# Deceptively easy math word problems for high school kids **URL:** \ **Category:** Miscellaneous and Personal Stuff I Must Share\ **Created:** [February 2, 2012, 7:31pm UTC](https://boards.straightdope.com/t/deceptively-easy-math-word-problems-for-high-school-kids/611563 "2012-02-02T19:31:57Z")\ **Posts on this page:** 20\ **Page:** 6
**Author:** ![Bosstone](https://avatars.discourse-cdn.com/v4/letter/b/22d042/32.png) [@Bosstone](https://boards.straightdope.com/u/Bosstone)\ **Post date:** [February 4, 2012, 8:08pm UTC](https://boards.straightdope.com/t/deceptively-easy-math-word-problems-for-high-school-kids/611563/101 "2012-02-04T20:08:55Z")
> [@Left\_Hand\_of\_Dorkness](#): > > Am I missing something? No, because you’re not a kid. > [@Shark\_Sandwich](#): > > Surprisingly easy, especially if you draw it. Most kids will say they’ll drain water at an equal rate. ---
**Author:** ![cochrane](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/cochrane/32/10441_2.png) [@cochrane](https://boards.straightdope.com/u/cochrane)\ **Post date:** [February 4, 2012, 8:26pm UTC](https://boards.straightdope.com/t/deceptively-easy-math-word-problems-for-high-school-kids/611563/102 "2012-02-04T20:26:57Z")
> [@from\_a\_to\_z](#): > > Well, near be it from me to look at a problem wrong, and/or to overlook the obvious, but for me the answer of 20 minutes assumes that each cut has to take the same amount of time. > > But regardless of how long the first cut takes – for example, assuming that the board is of equal consistency throughout, then cutting off a corner of the board – the second cut can be to cut off a corner of the smaller piece. And the second cut would take a shorter time than the first cut, no? So an answer would be 10+ minutes. > [@brocks](#): > > Even if the cuts are of equal length, if you use my saw, the second cut will take a lot longer than the first, because the teeth got dull from the first cut. Eh. To me, both of these are examples of overthinking the question. Why introduce variables into the question that weren’t mentioned in it? ---
**Author:** ![TriPolar](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/tripolar/32/3008_2.png) [@TriPolar](https://boards.straightdope.com/u/TriPolar)\ **Post date:** [February 4, 2012, 8:48pm UTC](https://boards.straightdope.com/t/deceptively-easy-math-word-problems-for-high-school-kids/611563/103 "2012-02-04T20:48:37Z")
> [@cochrane](#): > > Eh. To me, both of these are examples of overthinking the question. Why introduce variables into the question that weren’t mentioned in it? Because that’s what Dopers do. ---
**Author:** ![MaxTheVool](https://avatars.discourse-cdn.com/v4/letter/m/9fc29f/32.png) [@MaxTheVool](https://boards.straightdope.com/u/MaxTheVool)\ **Post date:** [February 4, 2012, 9:00pm UTC](https://boards.straightdope.com/t/deceptively-easy-math-word-problems-for-high-school-kids/611563/104 "2012-02-04T21:00:45Z")
Assume the earth is a perfect solid sphere. Construct a metal band all the way around the earth’s equator, snug with the ground. Now increase the length of that band by 1 foot, distributed evenly. Would it be possible to slip a knife blade between the band and the earth’s surface? ---
**Author:** ![Musicat](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/musicat/32/20189_2.png) [@Musicat](https://boards.straightdope.com/u/Musicat)\ **Post date:** [February 4, 2012, 9:21pm UTC](https://boards.straightdope.com/t/deceptively-easy-math-word-problems-for-high-school-kids/611563/105 "2012-02-04T21:21:39Z")
> [@MaxTheVool](#): > > Would it be possible to slip a knife blade between the band and the earth’s surface? How thick is the knife blade? ---
**Author:** ![MaxTheVool](https://avatars.discourse-cdn.com/v4/letter/m/9fc29f/32.png) [@MaxTheVool](https://boards.straightdope.com/u/MaxTheVool)\ **Post date:** [February 5, 2012, 3:47am UTC](https://boards.straightdope.com/t/deceptively-easy-math-word-problems-for-high-school-kids/611563/106 "2012-02-05T03:47:54Z")
> [@Musicat](#): > > How thick is the knife blade? If you are asking, you already have the wrong answer. ---
**Author:** ![Indian](https://avatars.discourse-cdn.com/v4/letter/i/c0e974/32.png) [@Indian](https://boards.straightdope.com/u/Indian)\ **Post date:** [February 5, 2012, 4:23am UTC](https://boards.straightdope.com/t/deceptively-easy-math-word-problems-for-high-school-kids/611563/107 "2012-02-05T04:23:56Z")
> [@MaxTheVool](#): > > Assume the earth is a perfect solid sphere. Construct a metal band all the way around the earth’s equator, snug with the ground. Now increase the length of that band by 1 foot, distributed evenly. > > Would it be possible to slip a knife blade between the band and the earth’s surface? Using algebra, yes one can slip a knife. D1= diameter of first circle D2=diameter of 2nd (big) circle C1= circumference of 1st circle C2= circumference of 2nd (big) circle C2=C1+1 The space between the spheres will be( D2-D1)/2 D2-D1= [(C1+1)/pi-C1/pi)]=[C1+1-C1]/pi=1/pi Distance between spheres is =(1/pi)/2= 1/(2xpi)= 1/6.28=0.15 foot= 4.8 cms Yes, the problem is deceptive. ---
**Author:** ![Inner\_Stickler](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/inner_stickler/32/318_2.png) [@Inner\_Stickler](https://boards.straightdope.com/u/Inner_Stickler)\ **Post date:** [February 5, 2012, 4:35am UTC](https://boards.straightdope.com/t/deceptively-easy-math-word-problems-for-high-school-kids/611563/108 "2012-02-05T04:35:29Z")
> [@Indistinguishable](#): > > Put another way, giving anyone a test with conflicting instructions is dooming them to failure, one way or another; there’s no call to feel smug, then, when they happen to fail the unpassable test. Do you also feel frustrated when you begin a recipe at step 2 and your pie never cooks because you didn’t preheat the oven in step 1? The point of the test isn’t to trip students up, it’s to underline the importance of reading all the instructions before doing anything and hopefully to go about it in an amusing way. If you did poke holes in your paper and so on but learned the lesson about instructions, then you didn’t fail the test at all. ---
**Author:** ![Musicat](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/musicat/32/20189_2.png) [@Musicat](https://boards.straightdope.com/u/Musicat)\ **Post date:** [February 5, 2012, 5:28am UTC](https://boards.straightdope.com/t/deceptively-easy-math-word-problems-for-high-school-kids/611563/109 "2012-02-05T05:28:40Z")
> [@MaxTheVool](#): > > If you are asking, you already have the wrong answer. Not at all. If indian’s calcs are right, a knife thicker than 4.8cm would not work. ---
**Author:** ![Chef\_Troy](https://avatars.discourse-cdn.com/v4/letter/c/85f322/32.png) [@Chef\_Troy](https://boards.straightdope.com/u/Chef_Troy)\ **Post date:** [February 5, 2012, 5:45am UTC](https://boards.straightdope.com/t/deceptively-easy-math-word-problems-for-high-school-kids/611563/110 "2012-02-05T05:45:40Z")
> [@Malacandra](#): > > I disagree; on the assumption that you’re using the same units throughout, “total temperature” is meaningful or else you could never work out “average temperature” – which is a concept I’m assuming you’re cool with. I think the trap is as per my previous post. I would have thought the problem is that since there’s no overlap in the stars seen by John and by his father (i.e., there is no color of star that’s seen by both of them), there can be no meaningful total of stars seen by John AND his father, since there are no stars in that set. ---
**Author:** ![Indian](https://avatars.discourse-cdn.com/v4/letter/i/c0e974/32.png) [@Indian](https://boards.straightdope.com/u/Indian)\ **Post date:** [February 5, 2012, 6:11am UTC](https://boards.straightdope.com/t/deceptively-easy-math-word-problems-for-high-school-kids/611563/111 "2012-02-05T06:11:03Z")
> [@MaxTheVool](#): > > If you are asking, you already have the wrong answer. Max, Don’t you know dopers are experts in pedantry?😃 ---
**Author:** ![Indian](https://avatars.discourse-cdn.com/v4/letter/i/c0e974/32.png) [@Indian](https://boards.straightdope.com/u/Indian)\ **Post date:** [February 5, 2012, 12:29pm UTC](https://boards.straightdope.com/t/deceptively-easy-math-word-problems-for-high-school-kids/611563/112 "2012-02-05T12:29:44Z")
> [@Fool\_in\_the\_Rain](#): > > Not trying to sound snarky or lecturing, but, the point of the question is to read the entire problem before answering it. Some would immediately start counting the people, others would read the whole thing, realize the question, and then start counting. > > It’s along the lines of a **50 question college entrance** exam I once saw, where at the top of the first page, above where you write your name it says, “Do not write anything on this test before reading all the questions first.” > > On page 5, question 50 says: Do not write anything on this test. > > It’s tricky, but simple if you read everything before you start. This sounds like a very expensive way of testing attention skills. ---
**Author:** ![Left\_Hand\_of\_Dorkness](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/left_hand_of_dorkness/32/7156_2.png) [@Left\_Hand\_of\_Dorkness](https://boards.straightdope.com/u/Left_Hand_of_Dorkness)\ **Post date:** [February 5, 2012, 2:25pm UTC](https://boards.straightdope.com/t/deceptively-easy-math-word-problems-for-high-school-kids/611563/113 "2012-02-05T14:25:40Z")
> [@indian](#): > > Using algebra, yes one can slip a knife. > > D1= diameter of first circle > D2=diameter of 2nd (big) circle > > C1= circumference of 1st circle > C2= circumference of 2nd (big) circle > > C2=C1+1 > > The space between the spheres will be( D2-D1)/2 > > D2-D1= [(C1+1)/pi-C1/pi)]=[C1+1-C1]/pi=1/pi > > Distance between spheres is =(1/pi)/2= 1/(2xpi)= 1/6.28=0.15 foot= 4.8 cms > > Yes, the problem is deceptive. Very persuasive math, and this one totally got me when I first read it! Here’s how I had to process the explanation; it might help others who find it difficult to read math: -The question is really, by how much does the diameter of the band increase when you increase the circumference by a foot? -That diameter increase will be divided in half (half on each side of the globe). -When you increase the diameter of a circle, the circumference increases by that same amount times pi. -Conversely, when you increase the circumference of a circle, the diameter increases by that same amount divided by pi–i.e., by a little less than a third of the same amount. -Since you’re increasing the circumference by 1 foot, the diameter increases by a foot divided by pi–i.e., a little less than four inches. -That four inch increase is cut in half–half on each side of the globe. -It’s therefore a little less than two inches on each side. ---
**Author:** ![Indian](https://avatars.discourse-cdn.com/v4/letter/i/c0e974/32.png) [@Indian](https://boards.straightdope.com/u/Indian)\ **Post date:** [February 5, 2012, 3:49pm UTC](https://boards.straightdope.com/t/deceptively-easy-math-word-problems-for-high-school-kids/611563/114 "2012-02-05T15:49:57Z")
> [@Left\_Hand\_of\_Dorkness](#): > > Very persuasive math, and this one totally got me when I first read it! > > Here’s how I had to process the explanation; it might help others who find it difficult to read math: > -The question is really, by how much does the diameter of the band increase when you increase the circumference by a foot? > -That diameter increase will be divided in half (half on each side of the globe). > -When you increase the diameter of a circle, the circumference increases by that same amount times pi. > -Conversely, when you increase the circumference of a circle, the diameter increases by that same amount divided by pi–i.e., by a little less than a third of the same amount. > -Since you’re increasing the circumference by 1 foot, the diameter increases by a foot divided by pi–i.e., a little less than four inches. > -That four inch increase is cut in half–half on each side of the globe. > -It’s therefore a little less than two inches on each side. Very logical deduction.🙂 ---
**Author:** ![Baffle](https://avatars.discourse-cdn.com/v4/letter/b/dec6dc/32.png) [@Baffle](https://boards.straightdope.com/u/Baffle)\ **Post date:** [February 5, 2012, 6:23pm UTC](https://boards.straightdope.com/t/deceptively-easy-math-word-problems-for-high-school-kids/611563/115 "2012-02-05T18:23:55Z")
> [@lawbuff](#): > > Take four 9’s; 9-9-9-9; and put them in a mathematical equation to equal 100. There are 2 answers that I know of. 99 + (9/9) 99 / .99 99 + .99… (.99 repeating) ---
**Author:** ![Musicat](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/musicat/32/20189_2.png) [@Musicat](https://boards.straightdope.com/u/Musicat)\ **Post date:** [February 5, 2012, 6:35pm UTC](https://boards.straightdope.com/t/deceptively-easy-math-word-problems-for-high-school-kids/611563/116 "2012-02-05T18:35:35Z")
> [@Baffle](#): > > 99 + .99… (.99 repeating) It seems to me that that will never equal 100, but come infinitely close. ---
**Author:** ![Inner\_Stickler](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/inner_stickler/32/318_2.png) [@Inner\_Stickler](https://boards.straightdope.com/u/Inner_Stickler)\ **Post date:** [February 5, 2012, 6:45pm UTC](https://boards.straightdope.com/t/deceptively-easy-math-word-problems-for-high-school-kids/611563/117 "2012-02-05T18:45:11Z")
.999 repeating is merely another way of representing 1. ---
**Author:** ![Baffle](https://avatars.discourse-cdn.com/v4/letter/b/dec6dc/32.png) [@Baffle](https://boards.straightdope.com/u/Baffle)\ **Post date:** [February 5, 2012, 6:45pm UTC](https://boards.straightdope.com/t/deceptively-easy-math-word-problems-for-high-school-kids/611563/118 "2012-02-05T18:45:39Z")
> [@Musicat](#): > > It seems to me that that will never equal 100, but come infinitely close. That’s the ‘gut feeling’ mistake. Wikipedia has [an article](http://en.wikipedia.org/wiki/.999) on the number, but the proof that convinced me was simple: 1/3 = .333 repeating 2/3 = .666 repeating 1/3 + 2/3 = 3/3 = 1 .333 repeating + .666 repeating = .999 repeating = 1 ---
**Author:** ![Quercus](https://avatars.discourse-cdn.com/v4/letter/q/7ab992/32.png) [@Quercus](https://boards.straightdope.com/u/Quercus)\ **Post date:** [February 6, 2012, 2:25pm UTC](https://boards.straightdope.com/t/deceptively-easy-math-word-problems-for-high-school-kids/611563/119 "2012-02-06T14:25:15Z")
“As I was going to Saint Ives…” ---
**Author:** ![Indian](https://avatars.discourse-cdn.com/v4/letter/i/c0e974/32.png) [@Indian](https://boards.straightdope.com/u/Indian)\ **Post date:** [February 6, 2012, 3:00pm UTC](https://boards.straightdope.com/t/deceptively-easy-math-word-problems-for-high-school-kids/611563/120 "2012-02-06T15:00:44Z")
> [@Quercus](#): > > “As I was going to Saint Ives…” what happened on the way? 😉 [Previous page](https://boards.straightdope.com/t/deceptively-easy-math-word-problems-for-high-school-kids/611563.md?page=5) [Next page](https://boards.straightdope.com/t/deceptively-easy-math-word-problems-for-high-school-kids/611563.md?page=7)