# The Three Questions...

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The Questions

1. A bat and a ball cost \$1.10 in total. The bat costs \$1.00 more than the ball. How much does the ball cost? ____cents

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

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 the lake? _____days

Trust me on this ... just answer the questions and post them and then I will put the article up about the questions and the analysis by the researchers...

A...

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Here is the real question. If one person doesn't know what he is talking about. Do two people who don't know what they are talking about, know more or less than the one person?!

No really

1. The ball cost 5 cents.

2. It takes five minutes to make 100

3. 47 days to reach half.

And if my answers are correct which I think they are, I would like to state that I didn't cheat

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Oh, and it only took about four minutes to solve

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1. A bat and a ball cost \$1.10 in total. The bat costs \$1.00 more than the ball. How much does the ball cost? ____cents

bat + ball = 110

bat = ball + 100

--------------------- 2 equations, 2 variables

(ball + 100) + ball = 110 (substitution)

2balls + 100 = 110 (collecting like terms)

2balls = 10 (subtract 100 from both sides)

ball = 5 (divide both sides by 2)

Very simple. Even I can do it. And I don't know anything about math.

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The Questions

1. A bat and a ball cost \$1.10 in total. The bat costs \$1.00 more than the ball. How much does the ball cost? ____cents

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

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 the lake? _____days

Trust me on this ... just answer the questions and post them and then I will put the article up about the questions and the analysis by the researchers...

A...

1.00 + ball = 1.10. ball = 0.10

five machines take five minutes (I am assuming they are working simultaniously to make five widget. Each machine takes five minutes to make one widget. 100 machines take five minutes to make 100 widgets if they are work at the same time.

47 days

Ba'al Chatzaf

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1.00 + ball = 1.10. ball = 0.10

Derek got ball = 0.05

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1.00 + ball = 1.10. ball = 0.10

Derek got ball = 0.05

He is wrong. The algebra is plain and trivial.

Ba'al Chatzaf

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Oh Bob. A dollar more than a nickle is 1.05. \$1.05 and \$.05 is \$1.10. Derek is of course right. You are right too, the algebra is plain and trivial.

x + y = 1.10

x - y = 1.00

2x = 2.10

x = 1.05

y = .05

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Article and analysis? I'm afraid the weekend's about done...

\$.10

5 minutes

47 days

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'more than' means a difference. The bat is not a dollar, it's a dollar more than the ball.

I'm interested in the researchers analysis of these questions and the weekend is fading away...

Evidently #1 is a much harder problem than it appears at first glance...

I think 2 and 3 are just there to make #1 seem equally as trivial.

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Never mind Adam, I looked it up. People who answered \$.10 are intuitive thinkers and much more likely to believe in god. If you answered \$.05 you are an analytical thinker and less likely to believe in god.

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Never mind Adam, I looked it up. People who answered \$.10 are intuitive thinkers and much more likely to believe in god. If you answered \$.05 you are an analytical thinker and less likely to believe in god.

Nice of you to keep that too yourself.

Do you go to the new line waiting to see a mystery movie that you have just seen and tell folks the ending also?

Nice of you to provide the link though...oops...nevermind. http://bigthink.com/praxis/a-three-question-math-quiz-that-predicts-whether-you-believe-in-god

A....

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According to a Harris Poll conducted last year, about three-quarters of Americans—74 percent, to be precise—believe in God. That is a lot of people, but the figure is notably lower than it was in identical polls conducted over the past decade. In 2005, 2007 and 2009, 82 percent of Americans said they were believers. What can explain this nearly 10 percent decline in religious belief? I won’t try to speculate. Instead, I’ll explore one tentative explanation some psychologists have offered recently for understanding why some people believe in God while others don’t. People who are more disposed to analytical thinking, the hypothesis goes, are less inclined to believe in a deity.

In 2012, in the journal Science, social psychologists Will M. Gervais and Ara Norenzayan published the results of five studies suggesting this might be the case. I’ll discuss the findings in a moment. First, it’s time to test yourself.

Unfortunately, the survey was conducted with 179 Canadian college students and we all know what that means.

The Upshot

Are the authors implying that religious people are unintelligent? No. The authors insist that they take no position on whether intuitive or analytical decision-making is the superior mode:

[W]e caution that the present studies are silent on long-standing debates about the intrinsic value or rationality of religious beliefs...or about the relative merits of analytic and intuitive thinking in promoting optimal decision making.

Instead, Gervais and Norenzayan draw on Nobel Prize winner Daniel Kahneman’s view that human cognition can best be conveyed as the interaction of two “systems.” System 1 is the fast, almost instinctive process that makes instant, gut, unreflective judgments, while System 2 is the slow, effortful process that draws on our powers of analytical reasoning. Of the two processes,

one (System 1) relies upon frugal heuristics yielding intuitive responses, while the other (System 2) relies upon deliberative analytic processing. Although both systems can at times run in parallel, System 2 often overrides the input of system 1 when analytic tendencies are activated and cognitive resources are available...

Available evidence and theory suggest that a converging suite of intuitive cognitive processes facilitate and support belief in supernatural agents, which is a central aspect of religious beliefs worldwide...Religious belief therefore bears many hallmarks of System 1 processing.

The authors reason that since “religious belief emerges through a converging set of intuitive processes, and analytic processing can inhibit or override intuitive processing...analytic thinking may undermine intuitive support for religious belief.” Seeing people through the Kahnemanian lens thus “predicts that analytic thinking may be one source of religious disbelief.”

There are many other reasons people might decide not to believe in God, of course, and it would be a mistake to construe religious believers as unreflective, shallow-thinking fools. (That would itself be a snap, narrow-minded, System-1-style judgment.) But the research from Gervais and Norenzayan turns a useful lens on a puzzling aspect of human psychology.

A...

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'more than' means a difference. The bat is not a dollar, it's a dollar more than the ball.

I'm interested in the researchers analysis of these questions and the weekend is fading away...

Evidently #1 is a much harder problem than it appears at first glance...

I think 2 and 3 are just there to make #1 seem equally as trivial.

That problem was presented ambiguously.

If one reads it plainly it comes out 1.00 plus (cost of ball) = 1.10

If one does not read it plainly then it comes out differently.

Ba'al Chatzaf

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'more than' means a difference. The bat is not a dollar, it's a dollar more than the ball.

I'm interested in the researchers analysis of these questions and the weekend is fading away...

Evidently #1 is a much harder problem than it appears at first glance...

I think 2 and 3 are just there to make #1 seem equally as trivial.

That problem was presented ambiguously.

If one reads it plainly it comes out 1.00 plus (cost of ball) = 1.10

If one does not read it plainly then it comes out differently.

Ba'al Chatzaf

Interesting take Bob, now what precisely do you mean by "not read it plainly?"

A...

remember I am barely conversant in algebra, geometry was my favorite, I got lost in "imaginary numbers."

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A well posed question should not be able to be read in two or more ways. Real questions can only be put in a way with one interpretation. If there are two or more then the question is ill posed.

Ba'al Chatzaf

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A well posed question should not be able to be read in two or more ways. Real questions can only be put in a way with one interpretation. If there are two or more then the question is ill posed.

Ba'al Chatzaf

Wouldn't that be dependent on the intent of the questioner?

A...

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A well posed question should not be able to be read in two or more ways. Real questions can only be put in a way with one interpretation. If there are two or more then the question is ill posed.

Ba'al Chatzaf

Wouldn't that be dependent on the intent of the questioner?

A...

The well possedness of the question is a separate issue from the intent of the questioner.

Plain talk stands on its own regardless of intention.

Ba'al Chatzaf

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Interestingly, 4th grade common core math is overflowing with this type of bat and ball problem. Many are specifically that format. Others are just generally ambiguous, and require the student to have access to information that is not explicitly stated in the problem. My son's teacher's solution? Choose an interpretation, do the work and turn it in early. If you chose the wrong interpretation, she'll give it back for corrections along with the missing information.

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In Bob's defense, the very first 13 words, the majority of the statement (57% of the words,)...

"A bat and a ball cost \$1.10 in total. The bat costs \$1.00..."

Perhaps the rest of the test reliably captures intuitive vs. analytical modes, but this question is sensitive mostly to things like insufficient scepticism (by which I mean non-trusting,) over-confidence, and rushing.

Myself, I went to question two at the point quoted above. When I went back to one, I saw the latter part was: "How much does the ball cost?" It is profoundly misleading, so it tests scepticism, not preference for intuition.

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Interestingly, 4th grade common core math is overflowing with this type of bat and ball problem. Many are specifically that format. Others are just generally ambiguous, and require the student to have access to information that is not explicitly stated in the problem. My son's teacher's solution? Choose an interpretation, do the work and turn it in early. If you chose the wrong interpretation, she'll give it back for corrections along with the missing information.

Ok, so there is a "right" answer.

I don't get the turn it in early idea at all.

Wonder if they are screening for certain "mind-types" early in their "education?"

A...

Paranoia is a healthy state of mind...

and we all know the song...paranoia strikes deep...

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That problem was presented ambiguously.

If one reads it plainly it comes out 1.00 plus (cost of ball) = 1.10

If one does not read it plainly then it comes out differently.

Oh c'mon Phil, admit you screwed up. And then you went into your usual prancing and preening like you're so much smarter than everyone else.

Another thing, Phil, what have you done with the real Bob?

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Please. None of the questions are even slightly ambiguous and all have a right answer. Totally about reading comprehension. Pure mental laziness to jump to a conclusion without reading the questions. An illustration of thinking being volitional. This puts all of the complicated convoluted philosophical discussions here in a new light. As in, if you can screw this up, how much else is bullshit?

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Interestingly, 4th grade common core math is overflowing with this type of bat and ball problem. Many are specifically that format. Others are just generally ambiguous, and require the student to have access to information that is not explicitly stated in the problem. My son's teacher's solution? Choose an interpretation, do the work and turn it in early. If you chose the wrong interpretation, she'll give it back for corrections along with the missing information.

Ok, so there is a "right" answer.

I don't get the turn it in early idea at all.

Wonder if they are screening for certain "mind-types" early in their "education?"

A...

Paranoia is a healthy state of mind...

and we all know the song...paranoia strikes deep...

The turn it in early idea was a reaction to parents' complaints. On Monday of each week, the students are given a word problem to solve, and the solution is due on Friday. One word problem, and the grade is weighted the same as a test grade. Now, the solution goes on for 3 pages because the student has to draw pictures and create models and write paragraphs of explanation, but that's not relevant to this discussion. Anyway, after so many complaints, the teacher announced that the students could turn the work in anytime before Friday and be allowed to make any needed corrections.

I don't think there's anything more nefarious going on than a school trying to save face after making a stupid decision. (My son attends a small private school, so I am less distrustful than if he were in public school.)