# Logic IQ Test

I am currently trying to norm an iq test. I would appreciate your participation. I am sure that you will find it interesting; go to:
http://www.geocities.com/uiowa52405/iq.htm

and click on logical iq test-the test is timed, for maximum time of 25 minutes.

Dj Sneaky Whiskers
Mine was interesting, in the sense that one question was of the form "How many painters would be required to paint X rooms in Y days, given that A painters can paint B rooms in C days?" But the answers were all in minutes!

Also, I got that same question twice in the same session, so I think the randomizer needs sorted out. I don't mind getting the same question twice, as long as it's actually possible to answer Okay, just took a look at the answers, and here's my jip with IQ tests

"Your mother's brother's brother-in-law is also:

A : uncle

B : cousin

C : father

D : grandfather

I ask, how big is the mother's family? She could easily have a sister and a brother, her sister is married, and so the mother's brother's brother-in-law could be an uncle.

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jammieg
Some very challenging questions Meninger, it is an interesting test.
How were you able to solve the selective sampling problem? I mean most people who volunteer for a specific test have a fair idea of what they are good at and will avoid tests they are bad at, unless they are like me and hell-bent for mathematical leather.

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I just helped to design the site associated with the test. However, the person who created the test was Henry Wyeth (he just asked me to advertise the test over the internet since he hardly spends time on the internet). I am not too familiar with his methods in designing tests; he just asked me to design a webpage for him in which he could post the questions. Yeah, I agree it is pretty challenging; I had looked over the test but did not officially taken it so far. He says that it is some kind of private research project that he is doing, implying the importance of the project, but think it is probably just a hobby of his. If you look at the score distribution page, the higest score so far is an 83.33 percent or something like that, which would correspond to (according to his scale) an iq between 125-135.

jammieg
It revealed to me just how overly reliant I am with logic and the depth of my mathematical ineptitude- missing the simple math problems and stuggling for 3 minutes with spider legs. I realized that I actually have an aversion toward math in general if not some form of mathematical retardation, if you don't believe me check out "Fuzzy probability/intuition problem",
in retrospect how did I possibly get 37% ,what was I thinking! If I were someone else it would make me laugh.

The developement of mathematics begins like rubbing two sticks together and progresses to a book of matches then a lighter and maybe even a blowtorch someday, logic begins with a smashed rock that reveals a shard and is used to cut with progressing to a butter knife, then maybe a rusty knife and someday a scaple. So some mathematicians may end up one day with a blowtorch and a butter knife and being so use to using the blowtorch as to try and perform surgery with it, the logician ends up trying to cut throw a metal door with a chipped scaple. Some people get too use to using their best way of thinking. If one's only tool wear a hammer all problems would look like nails.

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FreeHueco
My only beefs with the quiz..

Regular ice cream is not 100% fat, therefor it would take fewer than 100 cups to equal the fat content( I believe it's only 25% fat or somewhere in there).

If 3 is subtracted from 30, can it be subtracted from 30 again?

Question #22 has an incorrect answer I believe. If she ran for an hour, she would cover 2.5 miles in the first 30 minutes, and 5 miles in the next 30 minutes, giving her an average speed of 7.5 MPH. Am I wrong?

Mike

Originally posted by FreeHueco
Regular ice cream is not 100% fat, therefor it would take fewer than 100 cups to equal the fat content( I believe it's only 25% fat or somewhere in there).

If 3 is subtracted from 30, can it be subtracted from 30 again?

Question #22 has an incorrect answer I believe. If she ran for an hour, she would cover 2.5 miles in the first 30 minutes, and 5 miles in the next 30 minutes, giving her an average speed of 7.5 MPH. Am I wrong?

You're right about the iced cream thing. It doesn't say that it has 1% of the fat of regular iced cream, it says 99% fat free, which is usually, by weight or volume, not in comparison to other iced cream.

About the jogger thing, 6.7 (6 and 2/3) is correct. Average speed is calculated in reference to time. You are running at 10mph for half the time that you are running at 5mph. So you have 3 "parts". (10*1 +5*2)/3 = 6.66

However, there are large problems with the test. For example, the question regarding the computer price being cut lists the answer as "33", but I put "33.33333333333333333333" and was counted wrong, apparently.

Suppose I have two siblings, and at least one is a girl. What are the odds that I have two sisters? (answer in fraction e.g. 3/4)

1/2, assuming that male/female chance is a 50/50 ratio
1/3

The birth of one child is independent of the birth of the others, so it should be 1/2.

(tricky question) Choose the correct answer; there is only one correct answer

A_ : A is the correct answer
B : B is the correct answer
C_ : C is the correct answer
D_ : C is the correct if B is false

This question doesn't make any sense. The only one that you can rule out is D. If I choose A, then everything is perfecty fine. B and C can be false, which makes D false. Also, D left out "answer".

I think that I got the 3x103 one wrong because I included a comma in the answer.

There are five boxes with 36 coins randomly distributed inside of them. Pick the BEST answer.

A_ : Each box contains an even number of coins
B_ : It is possible to have an odd number of coins in each box
C : There has to be both even and odd numbered distributions
D_ : none of the above

6*4 + 12 = 36. All even numbers.

Some "geniuses" have a high IQ. Therefore:

A_ : All people with high IQ are "geniuses."
B_ : Some geniuses do not have a high IQ
C_ : Some people with high IQs are geniuses
D : Both B and C are true

This is incorrect. Nowhere is any information given from which it can be inferred that some geniuses do not have high IQs. The statement "some geniuses have high IQs" being true does not mean that "all geniuses have high IQs" is false. It only makes a statement about some geniuses. It does not make a statement about the others.

A : C is false
B_ : C is true
C_ : C is false
D_ : D is true

This has problems like the other one like it. for example, picking D is perfectly fine. D does not contradict itself.

There are a total of 12 oranges 12 apples and 12 mangoes in 3 bags. What is the probability of obtaining an orange from one bag?

A_ : 4/12
B_ : 3/12
C_ : 12/64
D : cannot be determined

Oh, contraire. Probability is a statement about the unknown. You use known facts to determine a probability of the unknown. Using the known facts, the answer is (1-probality that no oranges are obtained=24/36 * 23/35 *... * 13/25 = 24!/12! * 36!/24! = 36!/12!)

There are 2 boxes, each box holding 4 mustard and 4 ketchup packets. You randomly draw 1 packet from each box. What is the "probability" that at least 1 of the packets you draw is mustard (e.g 3/4)?

3/4
1/3

The probability is (1-probability that you draw ketchup both times=1-1/2*1/2=1-1/4=3/4)

Your mother's brother's brother-in-law is also:

A_ : uncle
B_ : cousin
C : father
D_ : grandfather

One definition of of "uncle" is "the husband of one's aunt" (webster.com). This means that either uncle or father could be correct.

FreeHueco
Originally posted by Dissident Dan
About the jogger thing, 6.7 (6 and 2/3) is correct. Average speed is calculated in reference to time. You are running at 10mph for half the time that you are running at 5mph. So you have 3 "parts". (10*1 +5*2)/3 = 6.66

Doesn't that only work if you know how long she ran for? Did she run for a certain amount of time, or did she run a set distance? Certainly she could have been in a race that lasts for a set time (ie. a 24 hour mountain bike race, where the winner is the one that covers the most distance). Maybe not common, but don't we need to know it?

If she ran a 3 mile race, you are correct though.

However, there are large problems with the test. For example, the question regarding the computer price being cut lists the answer as "33", but I put "33.33333333333333333333" and was counted wrong, apparently.

Didn't it say to use the nearest whole number?

Originally posted by FreeHueco
Doesn't that only work if you know how long she ran for? Did she run for a certain amount of time, or did she run a set distance? Certainly she could have been in a race that lasts for a set time (ie. a 24 hour mountain bike race, where the winner is the one that covers the most distance). Maybe not common, but don't we need to know it?

I don't think that you know the distance that she ran, but you know, lengthwise, that she ran half at 5mph at half at 10mph. For 5mph, since you know that you are running the same distance as at 10mph, but at half the speed, you know that you are running that for twice as long, timewise. So, the 10mph makes up 1 part, timewise, and the 5mph makes up 2 parts, timewise.

However, there are large problems with the test. For example, the question regarding the computer price being cut lists the answer as "33", but I put "33.33333333333333333333" and was counted wrong, apparently.

Didn't it say to use the nearest whole number?

Hmm, I don't know. I have a bad habit of overlooking instructions like that on easy problems.

FreeHueco
Originally posted by Dissident Dan
I don't think that you know the distance that she ran, but you know, lengthwise, that she ran half at 5mph at half at 10mph. For 5mph, since you know that you are running the same distance as at 10mph, but at half the speed, you know that you are running that for twice as long, timewise. So, the 10mph makes up 1 part, timewise, and the 5mph makes up 2 parts, timewise.

The question does not specify whether the half is distance or time. That needs to be known, otherwise the answer is unobtainable.

I haven't taken the test fully yet, however, I can give my humble critiques on some of your comments and since Dan seemed to have posted the furthest resolution to all of the arguments, I can start by looking at what he had to say:

-With one exception on a question he did not discuss-
"If 3 is subtracted from 30, can it be subtracted from 30 again?"

I can see how people got confused on this question. But ultimately I understand where he (Wyeth) is coming from. The confusion comes from looking at the number 3 as a separate entity. The only quantity that exist is 30, and the question is basically asking "how many 3's exists in 30?" Although I am not a psych major, I have taken some psychology courses, and it is a common psychological error due to the way the mind processes things. I think he purposely put this question to have a good laugh. To put it simply: you can only subtract from something that exist-you do not subtract with something. You are only taking away from something that exist; and in this question it is not asking you to take away from 3, but it is asking you to take away from 30.

-I am a bit confused on the ice cream question also, but he might have a logical explanation for this.

-"Suppose I have two siblings, and at least one is a girl. What are the odds that I have two sisters? (answer in fraction e.g. 3/4)"

I asked him about this question and he told me that he had a sufficient explanation for it and that putting 1/2 as the answer is a common mistake. He told me that this question was supposed to be one of the harder questions; same with the mustard packet question.

-"There are five boxes with 36 coins randomly distributed inside of them. Pick the BEST answer."

He told me that this one was a mistake of his and that he would fix it as soon as possible.

-"Some "geniuses" have a high IQ. Therefore:"

This question was a bit weird also. But basically the question can be looked at from one perspective," that only some geniuses have a high iq." For example, you asked me my opinion on how many geniuses have a high iq and I said some have a high iq than I would be wrong if all geniuses had a high iq. I don't like this question though.

A : C is false
B_ : C is true
C_ : C is false
D_ : D is true

The question assumes that their is only one correct answer. C cannot be true, so neither can B since it claims that C is true. Basically, since C is false, and we know this, A makes a correct statement saying that C is false. We know that D is not correct because we know that there can only be one true statement and we have already found it.

-"There are a total of 12 oranges 12 apples and 12 mangoes in 3 bags. What is the probability of obtaining an orange from one bag?"

This is one of the hardest math problems on the test, it has to be, or the test is absolutely ridiculous in the level of difficulty. My opinion on this question is that the answer is wrong by saying that the answer cannot be determined since probabilities can always be determined due to our definition of probability itself-our furthest estimation due to an uncertainty. But I disagree in saying that 1/3 is the answer. pretend that we had 3 of each fruits instead of 12. The trick is to replicate the nature of the solving the problem if we would have done it in real life (with real oranges, apples, mangoes). And thus we would have had to label each of the oranges-e.g. with markings such as number 1,2,3 and we would have had to do this with each of the fruits. Remember this statement, "probability applies only after all of the concrete possibilities have been assessed" so you cannot say that the identity of each orange is independent of probability because in technicality probability is only calculated after coming to an absolute uncertainty in the nature of the facts. The easiest way to do probabilities is to make probability branches. Pick a subset of possibilities that be inclusive in all of the possibility combinations. For example, for the first bag, the total number of orange combinations that could be in that bag is 2^n which would be eight-bag one can have no oranges, all of the oranges, orange #1, orange #2, orange #3, 1 and 2, 1 and 3, 2 and 3 (totalling eight combinations). We know that any of the final combinations will have one of these possibilities and thus we can be biased and branch all of the possibilities from just eight points. We can make subbranches from here and finally resolve the final probability which I will do later. I don't understand why he put this one on the test; either he does not understand the full logic of the question, or he got it from a mathmatician from the University and expects that anyone with an iq of 160 would solve this question in no time.

-"Your mother's brother's brother-in-law is also:"

He told me that the answer was supposed to be correct as it is. I am not sure if I agree. Maybe he sees something I don't.

-"(tricky question) Choose the correct answer; there is only one correct answer

A_ : A is the correct answer
B : B is the correct answer
C_ : C is the correct answer
D_ : C is the correct if B is false "

He told me that he misphrased this question and that he would fix it as soon as possible.

Jammieg, getting a low score on this test does not say much about your iq in general so I would not worry too much about your scores on this test. I think that he stress analytical sensitivity than anything else to measure a strong genetic iq. Lots of people could have done fairly well on this test: for example a score of 70 percent. But anyone who has been doing logic problems for a while could have scored this fairly well; afterall education does increase iq, but this is crystallized iq. Anyone who scores, for example, an 85 percent on this test, would probably have a fairly strong genetic iq. Anyone who scores lower than 60 would probably be an indication that this person had not done much logic problems or difficult math problems, or challenging in his life. You can easily improve your logical iq just by challenging yourself.

Originally posted by Meninger
-"Suppose I have two siblings, and at least one is a girl. What are the odds that I have two sisters? (answer in fraction e.g. 3/4)"

I asked him about this question and he told me that he had a sufficient explanation for it and that putting 1/2 as the answer is a common mistake. He told me that this question was supposed to be one of the harder questions; same with the mustard packet question.

I still don't buy his answer. If you know that one is a girl, then you are really only considering 1 siblings--the unknown. From the known data given in the question, the probability of having a girl on any given trial 1/2. We cannot assume any link between what one sibling is and what another is, and that information is not presented. So one can only treat the second sibling as an independent even with probability of 1/2 either way.

He got me with the "A: C is false" one though.

Well, here is a paraphrase of his explanation and he seems to be right:

-"Suppose I have two siblings, and at least one is a girl. What are the odds that I have two sisters? (answer in fraction e.g. 3/4)"

You have to actually do the problem like you would in a real life situation; in a way it is similar to the nature of my answer on one of the other questions.

The possibilities are:

girl (firstborn), girl

girl (firstborn), boy

boy (firstborn), girl,

boy(firstborn), boy-you can rule this one out

So we are left with:

girl, girl

girl, boy

boy, girl,

only one of three has both girls in the combination. Thus 1/3

Kind of a strange question, but it ultimately it seems to have logical sense.

jammieg
I have to agree with Dan on this one.
I suspect that this is more of a problem of creative lateral thinking or insight or something than logic, for instance:
Suppose I have two coins (in a hat) and at least one of them is heads. What are the odds I have two heads? That's the practical way of viewing it, that's common logic.
I think this may be impractical logic and improper english to infere from "suppose I have", to mean, suppose I'm going to have, or suppose I had.
It adds another demension of time frame that isn't stated but must be intuited from the fact the test designer isn't looking for the most probable answers that logic alone dictates.
"Suppose I have two siblings and at least one is a girl" might be viewed in the predictive sense of "suppose" because of the nature of the test designer for mind bending trickery, but if that's the case why not go for the bigger insight leap of not excluding the "I" which could comprise 3 total people along a time frame, but then you would have to factor in you could have been born of any one of those three along the time frame though my mathematical cogs are rust locked this seems like a very complicated mathematical problem and I get 2/7 probability? of having two sisters(relative to oneself not relative to existing in the whole group) along a time frame considering a 3 person group and exluding the outcome of all brothers. On a logic test it is impractical logic to assume the improbable is right and the probable is wrong, but it is a good puzzler.

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Yeah, I figured out why the answer could not be determined for this question:

"-"There are a total of 12 oranges 12 apples and 12 mangoes in 3 bags. What is the probability of obtaining an orange from one bag?"

It is not as complicated as I thought. You could go through all of the math to eventually come at this conclusion, but one who is experienced with logic, or simply as a great iq can figure the answer out in no time. Nevertheless, this still seems to be one of the more difficult questions that is included in the test.

If you want to work the math out you don't have to do it with the number 12, you can also use 1, 2, or 3-preferably one.

If you were to do the math, even with using the number one, the problem is still complicating. But you could have also noticed that the final answer, that is the nature of the final probability cannot go so far as to predict your probability of picking out a orange from the bag. However, you can determined the probability of a specific probability of obtaining an orange from the bag. For example, the probability of your probability of obtaining an orange from one bag being 1/3 is 1/27. So the answer cannot be determined, that is the answer that the question is asking. It is in this sense that the question can require a lot of work, but with enough experience or foresight one can have already concluded this matter. I have to admit though, this is an excellent problem. I have actually learned a lot from doing this problem. I have never actually done such as higher order probability problem before and it was nice to discover the nature of the problem myself.

jammieg
531,631 out of 531,632 if assumed 12 fruit per bag. I guess that's what the test designer was pointing to that one can't assume 12 fruit per bag, it could be 35.9 fruit in one bag and the rest in the other two.

... but even then, even if the bags were of random variable sizes even if the fruit we of random variable sizes, wouldn't the mean statistical average still be 12 by 12 by 12 for both fruit size and bag size, wouldn't it then be a probability of a statistical average of a statistical average? There's one person I know who would not only be able to answer it or say it's impossible but enjoy doing it as well-Pymitial of the math forum.

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