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chetan2u
Samuel has a big drawer full of exactly 59 packets, each containing a marker which is either black or blue or red in colour. All 59 packets are sealed and are completely identical from outside. It is not possible to know which colour marker is inside unless the packet is fully opened. Out of 59, 23 packets contain a black marker each. How many packets contain a blue marker?

(1) If Samuel withdraws packets without looking at their contents, he needs to draw minimum 42 packets to ensure that he has at least one marker of each colour out of red, blue, black.

(2) Probability of picking a packet containing red marker is same as the probability of picking a packet containing blue marker.

Hi Chetan ,

Statement B is ok to understand .
But i have trouble understanding statement 1 .
Can you please explain statement 1 and how to interpret such statement in general
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Hi

In this Questions We have total number of packets = 59
and no of black markers =23
we don't know about the number of red or blue markers.

1) he needs to draw minimum 42 packets to ensure that he has at least one marker of each colour out of red, blue, black.
Now to be sure that he has at least one marker of each colours, let initial all markers are black, Bad luck :sad:
So first 23 markers are black.
Now out of 42 , 23 are black. this means 42-23=19. in 19, 18 are of one colour and we have last marker of the third one. (we have to take the worst condition to ensure that markers of all colours have been drawn)
that means, say blue = 18 and last one is for red.
So number of red = 59-23-18=18.
(if we take second colour to be red, then we get third colour blue = 18). so its a single unique combination possible.
hence we get the number of markers of each colour.

SUFFICIENT



arvind910619

Samuel has a big drawer full of exactly 59 packets, each containing a marker which is either black or blue or red in colour. All 59 packets are sealed and are completely identical from outside. It is not possible to know which colour marker is inside unless the packet is fully opened. Out of 59, 23 packets contain a black marker each. How many packets contain a blue marker?

(1) If Samuel withdraws packets without looking at their contents, he needs to draw minimum 42 packets to ensure that he has at least one marker of each colour out of red, blue, black.

(2) Probability of picking a packet containing red marker is same as the probability of picking a packet containing blue marker.

Hi Chetan ,

Statement B is ok to understand .
But i have trouble understanding statement 1 .
Can you please explain statement 1 and how to interpret such statement in general[/quote]
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Hi

In this Questions We have total number of packets = 59
and no of black markers =23
we don't know about the number of red or blue markers.

1) he needs to draw minimum 42 packets to ensure that he has at least one marker of each colour out of red, blue, black.
Now to be sure that he has at least one marker of each colours, let initial all markers are black, Bad luck :sad:
So first 23 markers are black.
Now out of 42 , 23 are black. this means 42-23=19. in 19, 18 are of one colour and we have last marker of the third one. (we have to take the worst condition to ensure that markers of all colours have been drawn)
that means, say blue = 18 and last one is for red.
So number of red = 59-23-18=18.
(if we take second colour to be red, then we get third colour blue = 18). so its a single unique combination possible.
hence we get the number of markers of each colour.

SUFFICIENT



arvind910619

Samuel has a big drawer full of exactly 59 packets, each containing a marker which is either black or blue or red in colour. All 59 packets are sealed and are completely identical from outside. It is not possible to know which colour marker is inside unless the packet is fully opened. Out of 59, 23 packets contain a black marker each. How many packets contain a blue marker?

(1) If Samuel withdraws packets without looking at their contents, he needs to draw minimum 42 packets to ensure that he has at least one marker of each colour out of red, blue, black.

(2) Probability of picking a packet containing red marker is same as the probability of picking a packet containing blue marker.

Hi Chetan ,

Statement B is ok to understand .
But i have trouble understanding statement 1 .
Can you please explain statement 1 and how to interpret such statement in general
[/quote]

Hi gmatbusters,

Thanks for the explanation :-D
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chetan2u
Samuel has a big drawer full of exactly 59 packets, each containing a marker which is either black or blue or red in colour. All 59 packets are sealed and are completely identical from outside. It is not possible to know which colour marker is inside unless the packet is fully opened. Out of 59, 23 packets contain a black marker each. How many packets contain a blue marker?

(1) If Samuel withdraws packets without looking at their contents, he needs to draw minimum 42 packets to ensure that he has at least one marker of each colour out of red, blue, black.

(2) Probability of picking a packet containing red marker is same as the probability of picking a packet containing blue marker.

Hi Chetan ,

Statement B is ok to understand .
But i have trouble understanding statement 1 .
Can you please explain statement 1 and how to interpret such statement in general


Hi...

Sorry missed out on your question earlier..
So the solution would be..

There are 59 packets. 23 are black markers...
So 59-23=36 contain red or blue..

I) statement I tells us that Taking 42 out ensures that we have one of each colour..
So it gives us the max two colours to be 41 and third one was the 42nd that was picked up...
Black are 23, so the second highest =41-23=18..
So these 18 can be red or blue..
The third therefore would be 59-23-18=59-41=18
So the third also will be 18..
So the number of markers are :-
a) Black - 23
b)Red and Blue - 18 each..
Sufficient

II) statement II tells us Probability of picking red and blue is same..
So number of red and blue is same..
But red + blue = 59-23=36
So red=36/2=18
Sufficient

D
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Samuel has a big drawer full of exactly 59 packets, each containing a marker which is either black or blue or red in colour. All 59 packets are sealed and are completely identical from outside. It is not possible to know which colour marker is inside unless the packet is fully opened. Out of 59, 23 packets contain a black marker each. How many packets contain a blue marker?

(1) If Samuel withdraws packets without looking at their contents, he needs to draw minimum 42 packets to ensure that he has at least one marker of each colour out of red, blue, black.

(2) Probability of picking a packet containing red marker is same as the probability of picking a packet containing blue marker.

Isn't it incorrect to assume that we do not have any black markers in the remaining 36(59-23) packets? Question statement should say Out of 59, exactly 23 packets contain a black marker.
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Hi! Thanks for the explanations. But do you think this is a valid question?
Why do we take the worst condition? The minimum possible number of packets to draw to have the favorable results can be 3. Why do we account for the bad luck? I think Statement 1 is not very correctly formulated. Please, correct me if I am missing something.
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m struggling to understand how Statement 1 alone is sufficient for this problem. Here is where my logic is getting stuck:
The Core Setup:
Total packets = 59
Black = 23
Remaining (Blue + Red) = 59 -23=36
Statement 1: Minimum 42 draws are needed to ensure at least one marker of each color.
My Confusion:
From Statement 1, using the worst-case formula (Sum of two largest+1=42), I get that the sum of the two largest groups must be 41.
However, I don't understand why Black (23) has to be one of those two largest groups.
For example, couldn't the distribution hypothetically be Red = 24, Black = 23, Blue = 12 In this case, Red and Black are the two largest groups (24+23=47), which would require 47+1=48 worst-case draws.
Since 48 doesn't match Statement 1's 42 draws, why are we assuming Black is automatically one of the top two? What am I missing about how the constraints lock the numbers in place?
Can an expert please explain the logical step I'm skipping? Thanks!
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As you said taking Red = 24, Black = 23, Blue = 12 requures 24+23+1 or 48 draws. But we are given that minimum draws are 42.

Now this means the remaining two are 59-23 or 36.
Next if black is not on of top two, then tge minimun draws would have beeb 36+1 or 37, a situation that is not true.

So if we remove 23 for black and one for the least, the second highest would be 42 -(1+23) = 18. The lowest would be 59-23-18 or 18 again.

Thus both red and blue are 18 each.


laborumpossimus
m struggling to understand how Statement 1 alone is sufficient for this problem. Here is where my logic is getting stuck:
The Core Setup:
Total packets = 59
Black = 23
Remaining (Blue + Red) = 59 -23=36
Statement 1: Minimum 42 draws are needed to ensure at least one marker of each color.
My Confusion:
From Statement 1, using the worst-case formula (Sum of two largest+1=42), I get that the sum of the two largest groups must be 41.
However, I don't understand why Black (23) has to be one of those two largest groups.
For example, couldn't the distribution hypothetically be Red = 24, Black = 23, Blue = 12 In this case, Red and Black are the two largest groups (24+23=47), which would require 47+1=48 worst-case draws.
Since 48 doesn't match Statement 1's 42 draws, why are we assuming Black is automatically one of the top two? What am I missing about how the constraints lock the numbers in place?
Can an expert please explain the logical step I'm skipping? Thanks!
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Got it now
thank you so much

chetan2u
As you said taking Red = 24, Black = 23, Blue = 12 requures 24+23+1 or 48 draws. But we are given that minimum draws are 42.

Now this means the remaining two are 59-23 or 36.
Next if black is not on of top two, then tge minimun draws would have beeb 36+1 or 37, a situation that is not true.

So if we remove 23 for black and one for the least, the second highest would be 42 -(1+23) = 18. The lowest would be 59-23-18 or 18 again.

Thus both red and blue are 18 each.



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