkeeper the amount he had received.  The horsedealer had himself bought the horse for 10.  How much did the horsedealer lose altogether?

(1) Nothing.     (2) 20.      (3) 10.     (4) 30.      (5) 40.


[Dear reader of the BB Web site:
Let me interrupt myself to invite you to try to answer the horsedealer
problem above before you read the rest of my letter to Mensa.]


It is not made clear at all what "How much did the horsedealer lose altogether?" specifically means.  It could be taken as meaning,

"How much did the horsedealer lose altogether in cash?"

or it could mean

"How much did the horsedealer lose altogether in cash and lost profits?"

or it could mean

"How much did the horsedealer lose altogether in cash and lost profits and horses?"

If the question is how much altogether in cash, then the answer is that he lost 40, consisting of the 10 in change that he paid to the thief plus the 30 he refunded to the shopkeeper.

If the question is how much he lost altogether in cash and lost profits, then the answer is the same 40 from the interpretation above plus another 10 for the profit he lost on the sale, for a total of 50, since he bought the horse for 10 and would have sold it for 20.  Notice that this legitimate answer, of 50, is not even offered as one of the possible answers.

If the question is how much he lost altogether in cash and lost profits and horses, then the answer is the same 50 from the interpretation above plus another 10 for the loss of the horse itself, for a total of 60, since the horsedealer now has an inventory deficiency of paid-for horses to the tune of one 10 horse.  Notice that this legitimate answer, of 60, is also not even offered as one of the possible answers.

I answered 40 because that is the largest amount you offer as a possible answer, but I object to the wording of the question.  And if the correct answer is indeed 40, how do you or the test writer respond to my arguments for 50 and 60 as answers?


Update of May 1, 2001  Soon after this page first appeared I started receiving e-mails explaining how I had made a mistake in my analysis of the horsedealer question above.  I did indeed make a mistake, and if you've already caught it then you probably have a better shot at Mensa-hood than I will ever have.  You can and should read more by taking a detour here.


     Problem #6 in Test 6 should not be a test question at all, because it is merely an old riddle . . .


6.  A man, pointing to a portrait, exclaimed, "I have no sisters or brothers, but that man's father is my father's son."

The man whose portrait he was looking at was

(1) His father.     (2) Himself.      (3) His son.     (4) His uncle.

. . .  although I learned it as a true rhyming riddle, thus:

Sisters and brothers have I none,
But that man's father is my father's son.

Anyway, the point is that I did not have to spend time sorting through the four possible answers because I knew the answer from having heard and read the riddle so many times before.  Why is this problem included in your test if all one needs to do to answer it is remember the answer to a riddle that has been read and figured out by thousands, if not millions, of people already?  This is a timed test, and it seems unfair that my fellow testees who happen not to have run across this riddle before should have to spend more than the two seconds I spent on it.  Or was I on my honor to pretend I didn't know the answer?

There are problems with two other questions in the Inferences section -- the one about the marrying age in England and the one about the aquarium fish -- but I'm tired of complaining.  Score my enclosed test booklet as you will, but I do ask, even if you judge me as unqualified further to pursue Mensa-hood, that you consider my complaints about this particular qualifying test.




Dear reader:
where I went wrong
or whether my complaints are justified.





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