No, because you’re not a kid.
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.
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?
How thick is the knife blade?
If you are asking, you already have the wrong answer.
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.
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.
Not at all. If indian’s calcs are right, a knife thicker than 4.8cm would not work.
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.
Max,
Don’t you know dopers are experts in pedantry?
This sounds like a very expensive way of testing attention skills.
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.
99 + (9/9)
99 / .99
99 + .99… (.99 repeating)
It seems to me that that will never equal 100, but come infinitely close.
.999 repeating is merely another way of representing 1.
That’s the ‘gut feeling’ mistake. Wikipedia has an article 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
“As I was going to Saint Ives…”
what happened on the way?
