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Re: In the jar there are white and black marbles (W>0 and B>0). [#permalink]
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Bunuel wrote:
GMAT TIGER wrote:
Bunuel wrote:
Try this one from me.

In the jar there are white and black marbles (W>0 and B>0). How many black marbles are there?

(1) There are total 101 marbles in the jar.
(2) From any two marbles from the jar at least one is white.

Again, please share your way of thinking, difficulty level and quality.

Explanation of the answer to follow.


C. If white marbles were 100 and 1 Black marble, then only you get at least 1/2 while drawing 2 marbles from the jar. But you do not get answer (no. of black and white marbles) until you mix 1 and 2.


GMAT TIGER I didn't get the reasoning of your answer can you please specify. Anyway what's your answer, how many black marbles are there? C is incorrect.

Maybe you misunderstood the statements, or I stated them ambiguously


I guess I overlooked - thought white for black. It is B.
Given that: w>0 and b>0.

(1) Total = 101 tells nothing about individusl msrbles.
(2) If any two marbles from the jar are drawn, at least one is a white. That means black cannot be more than 1. so Black = 1 irrespective of whites.

Another good one. Are you gmat instructer/question writer?
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Re: In the jar there are white and black marbles (W>0 and B>0). [#permalink]
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Yes you're right. Answer B. +1.

Thats what I like in this problem: the number of black marbles are in no connection with total number of marbles. Simple logic.

I'm neither gmat instructor nor question writer, I'm just preparing for GMAT. Just found that composing questions helps me to understand better the logic of the quant problems in GMAT.
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Re: In the jar there are white and black marbles (W>0 and B>0). [#permalink]
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Awesome question..:) I arrived at E.
Line of reasoning: At least one white means that number of white > 50% of total...however even after combining we cannot tell the exact number of whites..it can be 60%(Total) or 70%(Total)..

The catch is the word "any" in B. If ANY two marbles are picked and if black can be 1(max) means, there is only one black !!!!
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Re: In the jar there are white and black marbles (W>0 and B>0). [#permalink]
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Economist wrote:
Awesome question..:) I arrived at E.
Line of reasoning: At least one white means that number of white > 50% of total...however even after combining we cannot tell the exact number of whites..it can be 60%(Total) or 70%(Total)..

The catch is the word "any" in B. If ANY two marbles are picked and if black can be 1(max) means, there is only one black !!!!


Thanks Economist, I knew that this trap ("any" in second statement) would work.

And yes answer is 1 black marble, (2) alone is sufficient. B.
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Re: In the jar there are white and black marbles (W>0 and B>0). [#permalink]
I guess thats the best way to practice gmat.

Your questions are perfectly up to the real gmat standard.

lol................ +1


Bunuel wrote:
Yes you're right. Answer B. +1.

Thats what I like in this problem: the number of black marbles are in no connection with total number of marbles. Simple logic.

I'm neither gmat instructor nor question writer, I'm just preparing for GMAT. Just found that composing questions helps me to understand better the logic of the quant problems in GMAT.
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Re: In the jar there are white and black marbles (W>0 and B>0). [#permalink]
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Bunuel wrote:
Yes you're right. Answer B. +1.
I'm neither gmat instructor nor question writer, I'm just preparing for GMAT. Just found that composing questions helps me to understand better the logic of the quant problems in GMAT.


Awesome question.....! U preparing for GMAT! U mite end up getting 900 score in it :D LOL!!
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Re: In the jar there are white and black marbles (W>0 and B>0). [#permalink]
Goodday Bunuel
Can you please explain why it is B??...
Option B says : "From any two marbles from the jar at least one is white"...This means 1 or both are white but the question asks "how many?"....I am stuck here
Thanks in advance..
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Re: In the jar there are white and black marbles (W>0 and B>0). [#permalink]
If there were 2 black balls, there is a chance of picking up two black balls.
But the second statement states that from any two marbles from the jar AT LEAST 1 is white meaning there is only 1 black ball in the jar.

srinjoy28 wrote:
Goodday Bunuel
Can you please explain why it is B??...
Option B says : "From any two marbles from the jar at least one is white"...This means 1 or both are white but the question asks "how many?"....I am stuck here
Thanks in advance..
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Re: In the jar there are white and black marbles (W>0 and B>0). [#permalink]
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Bunuel wrote:
In the jar there are white and black marbles (W>0 and B>0). How many black marbles are there?

(1) There are total 101 marbles in the jar.
(2) From any two marbles from the jar at least one is white.


My take is B.

consider 1 alone) it tells us nothing about the number of white or black marbles in particular.

consider 2 alone) consider the total number of marbles to be 5 (for simplicity, it can be extended up to infinite number of marbles)
let the 5 marbles be --> A,B,C,D and E.
now option 2 says, if we pick any 2 marbles...at least 1 of them would be white.
if we form every possible group of 2 from these, we get - AB,AC,AD,AE,BC,BD,BE,CD,CE and DE. (10 groups, which is nothing but C(5,2))
since at least one of any two is white, we can safely say A,B,C and D are definitely white. E can be either black or white. but since our fact statement says W>0 and B>0; E has to be a black marble.
Hence, with statement 2 alone we can determine the number of black marbles...which would always be 1.

Good question. :)
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Re: In the jar there are white and black marbles (W>0 and B>0). [#permalink]
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Bunuel you were preparing for GMAT!!!!!!(P.S i just came to know that) sorry mate but there is no school for you not atleast on this planet my advice is please look in some other galaxy. For god's sake please tell me who can teach bunuel anything hahahaha. now i know from where the real competition comes in this exam. envy you bunuel
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Re: In the jar there are white and black marbles (W>0 and B>0). [#permalink]
ahhh!!! This was tricky!!!
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Re: In the jar there are white and black marbles (W>0 and B>0). [#permalink]
1) clearly insufficient
Number of Black marbles can be any number from 2-100

2)The catch here is “ANY” two marbles.suppose there are 200 marbles.if you pick the 100th and 200th marble,then either 100th is white,200th is white or both are white.similarly if you pick 50th and 100th marble,then either one of them is white or both are white.now if you pick 50th and 200th marble,then again either one of them is white or both are white but from above we get that 50th and 200th marble both are white.so basically all marbles will be white.there can be only black marble.
B is sufficient

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Re: In the jar there are white and black marbles (W>0 and B>0). [#permalink]
easy money.... just think of that "what if not?" question.

So the option B say at least one white marble will be picked up if you pick 2 marbles from the jar.

question: what if not?

what if I pick up no white.... in that case you must have at least 2 black marble in the jar and that is not plausible.
So there's only one black marble in the jar.
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Re: In the jar there are white and black marbles (W>0 and B>0). [#permalink]
OK I can't believe my eyes... Or I worked too hard my brain is gone..
Bunuel is preparing for GMAT... seriously? This shocks me more than any other news today....

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