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Can you do any better? IQ test

by Eva Amsen

There’s an article in New Scientist, all about how having a high IQ doesn’t imply that you’re smart. George Bush (junior) is the token example of stupidity coupled with high IQ.

It’s true. Some of the stupidest people I’ve met are very smart on paper. And some of the smartest people I know never did well on any standardized tests, including the IQ test.

The article lists some examples of questions that even people with high IQ get wrong.

Jack is looking at Anne, and Anne is looking at George; Jack is married, George is not. Is a married person looking at an unmarried person?

Apparently, most people (smart or not) say that you don’t have enough information to tell the answer. You totally do, and the answer is “yes” regardless of Anne’s marital status, but I can see how you can be tricked here when you’re in a hurry or half asleep and you see that “not enough info” is given as one of the possible answers.
Then there are three other questions , introduced as follows:

“When researchers put the following three problems to 3400 students in the US, only 17 per cent got all three right. Can you do any better?”

NO, of course I can’t DO ANY BETTER. There are only THREE questions, how can I do BETTER than the people who GOT ALL THREE RIGHT? Duh.
Fine, let’s look at the questions.

1) A bat and a ball cost $1.10 in total. The bat costs $1 more than the ball. How much does the ball cost?

Five cents, and the bat costs $1.05. That’s really cheap. When was this? 1905?

2) If it takes five machines 5 minutes to make five widgets, how long would it take 100 machines to make 100 widgets?

Apparently, it takes 5 minutes for a machine to make one widget. So, five minutes for any X number of machines to make X widgets.

3) In a lake, there is a patch of lily pads. Every day, the patch doubles in size. If it takes 48 days for the patch to cover the entire lake, how long would it take for the patch to cover half of it?

Well, that’s obviously the situation the day before, so 47 days.
Easy peasy.
Something is wrong.
(See extended post, so you can have a think about it yourself before reading what I noticed.)

FORTY-EIGHT days to cover a lake with lily pads that double every day? Really?? That is ONE BIG LAKE.

How big, exactly?

A lily pad can be pretty big, let alone a patch of lily pads, but let’s assume there is only ONE lily pad to begin with, and it’s no bigger than 15 cm in diameter. That’s just over 175 cm2.

If the next day there are two of those pads, and the days after that four, and then eight, and so on, then after 48 days there are 248 lily pads. They would cover an area of 175×248 cm2, which is about 4.9 MILLION km2.

The largest lake in the world, according to Google, is the Caspian Sea, with a surface area of 371 thousand km2.
So, there is no possible way in which it takes 48 days for ANY lake to be covered by a patch of lily pads doubling in size every day. In fact, at this rate, it would take less than a week longer for the lily pads to cover the surface of the entire planet. Weed control, anyone?

I guess I could do better after all…

(But I’m glad to see that commenter “Shambo” on the New Scientist article also spotted the ridiculously big lake. That at least makes two of us concerned about the world being taken over by lily pads. No wonder baseball bats are so cheap – no room left to play just a week from now!)

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Stephen Curry November 5, 2009 - 9:19 AM

Leave the lily pads alone – that could be the answer to global warming…

Sabine Hossenfelder November 5, 2009 - 9:56 AM

A smart person (not me) once said there’s as many IQs as there are IQ tests.
The problem comes with the idea that it’s possible to quantify a person’s use with a set of numbers to begin with, and in addition this set of numbers has very small cardinality.

Sabine Hossenfelder November 5, 2009 - 9:59 AM

This reminds me btw of a blogpost I recently wrote on a paper “Why are modern scientists so dull? And why that question is nonsense.”:http://backreaction.blogspot.com/2009/07/why-are-modern-scientists-so-dull-and.html

Alyssa Gilbert November 5, 2009 - 3:48 PM

LOL That’s exactly what I asked when I read the lily pad question too. Thanks for calculating it for us!

Cath Ennis November 5, 2009 - 5:39 PM

Yay! I got all 3 right (although I got the Anne-Jack-George one wrong).
Seeing as bats are so cheap, let’s go and buy one each and go and destroy lily pads with them. If you give X bats to X commenters, it should only take five minutes.

Eva Amsen November 5, 2009 - 5:51 PM

Heehee, great plan!

Åsa Karlström November 5, 2009 - 6:56 PM

ha, accordingly to my brain prior coffee and waking up in the morning, I have a very low IQ. Ah well, someone’s got to beat the odds, right? 😉

Shelley Edmunds November 6, 2009 - 5:17 AM

Then if you swap in those lily pads big enough to hold a small child we can pretty much lilypad the whole galaxy. OK maybe just the solar system.
(also, don’t try IQ test questions after a Friday afternoon beer …)

Richard Wintle November 6, 2009 - 4:16 PM

That married/unmarried question did my head in. The other three were easy enough, but only because I’d been alerted by the context of your post that they were trickier than they appear. Approaching them naively… actually I probably would have gotten them all right anyway, since once upon a time I was trained to think -as dark wizards do- about questions like these. In my days of high-school math contests, which, truth be told, I was not terribly good at.

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