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# M07-18

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Intern
Joined: 27 Oct 2017
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06 Jun 2018, 03:00
Hi Bunuel,

I have still not able to concrete my understanding of 1st statement.
I get it minimum there would be (atleast) 1 viper. But:-
1) What is the reference of "2 snakes" here , eg- There could be 5 snakes in total and
if we pick a pair one of them would be a viper (atleast) , surely.
2) Why is following condition wrong :-
3V2C :- If we pick a pair then there could be a chance that 2C might be taken, is it because of this we have taken 1C to avoid this kind of situation.
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Joined: 02 Sep 2009
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08 Jun 2018, 02:16
luffy92 wrote:
Hi Bunuel,

I have still not able to concrete my understanding of 1st statement.
I get it minimum there would be (atleast) 1 viper. But:-
1) What is the reference of "2 snakes" here , eg- There could be 5 snakes in total and
if we pick a pair one of them would be a viper (atleast) , surely.
2) Why is following condition wrong :-
3V2C :- If we pick a pair then there could be a chance that 2C might be taken, is it because of this we have taken 1C to avoid this kind of situation.

I tried examining this many, many times on previous 5 pages.

If there are 3 vipers and 2 cobras in the box, the first statement will not be satisfied:

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

If there are two cobras there, then we could pick two cobras and (1) will not be satisfied.
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08 Jun 2018, 05:17
From any two snakes from Pandora's box at least one is a viper.
It's saying from any 2 snakes so if total no of snakes if 4, V:1 or 2 or 3 and thus C: 3 or 2 or 1 respectively
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11 Jul 2018, 19:34
Bunuel wrote:
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.

Bunuel I did this logic and got it incorrect. Can you please help me to find out the gap?
S1: From any 2 snakes at least 1 is viper- It means probability of getting viper can be 1/2 or 1
If probability is 1/2 for viper it is 1/2 for cobra. We have to discard probability 1 since at least 1 has to be cobra. But we do not know how many snakes are there in box. It can be 98 or 2- Insufficient

S2. There are 99 snakes- InsufficienT

S1+S2= Insufficient because no has to be integer and by 99 we get decimal

Ans: E
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11 Jul 2018, 19:49
Cbirole wrote:
Bunuel wrote:
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.

Bunuel I did this logic and got it incorrect. Can you please help me to find out the gap?
S1: From any 2 snakes at least 1 is viper- It means probability of getting viper can be 1/2 or 1
If probability is 1/2 for viper it is 1/2 for cobra. We have to discard probability 1 since at least 1 has to be cobra. But we do not know how many snakes are there in box. It can be 98 or 2- Insufficient

S2. There are 99 snakes- InsufficienT

S1+S2= Insufficient because no has to be integer and by 99 we get decimal

Ans: E

You are missing the main point. From (1) it follows that the box can have 1 cobra and any number of vipers more than or equal to 1. Please read the whole discussion. I hope it helps.
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01 Sep 2018, 12:28
I think this is a high-quality question and I agree with explanation.
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Joined: 03 Aug 2018
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24 Sep 2018, 08:25
Approaching it via probability. Is my thinking correct?

Probability of both being snakes being a C = 0
Total snakes = C+V
P of 1st snake being C = C/(V+C)
P of 2nd snake being C = C-1/(V+C-1)

But since P of both being C = 0 then

C/(C+V) * (C - 1)/ (C+V-1) = 0
C*(C-1) = 0
C can be 0 or 1. Question states atleast 1 cobra, hence C=1

Would appreciate to know if above reason is okay.

This makes 1 sufficient.
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24 Sep 2018, 08:48
Hi Bunuel, I read all the replies and took a fair amount of time to comprehend this. I still don't understand first condition and how there is only one Cobra.
See, for example:
It says "From any two snakes from Pandora's box at least one is a viper"

Let's say there are 10 snakes.
I choose 5th and 6th snake: 5th is Cobra, 6th is Viper. The condition is true because it says from "any two snakes".

Then let's say I choose 2nd and 3rd snake: 2nd is Cobra and 3rd is Viper. The condition is still true.
So now we see 2nd and 5th both are Cobra and all conditions are satisfied. So how can we say there can be at most one cobra.
There can be at most one cobra IN A PAIR not overall.
So, statement 1 should be insufficient too. I don't understand how everyone has inferred there will be at most one cobra in total.

Please correct me where I'm wrong.
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24 Oct 2018, 02:05
indeed a perfect question ... it was more like how many integers are there in the set (X) where product of any two integers is 2 >> (1,2)

i probably wanna kill myself to not read the part that we want number of cobras...ughhhhhhhhhhhhhhhhhhh...kill me plz
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11 Nov 2018, 09:58
Hi Bunuel,
I am facing trouble in understanding S1
How can 2V,1C be a possibility? S1 says any two snakes. How can we take a case of 3 snakes (2V,1C) ?

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09 Dec 2018, 20:32
I think I finally get it. We know at minimum, there is one cobra and one viper in the box.

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

This tells us that there could never be a scenario when you reach in the box and have a cobra/cobra or cobra/other non-viper snake combination. At least one is viper means that we could reach in and grab viper/viper, viper/cobra, or viper/other non-viper snake. But we could never have a cobra/cobra scenario (aka 2 cobras). However, there is at least one cobra in the main box, so if we could never have 2 cobras, then has to be exactly 1 cobra in the box.
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25 Dec 2018, 17:35
Akshit03 wrote:
Hi Bunuel, I read all the replies and took a fair amount of time to comprehend this. I still don't understand first condition and how there is only one Cobra.
See, for example:
It says "From any two snakes from Pandora's box at least one is a viper"

Let's say there are 10 snakes.
I choose 5th and 6th snake: 5th is Cobra, 6th is Viper. The condition is true because it says from "any two snakes".

Then let's say I choose 2nd and 3rd snake: 2nd is Cobra and 3rd is Viper. The condition is still true.
So now we see 2nd and 5th both are Cobra and all conditions are satisfied. So how can we say there can be at most one cobra.
There can be at most one cobra IN A PAIR not overall.
So, statement 1 should be insufficient too. I don't understand how everyone has inferred there will be at most one cobra in total.

Please correct me where I'm wrong.

Hi Bunuel & chetan2u

Could one of you experts please comment on this? Even I am confused on the same exact thing. There can be at most one cobra in a pair but overall how are we concluding that we only have 1 cobra all together in lets say 100 or 1000 snakes?
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25 Dec 2018, 18:33
csaluja wrote:
Akshit03 wrote:
Hi Bunuel, I read all the replies and took a fair amount of time to comprehend this. I still don't understand first condition and how there is only one Cobra.
See, for example:
It says "From any two snakes from Pandora's box at least one is a viper"

Let's say there are 10 snakes.
I choose 5th and 6th snake: 5th is Cobra, 6th is Viper. The condition is true because it says from "any two snakes".

Then let's say I choose 2nd and 3rd snake: 2nd is Cobra and 3rd is Viper. The condition is still true.
So now we see 2nd and 5th both are Cobra and all conditions are satisfied. So how can we say there can be at most one cobra.
There can be at most one cobra IN A PAIR not overall.
So, statement 1 should be insufficient too. I don't understand how everyone has inferred there will be at most one cobra in total.

Please correct me where I'm wrong.

Hi Bunuel & chetan2u

Could one of you experts please comment on this? Even I am confused on the same exact thing. There can be at most one cobra in a pair but overall how are we concluding that we only have 1 cobra all together in lets say 100 or 1000 snakes?

Hi..
Statement I says that if we take any two snakes, there is atleast 1 viper.
Atleast means that if we pick two snakes, either both are viper or one is viper and one cobra.
Also we are talking of picking ANY two.

So say, there are 10 snakes as mentioned by the post you are referring to..
A) In 5th and 6th , 5th is viper and 6th a cobra
B) Now in 3rd and 4th, 3rd is viper and 4th is cobra.
Now comes into play the word ANY, so if I pick the 4th and 6th, I have TWO Cobras and none viper. But I have to have atleast one viper. This this scenario is not possible.

Only possibility is when we have one cobra only.
Because whenever we pick a pair with this cobra, there is one viper.
But if we pick any other two, both are viper..
So ATLEAST one is maintained.
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28 Jan 2019, 23:53
Bunuel wrote:
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.

There is at least one viper and at least one cobra in Pandora's box.

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

can i assume only two snakes are there?
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29 Jan 2019, 01:16
akurathi12 wrote:
Bunuel wrote:
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.

There is at least one viper and at least one cobra in Pandora's box.

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

can i assume only two snakes are there?

No, you cannot assume that.
There can be 10, but if you pick up any two, atleast one of them is viper.
So there will be at the most 1 other snake and rest will be viper.
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03 Feb 2019, 12:45
Top Contributor
1
Bunuel wrote:
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.

Given: There is at least one viper and at least one cobra in Pandora's box

Target question: How many cobras are there?

Statement 1: From any two snakes from Pandora's box at least one is a viper.
This is indirectly telling us that there is only 1 cobra in the box. Here's why:
If the box contained 2 cobras, then it would be possible to select 2 snakes that are both cobras, which would CONTRADICT statement 1.
If the box contained 3 cobras, then it would be possible to select 2 snakes that are both cobras, which would CONTRADICT statement 1.
If the box contained 4 cobras, then it would be possible to select 2 snakes that are both cobras, which would CONTRADICT statement 1.
. . . etc

So, the box must contain FEWER THAN 2 cobras.
We're told that there is AT LEAST ONE cobra in the box
So, it must be the case that the box contains EXACTLY 1 cobra
Since we can answer the target question with certainty, statement 1 is SUFFICIENT

Statement 2: The total number of snakes in Pandora's box is 99
There are many scenarios that satisfy statement 2. Here are two:
Case a: The box contains 30 cobras and 69 vipers. In this case, the answer to the target question is the box contains 30 cobras
Case b: The box contains 49 cobras and 50 vipers. In this case, the answer to the target question is the box contains 49 cobras
Since we cannot answer the target question with certainty, statement 2 is NOT SUFFICIENT

Cheers,
Brent
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11 Feb 2019, 17:11
I think this is a high-quality question and I agree with explanation. Awesome question. Although I got it incorrect, this was valuable.
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21 Mar 2019, 20:09
I think this is a high-quality question.
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07 Apr 2019, 07:25
I think this is a high-quality question and I agree with explanation.
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08 Apr 2019, 16:45
why are we assuming that there is only 2 types of snakes in the box?
Re: M07-18   [#permalink] 08 Apr 2019, 16:45

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# M07-18

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