MacRumors Forums Can anyone get this tricky math problem?

Feb 9, 2008, 04:13 PM   #51
techlover828
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Quote:
 Originally Posted by Doctor Q Can you prove which is larger, e^pi or pi^e, using properties of those numbers rather than simply computing the exponentials? It's a real question, not a trick. I had this problem on a test. If only I could remember the answer!
e is smaller right? so e^pi would be larger.
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Feb 9, 2008, 04:15 PM   #52
fridgeymonster3
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Quote:
 Originally Posted by Doctor Q Can you prove which is larger, e^pi or pi^e, using properties of those numbers rather than simply computing the exponentials?
I don't think your using the properties of those numbers since the properties are their actual values. If you use ln or maybe f(x) I think you can derive the answer. Not that I feel like doing the actual work, or taking the time to find the answer online . But i think with the natural log you can show the reason behind one being bigger than the other.
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Feb 9, 2008, 04:18 PM   #53
jsw
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Quote:
 Originally Posted by techlover828 e is smaller right? so e^pi would be larger.
Well, I'm not sure I follow that logic (for example 1 < 2, but 1^2 < 2^1), but this provides a better explanation.
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Feb 9, 2008, 04:19 PM   #54
techlover828
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Quote:
 Originally Posted by jsw Well, I'm not sure I follow that logic (for example 1 < 2, but 1^2 < 2^1), but this provides a better explanation.
i hate proofs, plus I'm only half way through souph year so haven't done proofs.
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Feb 9, 2008, 04:20 PM   #55
fridgeymonster3
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Quote:
 Originally Posted by jsw this provides a better explanation.
hey using exponential function like i suggested. wow, now only if i was smart enough to do the mathematical computation I would have posted the answer
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 Feb 9, 2008, 04:39 PM #56 Nermal Moderator     Join Date: Dec 2002 Location: Whakatane, New Zealand In a recent introductory offer, a special brand of brandy in a fanciful bottle was promoted at \$120 per bottle. If the brandy itself cost \$105 more than the container, how much was the empty bottle worth? 0
Feb 9, 2008, 04:47 PM   #57
techlover828
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Quote:
 Originally Posted by Nermal In a recent introductory offer, a special brand of brandy in a fanciful bottle was promoted at \$120 per bottle. If the brandy itself cost \$105 more than the container, how much was the empty bottle worth?
I want to say 15 but there must be something more, obviously.

edit: does it have anything to do with you changing bottle to container in one sentence?
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Feb 9, 2008, 04:49 PM   #58
swiftaw
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Quote:
 Originally Posted by Nermal In a recent introductory offer, a special brand of brandy in a fanciful bottle was promoted at \$120 per bottle. If the brandy itself cost \$105 more than the container, how much was the empty bottle worth?
Logic would seem to indicate \$7.50, but I'm sure I'm missing a trick somewhere.
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Feb 9, 2008, 04:50 PM   #59
Nermal
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Location: Whakatane, New Zealand
Quote:
 Originally Posted by techlover828 edit: does it have anything to do with you changing bottle to container in one sentence?
No. I'm quoting straight out of a book but the container and the bottle are the same thing.

Quote:
 Originally Posted by techlover828 I want to say 15 but there must be something more, obviously.
Quote:
 Originally Posted by swiftaw Logic would seem to indicate \$7.50, but I'm sure I'm missing a trick somewhere.
Bingo. Swift got it right, but as you can see above, some people say \$15!
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Feb 9, 2008, 04:52 PM   #60
fridgeymonster3
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Quote:
 Originally Posted by Nermal In a recent introductory offer, a special brand of brandy in a fanciful bottle was promoted at \$120 per bottle. If the brandy itself cost \$105 more than the container, how much was the empty bottle worth?
I have to say \$7.50 also

A = Brandy
B = Bottle

A = B + 105 (Brandy costs \$105 more than Bottle)

\$120 = (B+105) + B

B = \$7.50
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 Feb 9, 2008, 04:54 PM #61 swiftaw macrumors 603     Join Date: Jan 2005 Location: Omaha, NE, USA How about this one: Three hotel guests stay together. They receive a bill for \$30. They each put \$10 on the table, which the bellhop collects and takes to the till. The cashier informs the bellhop that the bill should only have been for \$25 and returns \$5 to the bellhop in \$1 bills. On the way back to the room the bellhop realizes that he cannot divide the bills equally between the guests. As they didn’t know the total of the revised bill, he dishonestly decides to put \$2 in his own pocket and give each of the guests \$1. Now that each guest has been given a dollar back, each of them has paid \$9. Three times 9 is 27. The bellhop has \$2 in his pocket. Two plus 27 is \$29. The guests originally handed over \$30. Where is the missing dollar? 0
Feb 9, 2008, 04:54 PM   #62
techlover828
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Quote:
 Originally Posted by fridgeymonster3 I have to say \$7.50 also A = Brandy B = Bottle A = B + 105 (Brandy costs \$105 more than Bottle) \$120 = (B+105) + B B = \$7.50
I'm stupid I love algebra
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Feb 9, 2008, 04:55 PM   #63
fridgeymonster3
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Quote:
 Originally Posted by EricNau I love this one: Give the next two numbers in this sequence: 9, 10, 11, 12, 13, 14, 21, ...
are the next two - 100, 1001??

having to do with binary number equivalents?
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Feb 9, 2008, 04:58 PM   #64
techlover828
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Quote:
 Originally Posted by swiftaw How about this one: Three hotel guests stay together. They receive a bill for \$30. They each put \$10 on the table, which the bellhop collects and takes to the till. The cashier informs the bellhop that the bill should only have been for \$25 and returns \$5 to the bellhop in \$1 bills. On the way back to the room the bellhop realizes that he cannot divide the bills equally between the guests. As they didn’t know the total of the revised bill, he dishonestly decides to put \$2 in his own pocket and give each of the guests \$1. Now that each guest has been given a dollar back, each of them has paid \$9. Three times 9 is 27. The bellhop has \$2 in his pocket. Two plus 27 is \$29. The guests originally handed over \$30. Where is the missing dollar?
that's a good one, I have no idea

Last edited by techlover828; Feb 27, 2008 at 06:49 PM.
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Feb 9, 2008, 05:06 PM   #65
fridgeymonster3
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Quote:
 Originally Posted by swiftaw How about this one: Three hotel guests stay together. They receive a bill for \$30. They each put \$10 on the table, which the bellhop collects and takes to the till. The cashier informs the bellhop that the bill should only have been for \$25 and returns \$5 to the bellhop in \$1 bills. On the way back to the room the bellhop realizes that he cannot divide the bills equally between the guests. As they didn’t know the total of the revised bill, he dishonestly decides to put \$2 in his own pocket and give each of the guests \$1. Now that each guest has been given a dollar back, each of them has paid \$9. Three times 9 is 27. The bellhop has \$2 in his pocket. Two plus 27 is \$29. The guests originally handed over \$30. Where is the missing dollar?
you are doing some voodoo wording there aren't you
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 Feb 9, 2008, 05:10 PM #66 techlover828 macrumors 68020     Join Date: Jun 2007 you need to subtract 2, not add it (\$10 - \$1) x 3 - \$2 = \$25. this is the bill amount 0
Feb 9, 2008, 05:11 PM   #67
swiftaw
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Quote:
 Originally Posted by techlover828 you need to subtract 2, not add it
Bingo
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Feb 9, 2008, 05:12 PM   #68
techlover828
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Quote:
 Originally Posted by swiftaw Bingo
ok, i cheated.
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Feb 9, 2008, 05:14 PM   #69
EricNau
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Location: San Francisco, CA
Quote:
 Originally Posted by swiftaw How about this one: Three hotel guests stay together. They receive a bill for \$30. They each put \$10 on the table, which the bellhop collects and takes to the till. The cashier informs the bellhop that the bill should only have been for \$25 and returns \$5 to the bellhop in \$1 bills. On the way back to the room the bellhop realizes that he cannot divide the bills equally between the guests. As they didn’t know the total of the revised bill, he dishonestly decides to put \$2 in his own pocket and give each of the guests \$1. Now that each guest has been given a dollar back, each of them has paid \$9. Three times 9 is 27. The bellhop has \$2 in his pocket. Two plus 27 is \$29. The guests originally handed over \$30. Where is the missing dollar?
There is no missing dollar.

You shouldn't be adding the \$2, you need to subtract it. Remember, the total is \$25, not \$30. Therefore, each guest paid \$9 x 3 = \$27 - the stolen \$2 = \$25.

EDIT: Darn, too slow. I heard that one years ago, but it took me a minute to remember the answer!

Has anyone figured out this sequence yet?

Give the next two numbers in this sequence: 9, 10, 11, 12, 13, 14, 21, ...
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Feb 9, 2008, 05:19 PM   #70
fridgeymonster3
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Quote:
 Originally Posted by EricNau Has anyone figured out this sequence yet? Give the next two numbers in this sequence: 9, 10, 11, 12, 13, 14, 21, ...
Dude, I just posted an answer above...Look Up!

Am I right or close?
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Feb 9, 2008, 05:22 PM   #71
swiftaw
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Quote:
 Originally Posted by EricNau Has anyone figured out this sequence yet? Give the next two numbers in this sequence: 9, 10, 11, 12, 13, 14, 21, ...
100, 1001 (It is the number 9 expressed in bases 10 through 2)
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 Feb 9, 2008, 05:23 PM #72 Dros macrumors 6502   Join Date: Jun 2003 A man hires you to tie a rope loop around the equator of spheres as an art project. You use a short length of rope to tie a rope around the 'equator' of a basketball, more rope to circle a hot air balloon, and a lot of rope to circle the Earth. When you tell him you finished, he thinks about it and says the rope is too snug against the sphere and that he was wanting the rope to be about a foot off the surface all the way around each of the 3 spheres. He points to little poles you can use to lift the rope off the surface, and goes to the 'rope room' to get you an extension. He comes back with around 6 ft of rope, and says he'll be back later with rope to extend the other two. Which sphere do you go to with the 6 ft of rope to extend the loop? 0
Feb 9, 2008, 05:23 PM   #73
EricNau
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Quote:
 Originally Posted by fridgeymonster3 Dude, I just posted an answer above...Look Up! Am I right or close?
Sorry 'bout that.

Yes, 100, 1001 are indeed the next two (and only two) numbers left in the sequence. Congratulations.

Each number in the sequence is "nine" represented in a different number systems starting with base-10 and ending with ternary and binary.

Last edited by EricNau; Feb 9, 2008 at 05:34 PM. Reason: typo
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Feb 9, 2008, 05:26 PM   #74
swiftaw
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Quote:
 Originally Posted by Dros A man hires you to tie a rope loop around the equator of spheres as an art project. You use a short length of rope to tie a rope around the 'equator' of a basketball, more rope to circle a hot air balloon, and a lot of rope to circle the Earth. When you tell him you finished, he thinks about it and says the rope is too snug against the sphere and that he was wanting the rope to be about a foot off the surface all the way around each of the 3 spheres. He points to little poles you can use to lift the rope off the surface, and goes to the 'rope room' to get you an extension. He comes back with around 6 ft of rope, and says he'll be back later with rope to extend the other two. Which sphere do you go to with the 6 ft of rope to extend the loop?
Any of them

The length of the original rope is 2*pi*r. where r is the radius of the sphere
The length of the extended rope needs to be 2*pi*(r+1).

So the difference = 2*pi*(r+1) = 2*pi*r = 2*pi which is approximately 6 feet it is independent of the radius of the sphere
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 Feb 9, 2008, 05:51 PM #75 JML42691 macrumors 68020     Join Date: Oct 2007 There are two known ways to make \$1.00 out of 50 coins, what are they? Assuming that we are using American currency: \$.01 \$.05 \$.10 \$.25 \$.50 0

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