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# M07-18

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Math Expert
Joined: 02 Sep 2009
Posts: 59712

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16 Sep 2014, 00:35
10
1
69
00:00

Difficulty:

65% (hard)

Question Stats:

44% (01:01) correct 56% (01:14) wrong based on 365 sessions

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There is at least one viper and at least one cobra in Pandora's box. How many cobras are there?

(1) From any two snakes from Pandora's box at least one is a viper.

(2) The total number of snakes in Pandora's box is 99.

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16 Sep 2014, 00:35
9
9
Official Solution:

This is a hard question that challenges test-taker's logic. It is simple once you understand it but hard if you have never solved it. If you made a mistake on this question, make sure you understand the logic so you can be armed with this new tool for the real test.

(1) Statement 1 tells us that from any two snakes from Pandora's box at least one is a viper. This does not mean that there are 2 snakes in the box or that there is only 1 viper. Instead, it indicates that at most, there is 1 cobra. This may mean 1 cobra and 1 viper or 1 cobra and 99 vipers. Make sure you understand this distinction. S1 tells us that there is only 1 cobra in the box, which is sufficient.

(2) The total number of snakes Pandora's box is 99. Clearly insufficient.

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15 Oct 2014, 12:04
1
Bunuel wrote:
Official Solution:

(1) From any two snakes from Pandora's box at least one is a viper. Since from ANY two snakes one is a viper then there cannot be 2 (or more) cobras and since there is at least one cobra then there must be exactly one cobra in the box. Sufficient.

(2) The total number of snakes Pandora's box is 99. Clearly insufficient.

Hi Bunuel,
Any specific types/patterns of word problems that you could suggest here.

Facing a lot of time issues especially when these word problems come in DS mode.
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09 Nov 2014, 16:26
Bunuel wrote:
Official Solution:

(1) From any two snakes from Pandora's box at least one is a viper. Since from ANY two snakes one is a viper then there cannot be 2 (or more) cobras and since there is at least one cobra then there must be exactly one cobra in the box. Sufficient.

(2) The total number of snakes Pandora's box is 99. Clearly insufficient.

Hi

From any two snakes from Pandora's box at least one is a viper
does not it mean that if 2 snakes were taken out from the box at least one is viper
if you consider this will the answer be different
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Joined: 02 Sep 2009
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10 Nov 2014, 02:58
1
shyam593 wrote:
Bunuel wrote:
Official Solution:

(1) From any two snakes from Pandora's box at least one is a viper. Since from ANY two snakes one is a viper then there cannot be 2 (or more) cobras and since there is at least one cobra then there must be exactly one cobra in the box. Sufficient.

(2) The total number of snakes Pandora's box is 99. Clearly insufficient.

Hi

From any two snakes from Pandora's box at least one is a viper
does not it mean that if 2 snakes were taken out from the box at least one is viper
if you consider this will the answer be different

Yes, it means exactly that. But what do you mean that the answer would be different?
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10 Nov 2014, 03:14
1
Bunuel wrote:
shyam593 wrote:
Bunuel wrote:
Official Solution:

(1) From any two snakes from Pandora's box at least one is a viper. Since from ANY two snakes one is a viper then there cannot be 2 (or more) cobras and since there is at least one cobra then there must be exactly one cobra in the box. Sufficient.

(2) The total number of snakes Pandora's box is 99. Clearly insufficient.

Hi

From any two snakes from Pandora's box at least one is a viper
does not it mean that if 2 snakes were taken out from the box at least one is viper
if you consider this will the answer be different

Yes, it means exactly that. But what do you mean that the answer would be different?

Sorry got it now
irrespective of the no of vipers, cobra can never be more than 1.
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24 Nov 2014, 09:34
Yes but we do know know how many snakes there are in the box.

For example if the number of snakes is 10 there could be 9 ; 1 or it could be 5;5.

Second one is clearly insufficient also

And both are insufficient.

99 Snakes 1 cobra 98 vipers, or 97/2

Thank you
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24 Nov 2014, 09:42
1
Princas1 wrote:
Yes but we do know know how many snakes there are in the box.

For example if the number of snakes is 10 there could be 9 ; 1 or it could be 5;5.

Second one is clearly insufficient also

And both are insufficient.

99 Snakes 1 cobra 98 vipers, or 97/2

Thank you

Let me ask you if there are 5 vipers and 5 cobras, would the second statement be correct?
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24 Nov 2014, 10:17
25
5
It took me sometime to understand statement 1 in the test. For those having trouble like me, hope this helps!
Statement 1: Any 2 snakes, possibilities ---> V, V or V, C or C, V.
There is no possibility for C, C. This means that there is only 1 cobra in the box. Sufficient.

Statement 2: Totally irrelevant and useless.
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26 Dec 2014, 00:35
Bunuel wrote:
Princas1 wrote:
Yes but we do know know how many snakes there are in the box.

For example if the number of snakes is 10 there could be 9 ; 1 or it could be 5;5.

Second one is clearly insufficient also

And both are insufficient.

99 Snakes 1 cobra 98 vipers, or 97/2

Thank you

Let me ask you if there are 5 vipers and 5 cobras, would the second statement be correct?

Hey Bunuel, it's still not clear for me concerning answer (1).

If we take your example with 10 snakes, doesn't it mean that we can have anything from (5V 5C; 6V 4C;...9V 1C) according to statement 1? A ratio of 6:4 V to C is still "at least 1 viper" for any 2 snakes.

Thanks for clarifying.
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26 Dec 2014, 07:59
6
3
TudorM wrote:
Bunuel wrote:
Princas1 wrote:
Yes but we do know know how many snakes there are in the box.

For example if the number of snakes is 10 there could be 9 ; 1 or it could be 5;5.

Second one is clearly insufficient also

And both are insufficient.

99 Snakes 1 cobra 98 vipers, or 97/2

Thank you

Let me ask you if there are 5 vipers and 5 cobras, would the second statement be correct?

Hey Bunuel, it's still not clear for me concerning answer (1).

If we take your example with 10 snakes, doesn't it mean that we can have anything from (5V 5C; 6V 4C;...9V 1C) according to statement 1? A ratio of 6:4 V to C is still "at least 1 viper" for any 2 snakes.

Thanks for clarifying.

NO. We cannot have more than 1 cobras. If there are 5 cobras and 5 vipers then the first statement will NOT hold. (1) says from ANY two snakes from Pandora's box at least one is a viper. If there are 5 cobras and 5 vipers then we could have two snakes from which BOTH are vipers.
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20 Jan 2015, 20:57
3
i see the goal here (trickery), but the question wording is wrong.

Implication of "any" two snakes is that there are more than 1 pair, otherwise proper english would be "the" two snakes.

This one should be dumped from the question bank.
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21 Jan 2015, 01:04
i see the goal here (trickery), but the question wording is wrong.

Implication of "any" two snakes is that there are more than 1 pair, otherwise proper english would be "the" two snakes.

This one should be dumped from the question bank.

What;s wrong in assuming that there are more than 1 pair?
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02 Mar 2015, 18:14
Excellent question, but I'm partial because I got it right.
It's more representative of the type of thinking on the verbal portion of the exam, IMO, which is another reason I like it, and it also reminded me of the Monty Hall problem for whatever reason.
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16 Mar 2015, 04:58
5
2
this is a good question.

Ex:

Stated in the question
There is at least one viper and at least one cobra in Pandora's box

Statement 1
From any two snakes from Pandora's box at least one is a viper.

Cases that are in scope and are correct are
1V 1C is correct
2V 1C is correct
3V 1C is correct
.
.
.
n-1V 1C is correct
where n >0 and n is an integer

Here the no of cobras are always one because in the question it is stated that there is at least one cobra in Pandora's box. So minimum value of no of cobras is 1

Note:
Cases that are out of scope.
1V 2C
2V 2C
3V 3C etc...

Notice the no of cobras is always greater one . But what does the statement 1 say "from any two snakes at least one is a viper."
So all the above cases are out of scope as there is a chance that from any two snakes none can be a viper.

Hope this helps.
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27 May 2015, 16:34
At least one is a Viper --> Couldn't there be two vipers - and therefore 0 cobras - and invalidate statement 1? Thanks.
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27 May 2015, 17:27
Look at the question. The condition u mentioned is out of scope. The question clearly says that there is atleast one V and one C in the box.
You should not consider the case where cobras are 0.

When only the condition in the question is considered

Possible cases are
1v 1c
2v 2c
Etc

Cases that are out of scope
1v 0c
2v 0c
3v 0c
.
.
.
Nv 0c
0v 1c
0v 2c
0v 3c
.
.
.
0v Nc
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10 Jun 2015, 19:55
Bunuel wrote:
KPMM07 wrote:
I think this question is poor and not helpful.

Please elaborate on this. The question is perfectly valid, though quite hard.

Interesting solution, but not sure how this is math (not counting/probability/algebra/arithmetic etc.)
More like it was a question testing your logical deduction.
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23 Sep 2015, 12:22
1
I think this is a poor-quality question and the explanation isn't clear enough, please elaborate.
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23 Sep 2015, 22:10
shavak wrote:
I think this is a poor-quality question and the explanation isn't clear enough, please elaborate.

You should specify what is unclear to you in the explanation. Also, reading the whole thread might help.

P.S. I think this is a prefect question.
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Re: M07-18   [#permalink] 23 Sep 2015, 22:10

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# M07-18

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