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

Question

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 · Accepted Answer

Official Solution:

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

This question is challenging and requires logical reasoning. Once you understand the logic behind it, the question becomes simple. However, if you have never encountered this type of problem before, it can be difficult to solve. If you made an error, it's important to review the solution and understand the reasoning, as it can be a valuable tool for similar problems on actual test.

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

Statement (1) states that from ANY two snakes in the box, at least one is a viper. This means that there cannot be two or more cobras in the box, because if there were, then we could choose two cobras and that would contradict the statement. Therefore, there must be at most one cobra in the box. And since we also know that there is at least one cobra in the box, there must be exactly one cobra. So, statement (1) is sufficient to answer the question.

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

Answer: A

Vips0000 · Answer

From question we know that we have atleast 1 Red ball and 1 Blue ball.
Stem 1: If we pick any two balls, one is red or both are red. what does it mean? this can happen only if there is only 1 blue ball. 
Suficient
Stem 2: Total number of balls is 99. Doent help us to reach anywhere. Not sufficient.

Hence Ans A it is.

hope it helps.

WoundedTiger · Answer

Hello,

At least one red ball and One blue ball means at least one ball of each type (but there can be more) from the Q. stem

Can we infer from Statement 1 that there are only 2 balls in the box.

There can be any no. of Balls in the box. But, At least one means surely there will be one but can be more of same type. 
If i say I have atleast 100US $ doesn't that mean that surely I have US $ 100 but might have more but not less.

Is my understanding correct??

Please confirm

Bunuel · Answer

Yes, at least one means  \geq{1} .

Vips0000 · Answer

Hi 
Yes your understanding is correct that at least 1 would mean 1 or more. However when we use stem 1, it says if u pick any 2 balls at least 1 would be red. This is possible if there is only one blue ball. You can pick any numbers to check this.
So since now we know the number of blue balls,which is 1, we can conclude that statement is sufficient.
Clear?:)

Chakrawarty · Answer

If we want atleast one of the snakes to be a viper each time 2 snakes are picked out, then there is no way we could have more than 1 cobra. Hence, option A

gmatsnightmare1 · Answer

I think the solution is incorrect and   I think the correct answer should be C.

My logic:

The question tells us that there is at least 1 of both types of snakes. 
And then we are told that this is an exact value type sufficiency question so we need to find the exact value of the # of cobras in the box.

Statement (1): From any 2 snakes from the box, at least 1 is a viper. I feel that this tells us that if you pick any 2 snakes at random, 1 or more of those would be a viper. So this only tells us the probability (snakes in the box being a viper) = 1/2.

Since only 2 types of snakes in the box, P(Cobras) = 1/2

But this does not give us the exact value of Cobras. So I feel Statement (1) is Insufficient.

Statement (2): Total snakes = 99

This doesnt tell us anything about the distribution of each type of snake in the box. Statement (2) Insufficient.

Remaining Answer Choices are C and E.

Let's take both together:

P(Cobras) = 1/2
Cobras + Vipers = 99

Here is where I think if the total was an even number, C would be correct as we can now get the exact value of cobras.

Would appreciate if anyone can point out what I am confusing here!

Bunuel · Answer

No, the answer is A. (1) says EVERY pair you could pick has at least one viper. That makes it impossible to have two cobras, because the pair “cobra and cobra” would have zero vipers. So there is at most one cobra. Since the question already says there is at least one cobra, the number of cobras is exactly one. Here is a longer discussion on this question that might help you: https://gmatclub.com/forum/m07-183752.html

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

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GMAT Data Sufficiency (DS) Questions

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

Prep Toolkit

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