In the jar there are white and black marbles (W0 and B0).

Question

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.

GMAT TIGER · Answer

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.

Bunuel · Answer

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

GMAT TIGER · Answer

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?

Bunuel · Answer

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.

Economist · Answer

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 !!!!

Bunuel · Answer

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.

GMAT TIGER · Answer

I guess thats the best way to practice gmat.

Your questions are perfectly up to the real gmat standard.

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

jeeteshsingh · Answer

Awesome question.....! U preparing for GMAT! U mite end up getting 900 score in it :D LOL!!

srinjoy28 · Answer

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..

gallantx · Answer

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.

thefibonacci · Answer

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.

anshul2014 · Answer

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

dina98 · Answer

ahhh!!! This was tricky!!!

Rohan1 · Answer

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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rrrkkk · Answer

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.

EllaWoodMN · Answer

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

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