BREAKING: Target Test Prep releases Brand New 2026 On Demand GMAT prep course

Redeem

Marbles

This topic has expert replies
Post new topic Post Reply
Previous Topic Next Topic
Legendary Member
Posts: 882
Joined: Fri Feb 20, 2009 2:57 pm
Thanked: 15 times
Followed by:1 members
GMAT Score:690

Marbles

by crackgmat007 » Sun Jul 19, 2009 7:32 pm
A jar contains 8 red marbles and y white marbles. If Joan takes 2 random marbles from the jar, is it more likely that she will have 2 red marbles than that she will have one marble of each color?

(1) y ≤ 8
(2) y ≥ 4

OA - B Pls explain
Top
Source: — Data Sufficiency |
Legendary Member
Posts: 1169
Joined: Sun Jul 06, 2008 2:34 am
Thanked: 25 times
Followed by:1 members

Re: Marbles

by aj5105 » Sun Jul 19, 2009 10:33 pm
crackgmat007 wrote:A jar contains 8 red marbles and y white marbles. If Joan takes 2 random marbles from the jar, is it more likely that she will have 2 red marbles than that she will have one marble of each color?

(1) y ≤ 8
(2) y ≥ 4

OA - B Pls explain
pick 2 marbles out of 8. 8C2 = 28.

pick 1 red, 1 white. 8C1 * y C1 (where y is the total white marbles)

you want to find out which of the two is big.

(B) gives the answer. even you take y = 4, 8*4 = 32, which is greater than 28. therefore any value greater than 4 gives a number greater than 32.
Top
Legendary Member
Posts: 882
Joined: Fri Feb 20, 2009 2:57 pm
Thanked: 15 times
Followed by:1 members
GMAT Score:690

by crackgmat007 » Mon Jul 20, 2009 9:48 am
I thought this problem is about probability because it says 'which one is more likely'. Let me know what you think.
Top
User avatar
Master | Next Rank: 500 Posts
Posts: 385
Joined: Sun May 24, 2009 3:55 pm
Thanked: 11 times
GMAT Score:740

by Domnu » Mon Jul 20, 2009 12:48 pm
This is a probability problem. Here's how I did it:

The probability of picking 2 red marbles is

56/[(8+y)(7+y)]

Here's how:

There are nCr(8, 2) ways to pick 2 red marbles, and nCr(8+y, 2) ways to choose marbles in general. Now, nCr(8,2) = 8!/(2!6!) = 56, and nCr(8+y,2) = (7+y)(8+y)/2, so we get the above.

Similarly, for choosing 1 red and 1 white marble, we have 8 ways of choosing a red marble and y ways of choosing a white marble, so our probability is

8y/nCr(8+y,2) = 16y/(8+y)(7+y)

We need to be able to definitely compare

16y/(8+y)(7+y) and 56/(8+y)(7+y)

Multiplying both out by denominators, we can just compare 16y and 56. If y <= 8, this doesn't give us anything... y could be 4, in which case 16y > 56, or y could be 2 in which case 16y < 56. So, cross off A. However, looking at B, if y >= 4, 16y > 56 always. So, our answer is B.
Have you wondered how you could have found such a treasure? -T
Top
Master | Next Rank: 500 Posts
Posts: 166
Joined: Sat Apr 18, 2009 10:41 pm
Thanked: 9 times
GMAT Score:770

by raghavsarathy » Mon Jul 20, 2009 5:05 pm
IMO - E

1. y <=8

The probability will change based on the value of y. If y=8 then the probability of having bith read marbles will be less and this probability will increase as the vlaue of y reduces.

However we cannot determine the value of this probability since y is not known

2. y>=4
Again here , the probability of choosing both red will be maximum when y=4 and will keep reducing as we increase the vlaue of y

Since value of y is not known we cannot determiine


Even using both statements y can have values from 4 to 8. Not sufficient

For me a sufficient soln would be something like

y<=7

Since we know the maximum value of the number of white marbles.

I am still not able to comprehend the OA !
Top
Post new topic Post Reply
• Page 1 of 1