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

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In the jar there are white and black marbles (W>0 and B>0). [#permalink] New post 09 Oct 2009, 14:08
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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.
[Reveal] Spoiler: OA

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Re: Jar of marbles. [#permalink] New post 09 Oct 2009, 14:36
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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.
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Re: Jar of marbles. [#permalink] New post 09 Oct 2009, 14:50
Expert's post
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
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Re: Jar of marbles. [#permalink] New post 09 Oct 2009, 22:58
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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: Jar of marbles. [#permalink] New post 09 Oct 2009, 23:21
Expert's post
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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NEW TO MATH FORUM? PLEASE READ THIS: ALL YOU NEED FOR QUANT!!!

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RESOURCES: [GMAT MATH BOOK]; 1. Triangles; 2. Polygons; 3. Coordinate Geometry; 4. Factorials; 5. Circles; 6. Number Theory; 7. Remainders; 8. Overlapping Sets; 9. PDF of Math Book; 10. Remainders; 11. GMAT Prep Software Analysis NEW!!!; 12. SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) NEW!!!; 12. Tricky questions from previous years. NEW!!!;

COLLECTION OF QUESTIONS:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS ; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


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Re: Jar of marbles. [#permalink] New post 10 Oct 2009, 02:59
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: Jar of marbles. [#permalink] New post 10 Oct 2009, 08:10
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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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PLEASE READ AND FOLLOW: 11 Rules for Posting!!!

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COLLECTION OF QUESTIONS:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS ; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


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Re: Jar of marbles. [#permalink] New post 10 Oct 2009, 08:30
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: Jar of marbles. [#permalink] New post 05 Jan 2010, 12:24
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] New post 19 Jan 2014, 05:32
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Re: In the jar there are white and black marbles (W>0 and B>0). [#permalink] New post 06 Feb 2014, 23:43
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] New post 25 Feb 2014, 10:18
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] New post 25 Feb 2014, 10:50
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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. :)
Re: In the jar there are white and black marbles (W>0 and B>0).   [#permalink] 25 Feb 2014, 10:50
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