I am not currently a Mensa member, but I have always scored between 150 and 170 on all IQ tests that I have taken.  The very fact that I have to state a range for my IQ scores already points to one inconsistency in the tests: Two "impersonal, scientific" tests cannot give the same results.  The magnitude of error for me has been between 12% and 13%.  With that out of the way, I would like to address your concerns.

One of your concerns was that the writers of the test obviously were lacking in their instructions: You say, "The instructions you provided are both imprecise and, in some cases, contradictory."

You show that the explanation for the "Classification" part contains a semantic error (referring to mammals simply as animals).  I prefer to believe that it was simply a wording mistake, but the mistake was in the explanation, not in the question itself.  It is true that these things should be very specific, but I don't think this small wording error has caused anyone real harm.  The definition of mammal is as follows

[ SNIPPED HERE ]

Definition (2) in both dictionaries implies what many people do not know, which is that, even though it's scientifically inaccurate (kingdom animalia contains nearly all forms of life, including Aves, or birds), the word animal is often used synonymously with the word mammal.

Thus, we can see that either the writer made a wording mistake or he was simply using the word animal to mean mammal.  However, I would agree with you that these things ought to be less confusing and perfectly accurate. It would be an improvement to use the word mammal.  However, it is practically irrelevant to the test, since it was not part of a question.

The instructions you cite thereafter are indeed contradictory, although I think that the exceptions to the rule state themselves quite clearly as such: "Indicate more than one if more than one satisfy the required conditions," "Place a cross against the two sums of money that he entered up wrongly."

The instructions for the test would better have read, "Each question has only one correct answer unless otherwise specified."

The question relating to the well-known riddle should definitely not have been included, as it gives an unfair advantage for simply having heard it before.  Ideally, IQ tests would not use already-known problems.

So, thus far, I would have to agree to your conclusions, although I do not think they are as drastic as you seem to think.  This test obviously was not as well thought-out as it could have been.

However, with regards to the problem of the horse sale, I think there is only one possible answer that makes sense.  This is my logic on the problem: We will not consider the horse to be anything but property (i.e., it is not equal to its possible selling value, as this could change).  However, it should be included in the losses/gains.

Let us assume that the horsedealer starts with an arbitrary amount of money, say £10.  The difference at the end will show exactly how much he lost.

Since the man originally had £10 and ended up with -£10, he lost only £20.  Yes, he did lose his horse, but the value of the horse is in question (it is only worth what he can sell it for).  Therefore, he gained a horse, and he lost a horse.  You could argue about the possible gains (i.e., he could have sold the horse for £20, and therefore it was worth more than the £10 he paid for it), and say that he lost £30 when losing the horse worth £20.  However, the £30 is irrelevant, since he essentially borrowed it and gave it back.  All he lost was the horse and the £10 he gave in change.  This would make the answer either £20 or £30.  I believe that only £20 makes sense since, from beginning to end, he came out £20 pounds behind.

Dan, I don't understand why the fact that the value of the horse is in question means it has no value.  The value of the net assets of St. Peter's Basilica in Vatican City is in question, but surely it's not zero.

In the case of valuing the horse, it would be contrary to generally accepted accounting principles to assume the value of an asset is nil.  Unless there's some reason not to, one would always account for the value of an item of merchandise at cost, in this case £10.  You seem to have assumed that because it's not exactly known, that value is zero.

This includes your two steps of including lost horses and lost profits.  If we include the lost profits, it is £30, and otherwise it is £20.  As I said, £20 makes more sense since he had a potential of making a profit on the horse, but no guarantee.  Therefore, at the beginning he lost £10 and gained a horse.  He was left with a horse, the worth of which is in question.  When he later lost that horse, he didn't lose £20 or £10; he just lost a horse, leaving him with a deficit of £10, since he earlier paid that sum.  The only other money he really lost was the £10 in change he gave to the buyer, which gives a deficit of £20.  This is the correct answer.

Your fault in logic is considering the £30 as lost money, when in fact he first received this money, then returned it.

All of the tests I have taken have had discrepancies, mis-wordings and confusing questions. Some have been better than others.  However, I wanted to point out the flaws in your own logic as well as tend to agree that these tests are not perfect.

Sincerely,

Dan Hulme

There is a much easier way to analyze the horesdealer problem.  The shopkeeper lost nothing.  The thief paid nothing and gained the horse and £10.  The horse cost the horsedealer £10.  So the horsedealer lost £20.
 

Hey, Johnny,

I would like to assist you with this question.  Let me first clear the air with a disclaimer.  I am not a member of MENSA.  Also, I don't know my IQ and if I did I wouldn't air it in public.

Joining an organization such as MENSA strikes me as not dissimilar to feeling pride for being a descendant of someone who sailed aboard the Mayflower or feeling shame for having been born with a low IQ or a birth defect.  This is not a slam against anyone who is a member; I'm sure there are many smart, interesting, kind and caring, if misguided, people who belong to MENSA.

Anyway, based on the facts posited in the horsedealer question, your (revised) answer of £30 is the only correct answer among the choices offered.  There a very easy way to get to the £30 conclusion, which I'll address later.

First, some analysis of the question "How much did the horsedealer lose altogether?"

The question is indeed ambiguously worded but presumably it refers to the horsedealer's ECONOMIC loss on THIS TRANSACTION.  He lost cash and a horse and perhaps his temper, pride, or sanity, but this by its context is a question of logic and economics.  Importantly, it's an economic question and NOT an accounting question.  These are two different things.  Answering an accounting question requires reference to some specified accounting conventions, which vary dramatically in purpose and operation across cultures, time and individual business enterprises.  We are not told which set of accounting standards or principles or methods to apply, and rightly so, because this question was not designed to test one's skill at applying accounting conventions.

This is also NOT a question about the loss incurred by the horsedealer since the beginning of time; it refers only to this particular sale transaction.

OK, so the stage is set.  It's clear the horsedealer lost £10 net cash on the sale of the horse (+30 - 10 - 30 = -10) AND he lost the horse itself, as measured by its market value.  So the horsedealer's total loss equals the sum of the lost £10 cash plus the market value of the horse.

The facts do not explicitly state the market value of the horse per se, but a market value of £20 is implied by the fact this was the price negotiated between unrelated parties, neither of whom was under a compulsion to buy or sell, each acting in his own self-interest.  This defines the very process by which market value is derived.

One might object that using a £20 market value in this case is dubious, that the buyer was clearly not a true arm's-length participant operating in an open market, because he was obviously a fraudster intent on ripping off the horsedealer, and thus the agreed £20 price was probably inflated.  But this objection suffers three problems.

First, the facts do not state the buyer knew at the time he agreed on the price that the £30 cheque was not backed by sufficient funds.  The facts do not even state that the cheque was written on the buyer's own account.  All we know is that the buyer had a £30 cheque in his possession, which he endorsed over to the horsedealer and the horsedealer in turn endorsed over to the shopkeeper and the shopkeeper in turn endorsed over to the bank and the bank rejected.  The fact the horsedealer never saw the buyer again might be explained any number of ways.  We cannot add facts not posited by the problem.

Second, even assuming arguendo that the buyer knew the cheque would bounce, that buyer was indeed motivated to negotiate the lowest price he could for the horse, just as any other open-market buyer would have been.  If he had struck the bargain at £18 rather than £20, he would have received £12 in change for his £30 cheque rather than only £10.  And of course the horsedealer was motivated to sell at the highest price.  Market forces were in place to hammer out a market-value price of £20 for the horse.

Third, there is not a shred of other evidence of the horse's market value stated in the problem that could lead one reasonably to conclude an alternative answer.  Whether the horsedealer paid zero or £10 or £1,000 for the horse makes utterly no difference.  The problem does not say whether the horsedealer had bought the horse as a foal three years earlier, or that he bought it the same day.  It does not tell us how much in expenses he had paid feeding and otherwise tending the horse prior to its sale.  It doesn't tell us the circumstances of the horse's acquisition by the horsedealer.  The horsedealer's original, historical cost of the horse of £10 is a red herring.  To illustrate this point, assume the horsedealer had paid £1,000 for the horse a year earlier and sold it for £20.  That £980 loss in value would have been incurred independent of this sale transaction, due to some earlier change in the horse or in market forces.  His loss ON THIS TRANSACTION would remain the same.  Again, don't confuse the accounting for the transaction with the economics of the deal.  When the horsedealer should "recognize" that loss by recording the "cost of goods sold" amount on his books is an accounting question and depends upon the conventions or rules to be applied.

All that matters to answer this question is the market value of the horse at the time of the sale.  Anyone who is confused by this need only substitute the word "gold" for "horse" in the question and this will become apparent.  The argument that one may ignore the value of the horse in answering this question could not have been propounded by anyone who has operated a for-profit enterprise.

Now for a MUCH easier way to solve the whole problem: The horsedealer is left holding a bad cheque for £30.  That is the value of the horsedealer's claim against the buyer and that is the amount of his loss if, as the posited facts imply, the horsedealer is able to collect nothing on his claim.  It's often easy to overthink these things when a little big-picture perspective, also known as "common sense," will provide the answer.

If this still isn't entirely clear, try the "gold" substitution trick: A speculator buys an ounce of gold for £1,000.  He later sells it for £1,500.  The £1,500 cheque bounces.  How much has the speculator lost?

A truly silly answer would be that he hasn't lost anything because it was just gold, not money.  An equally specious "accounting" answer would be that he has lost only his £1,000 historical cost of the gold.  Common sense economics says he's out £1,500.

Hope this helps.

-- Tim
 

In a follow-up email the next day, in reference to the analyses preceding his, Tim offered this: "I found it interesting that intelligent persons arrived at such diverse interpretations and conclusions.  The ambiguous phrasing of the facts can account for only part of this result."