The Bat and A Ball Problem

March 1, 2013 24
The Bat and A Ball Problem

If a baseball and a bat cost $1.10 together, and the bat costs $1.00 more than the ball, how much does the ball cost?

Was your answer that the ball cost 10 cents?

If so, you’d be wrong.

Here’s the solution:

Although $1.00 + $0.10 does equal $1.10,  if you take $1.00 – $0.10 you get $0.90, but the problem requires that the bat costs $1 more than the ball.

So, the ball must cost $0.05, and the bat must cost $1.05 since $1.05 + $0.05 = $1.10

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Still not convinced?  You can use algebra to solve the problem:

First, let’s set up the equation:

x + ($1.00 + x) = $1.10

$1.00 + 2x = $1.10

2x = $1.10 – $1.00

2x = $0.10

Finally, solve for x:

x = $0.05

Check your work:

x + ($1.00 + x) = $1.10, so

$0.05 + ($1.00 + $0.05) = $1.10

Why does the bat-and-a-ball problem have any significance?

If you answered 10 cents you are inclined to believe in religion.  If you answered 5 cents you are inclined to disbelieve.  Why? Because, according to research reported in the journal Science, the 10 cent answer indicates that you are an intuitive thinker, and the 5 cent answer indicates that you solve problems analytically, rather than following your instincts.

From Psychology Today:

Their study of 179 Canadian undergraduate students showed that people who tend to solve problems more analytically also tended to be religious disbelievers. This was demonstrated by giving the students a series of questions like the one above and then scoring them on the basis of whether they used intuition or analytic logic to reach the answers. Afterward, the researchers surveyed the students on whether or not they held religious beliefs. The results showed that the intuitive thinkers were much more likely to believe in religion.

…  Professor and Chairman Terrence Reynolds of the Department of Theology at Georgetown University finds it plausible that analytic thinking could make religious belief more difficult. “If one assumes that all rationality is tied to what we know directly through the five senses, that limits our understanding of meaning questions. Religion tends to focus on questions of meaning and value, which may not be available through analytic verification processes… by definition God is a being that transcends the senses.”

Quick Poll – What was your answer, and do you believe/disbelieve in religion?

Another interesting puzzle, which you may or may not consider tricky:

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?

A)  24 days

B)  47 days

C ) 48 days

D)  49 days

E)  none of the above (state your answer and why)

  • paulette

    47 days to cover half of the lake

  • David

    Also if one answered 10c, or just angrily gave up it could be that one has not been taught to think analytically.

    I confess 10c was all I could think, Although I had expected the answer not be the one which first came to mind.
    I most certainly do NOT believe in such things as religion.
    Was I in fact thinking analytically but with no real mental “tools” to gain any traction? (welcome to my nightmare)
    All I needed was the tools to figure out what I’d suspected. thank you for the insight.
    why oh why wait until higher education to introduce this to people!! (at least in my day anyway)

  • KaL

    1.05 – 5 = 1.00

    They said the bat costs 1.00 MORE than the ball. So the ball is 5 cents. I’m not good at mathematics but I pay attention to the way words are used.

  • Terry

    RE the lake question…in my book the answer is e…NOTA. Why you ask? To simply say that it takes the patch 48 days to fill the lake, and the patch doubles in size each day; the pool of answers could still be quite infinite because you are measurably omitting the rate of patch growth in relationship to the surface size of the lake itself…on proportion the answer of 47 marginally works but only if one “assumes” each day of patch growth is identifcal. however it works in whole when you inlclude the size of the lake.

    • Aron Sabaj

      You’re provided 2 axioms. 1. that each day the patch doubles in size. 2. It takes 48 days to cover the entire lake. From these, you can make the assumption that on the 48th day, the patch has doubled exactly to cover the whole lake otherwise it would conflict with the first axiom. So yes, you’re meant to assume.

  • Roy

    The 10cent ball may not be the answer you were looking for, but it IS an answer that fits the question.
    eg Q. What two numbers when added together make 5?
    A. There can be as many answers as you want, depending on whether or not you want to delve into fractions .

    • Cassandra Martinez

      That is what they are asking you could say no its .4999… Your wrong for saying its 5 because saying 60degrees is the same as 59degrees59’59”

  • Roy

    Furthermore. If asked what is the opposite of ‘right’, is the correct answer ‘left’? or ‘wrong’?

  • brian

    the article has error its 0.5 ceents

  • Jason

    There are two two correct answers to this question. The way that the question is worded does in no way suggest that the numbers have a second mathematical requirement. (the subtraction check.) I think that this is a very misleading analysis and proves nothing more that the most obvious answer is obvious.

    • pauletteb34

      There is only one answer. The bat must cost $1.00 MORE than the ball with a combined total of $1.10. Simply take the dollar out (because that will be added to the price of the bat ) and then split the remaining $0.10. It seems tricky at first…but THAT’S THE FUN of the question!!!

      • Cassandra Martinez

        Guess wat
        And .05 needs .05 over a dollar added to it to equal 110
        So adding 1.05 isnt adding 1.00
        Whcih you need to do because 1.05 is not a dollar
        1.00 is

  • Bob

    I agree with Jason and “the way that the question is worded”! May be obvious that it’s precisely $1.00 MORE, not $1,05 more!

    • Name

      But it is not $1.05 more. If the bat was $1.00 and the ball was 10 cents, you’d = $1.10 Right? Wrong. Because $1.00 – $0.10 = $0.90. And it has to be 1 dollar more than the ball. If you were to have the cost of the bat be $1.00, it would be mathematically impossible to solve. So, english wise, the problem does not apply that it can be over $1. But mathematically, it is saying you are going to have to fluctuate the cost of the bat.

  • Kam

    the price of the ball could be 9,8,7,6,4,3,2,1 cents and does not have to be 5 cents. all the other denominations are equally valid.

    • Secgu76

      You’re not very good with math, are you?

  • I forget my name

    That’s the easiest Question ever.
    The answers 5 cents!

  • Fred the cow


  • What ever my name is

    I’m speechless

  • I’m, err, John david bob?

    I don’t know my name and i can do that

  • Paul

    I’m a disbeliever of any religion. Apparently I’m not very good at critical thinking since I got the baseball and bat answer wrong and couldn’t figure it out. I suck at academic stuff too.

    I think aspiring to figure out the truth with whatever one’s critical thinking ability can also be a strong factor in whether he/she believes in a religion. Since many people are by default average in intelligence, it maybe more significant than critical thinking skills.

  • george

    my mind said 10 cents but i knew it was too easy but i didnt know how to figure it out.. what does that say about me?

  • george

    the lily pad on is 47

  • ed gomaz

    I got 1.10 but I new it was wrong. I wanted to do the math and figured the word “more” was relevant. Not very religious