The Bat and A Ball Problem

March 1, 2013 49
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”

    • Per Hansen

      10 cents is not an answer that fits the question.

      Let’s say the ball cost 10 cents, i.e. $0.10. As the bat costs $1 more than the ball, the bat would cost $1.10, right? The bat and the ball would then cost $1.10 + $0.10 = $1.20. So 10 cents is not an answer that fits the question.

      Let’s say the ball cost 9 cents, i.e. $0.09. As the bat costs $1 more than the ball, the bat would cost $1.09. The bat and the ball would then cost $1.09 + $0.09 = $1.18. So 9 cents is not an answer that fits the question.

      You can do similar calculations for other answers that you believe fit the question. Only if the sum turns out to be $1.10 you have found an answer that fits the question.

      Your Q and A is correct, but that Q is not parallel to the bat and ball question.

  • 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
        1.05>1.00
        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

        • Caroline

          That is not what the question is saying the question is the bat is exactly one dollar more than the ball so if the ball is $20 the bat would be $21 the same way as if the ball is 5 cents the bat would be 1.05 which equals 1.10

          • Jessica2248

            I think it said “more than a dollar more”, not one dollar more.

  • 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.

      • ?Bzay ?????????

        Good looking

  • 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?

    • Caroline

      It has to be exactly one dollar more so if it was 9 cents that would be 1.09+.09=1.18 that does not equal 1.10 the only way for it to equal 1.10 is to divide 10 by 2 and get 5 so that 1.05+.05=1.10

      • Privat Privat

        if bat costs 1 dollar how much is ball gona cost if its 1 dollar cheeper than the bat.

        or and if we run with the answer from above aka 0,05 then

        0,05+1,00=1,05

    • Brian Knight

      Wrong. The total is $1.10

      If the ball was 9 cents, the bat would be $1 more, making a total of $1.09, not possible. There is only 1 answer. $1.05 + 0.5 (ball) =$1.10

  • I forget my name

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

  • Fred the cow

    MOOOOOOO

  • 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?

    • Jessica2248

      That you think intuitively, rather than analytically. I think most of us do.

  • 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

  • Sam

    .10 CENTS IS THE CORRECT ANSWER
    Bat is one dollar more than the ball
    The correct equation:
    1.00 should be subtracted from the total sum of
    1.10 which is the total sum we are asked to work with. We were not asked to work with the total sum of 1.00 (as you equation erroneously states) but one dollar MORE than the combined total we are given.
    1.05 does not equate to being 1.00 more. It equates to being 1.05 more than the bat when you are given a total sum of 1.10 to work with. This is BS and trickery and why many people do not fully trust mathmatics and science. I believe in a creator god btw. The evidence… I walk outside my front door to a vast universe that was created by something that is completley incomprehensible to the limitations of the human mind. Only the immense ego of man would somehow think they have it all figured or CAN figure it all out. I do not believe in organized religion but i definately believe in.a higher power.. I got two out of three questions right. I’ll make that three with the correction of your bogus #1 answer.

    • Sam

      Should have said 1.00 more based on the combined total we are given.

      • paulette

        … but $1.00 is only 90 cents more than 10 cents.. to cost $1.00 more the bat would be 1.05 and the ball would be .05 … equalling $1.10.

        • Sam

          We are being given a sum for the Total price for the combined items. That sum is not 1.00. The sum we are given is 1.10. We are asked to decide what each items cost is based on that sum with the caveate that the bat is one dollar more.

          • paulette

            ok.. but if you have 5 cents and I have one dollar more than you… I would have to have 1 dollar and 5 cents, or I would not have 1 dollar MORE than you..

  • Jay A.

    “You believe in religion”

    And atheists believe in the talking snake on an exoplanet near the Andromeda galaxy.

    This is sincerely the stupidest conclusion anyone who’s ever conducted a reasearch has come to.

    • billybareblu

      This isn’t research into the belief of religion, it’s just a statistic that happens to match on people choosing a particular answer.

  • 1 Room Studios

    I get my bats from China, you guys are overpaying.

  • billybareblu

    I can understand initially getting the answer wrong, but I can’t understand continuing to argue the point after it is explained in the article as well as multiple times in the comments.

    • dukecheermom

      Exactly!!!

  • george orwell

    I understand the algebra used to determine the answer to the question. Makes sense. Here’s another riddle: If you walk into this store, grab a $1 bat, and .05 ball, and put them on the counter (assuming no taxes), can you give the clerk $1.05 to buy them?

  • Read the question carefully

    What a lot of you don’t seem to be getting is that the bat is a dollar more than the ball not a dollar more than the sum of the ball and the bat. Go and reread the question and you’ll see that that’s where you came unstuck.

  • Sorry mistyped

    Sorry I phrased that wrong- I meant to say the bat is a dollar more than the ball but the sum of the ball and the bat isn’t a dollar more than the ball. Just had a major dyslexic moment there…

  • Barbara

    Who makes this crap up? I mean, really? There are TWO points to this ridiculous equation – their point and the actual mathematical equation. Neither answer is wrong.

    • Dacker

      In the stated question, the bat can only be $1.05.
      all other answers are wrong.

  • Safe Search Kids

    None of this was making sense and even after reading the comments I was getting even more confised, then found an answer on a different site that explained it in a more simple way. So here goes… “If the ball cost 10 cents and the bat costs $1.00 more than the ball,
    then the bat would cost $1.10 for a grand total of $1.20. The correct
    answer to this problem is that the ball costs 5 cents and the bat costs —
    at a dollar more — $1.05 for a grand total of $1.10.”

    For me, it really came down to fact that no one here stated the problem of arriving at an incorrect total of $1.20. When I saw that, the light came on for me. For the bat to be a dollar MORE, you have to add a dollar to the cost of the ball to arrive at $1.10 total.

  • Joe

    I wouldn’t be goin to Harvard. I’d be buying out all those balls at $.05 each and ball out with the profit. Haaaa