You should have gotten to this page from here.
If you didn't, this won't make quite as much sense.
First, let me reproduce that section.
¤ Problem #2 in Test 6 admits of
more than one perfectly correct answer, which should not be the case.
TEST 6
INFERENCES
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.
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 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?
Now, as I said on the previous page, I did make a
mistake. (I maintain that the test question admits of more than one
legitimate answer, but not more than two.) My mistake was pointed out
to me, in varying degrees of accuracy and clarity, by several e-mail
correspondents over the last year or so. The best of those e-mail
conversations is shown below.
Subj: mensa test
Date: 2/5/2001 1:28:01 AM Central Standard Time
From:
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.
EVENT
CHANGE
NET ASSETS
Starting point >>
£10
Pays for horse
- £10
£ 0
Receives horse
+ horse
horse + £ 0
Receives check
+ check
horse + check + £ 0
Changes check
- check
horse + £ 0
Gets change for check
+ £30
horse + £30
Gives £10 in change
- £10
horse + £20
Gives horse
- horse
£20
Refund for bad check
- £30
- £10
Ending point >>
- £10
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
October 9, 2002: This page will be
updated with yet more correspondence sometime soon, some of it pretty darned interesting. At least I think it's interesting. I'm not sure, because most
of it is over my head.
