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# This will probably never appear on the GMAT but I did see it

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This will probably never appear on the GMAT but I did see it [#permalink]  17 Jan 2006, 21:29
This will probably never appear on the GMAT but I did see it somewhere else so... you can skip it if you do not know how to do it or do not want to bother with it.

There are 12 bags of coins where one of the bags contains fake coins. We were told that fake coins weigh 1 gram less than real coins. Find the least number of times we need to weigh in order to figure out which bag contains the fake coins.

A. 1
B. 2
C. 4
D. 8
E. 16

I left something out: Assume each bag has equal number of coins and the number of coins in a bag is 100.

Last edited by coolfish1103 on 18 Jan 2006, 01:13, edited 1 time in total.
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Re: Bag of Coins (Challenge Question) [#permalink]  17 Jan 2006, 22:18
good question. i go with

B. 2
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[#permalink]  17 Jan 2006, 22:28
It looks more of a puzzle.
I woulg go with 2.
Would sound illogical but i broke 12 into prime factors 2*2*3
and just chose the least prime no.
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[#permalink]  17 Jan 2006, 22:32
I have no idea but got 6. Since that is not a choice, 8 would be my answer.

6 6
3 3
1 1 1
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[#permalink]  17 Jan 2006, 22:43
I am getting 3.

Divide in 3 heaps of 4 each.

Weigh any two. If fake coin bag is among these two then one side will weigh less. If both weigh equal then the third group of 4 bags has the fake coin bag.

Now we have 4 bags. Same way make group of 2 bags each.

Weigh them and find out which group has the fake coin bag.

Now we have 2 bags. Weigh them with each other and we will find the bag.
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Re: Bag of Coins (Challenge Question) [#permalink]  17 Jan 2006, 22:45
Professor wrote:
good question. i go with: B. 2

if by chance, you get two different bags at first and second weig, you are done and it says at least..
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[#permalink]  17 Jan 2006, 22:53
From 12 bags how will you pinpoint to that one bag.
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[#permalink]  18 Jan 2006, 00:55
It is more of a puzzle I guess than math question because it requires more logic/tricks than just calculations in a sense..

Let me know when it is a good time to post the solution =)

Note: You are not limited to just the bags and the weights.
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[#permalink]  18 Jan 2006, 01:06
One way to do is
6/6 (One will have less weight)
3/3 (One will have less weight)
1/1 (if they are same than the third one else which one does not have weight!

So I guess answer is 3

we can also do
5/5 which will give answer either 2 or 3

if we start with 4/4 still answer will be 3

Can you really do it in 2 or 1?
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[#permalink]  18 Jan 2006, 01:14
I re-read my question and I realized that I forgot to put one line down. Sorry about that.
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[#permalink]  18 Jan 2006, 05:22
is it 2???

as per logic..

u pick up 1st bag...and it is = 1gms( real coins) ----> 1 try
u pick the 2nd bag and if ure lucky u get
a 2nd bag = 50gms ( fake coins) ---- > 2nd try...

again in ur first try u get a 50gm bag ( fake coins) , u have no idea if it is fake or real...pick up a bag and that has to be = 100gms ( real coins)
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[#permalink]  18 Jan 2006, 10:11
All the guys who says 2 please explain!..
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[#permalink]  18 Jan 2006, 10:29
Ok, letâ€™s be innovative...Assume my weight machine will tell me difference in to gramsâ€¦.

Lets create new two begs...
Beg 1:
Add 2 Coin from Bag 2
Add 3 Coin from Bag 3
Add 4 Coin from Bag 4
Add 5 Coin from Bag 5
Add 6 Coin from Bag 6

Beg 7
Add 2 Coin from Bag 8
Add 3 Coin from Bag 9
Add 4 Coin from Bag 10
Add 5 Coin from Bag 11
Add 6 Coin from Bag 12

Now Get Weigh of
(Beg1-Beg2)

If Delta is +1 gram = Answer is Beg 7
If Delta is +2 gram = Answer is Beg 8
If Delta is +3 gram = Answer is Beg 9
If Delta is +4 gram = Answer is Beg 10
If Delta is +5 gram = Answer is Beg 11
If Delta is +6 gram = Answer is Beg 12

If Delta is -1 gram = Answer is Beg 1
If Delta is -2 gram = Answer is Beg 2
If Delta is -3 gram = Answer is Beg 3
If Delta is -4 gram = Answer is Beg 4
If Delta is -5 gram = Answer is Beg 5
If Delta is -6 gram = Answer is Beg 6

So done in one Timm...
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[#permalink]  18 Jan 2006, 10:57
coolfish1103 wats the OA & OE:?::?:
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[#permalink]  18 Jan 2006, 14:59
Official Answer is 1.

One of the Explanation that is provided is very close to chiragr's answer.

Since the problem did not specify which weighing machine we can use, we may assume that we are using a machine that will tell us the actual numbers.

Use a marker to mark each bag with the numbers 1-12, then take coins out from each bag based on their bag number. Therefore, 1 coin will be taken out from Bag 1, 2 coins will be taken out from Bag 2, and so on till Bag 12. There should be a total of 78 coins take out from all the bags.

Suppose that real coins weigh 2 grams, which make fake coins weigh 1 gram. If they are all real coins, then the weighing machine should show 78x2 = 156 grams. If the weighing machine shows a different number, let's say 154, then we know that Bag 2 is the one with Fake Coins because 156-154 = 2.

If people like these type of questions, let me know and I will post more =)
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[#permalink]  18 Jan 2006, 18:34
coolfish1103 wrote:
Official Answer is 1.

One of the Explanation that is provided is very close to chiragr's answer.

Since the problem did not specify which weighing machine we can use, we may assume that we are using a machine that will tell us the actual numbers.

Use a marker to mark each bag with the numbers 1-12, then take coins out from each bag based on their bag number. Therefore, 1 coin will be taken out from Bag 1, 2 coins will be taken out from Bag 2, and so on till Bag 12. There should be a total of 78 coins take out from all the bags.

Suppose that real coins weigh 2 grams, which make fake coins weigh 1 gram. If they are all real coins, then the weighing machine should show 78x2 = 156 grams. If the weighing machine shows a different number, let's say 154, then we know that Bag 2 is the one with Fake Coins because 156-154 = 2.

If people like these type of questions, let me know and I will post more =)

i donot think 1 time works for this one. ok, we got the total weight 154, now how do you know which bag contains the fake one. you have to weight again, at least once.
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[#permalink]  18 Jan 2006, 21:06
Professor wrote:
i donot think 1 time works for this one. ok, we got the total weight 154, now how do you know which bag contains the fake one. you have to weight again, at least once.

You took out...

1 coin from Bag 1
2 coins from Bag 2
3 coins from Bag 3
4 coins from Bag 4
5 coins from Bag 5
6 coins from Bag 6
7 coins from Bag 7
8 coins from Bag 8
9 coins from Bag 9
10 coins from Bag 10
11 coins from Bag 11
12 coins from Bag 12

Suppose real coins weigh 2 grams, which makes fake coins weigh 1 gram.

You will have a total of 78 coins, if they were to be all real coins, then the weighing machine should show, 78 x 2 = 156 grams.

There is only 1 bag that contains fake coins, so you will know which bag contains the fake coins by knowing the real weight of the 78 coins.

That is my explanation, don't know if I left something out or something is wrong with it.
[#permalink] 18 Jan 2006, 21:06
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