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A jar contains 8 red marbles and y white marbles

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A jar contains 8 red marbles and y white marbles

by rakeshd347 » Sat Oct 05, 2013 5:49 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 IS B
Last edited by rakeshd347 on Sat Oct 05, 2013 10:54 pm, edited 1 time in total.
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Source: — Data Sufficiency |
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by theCodeToGMAT » Sat Oct 05, 2013 6:37 pm
Red = 8
White = y

to find:
8 * 7 / (8+y)(7+y) > 2 * 8 * y/(8+y)(7+y)
y <3.5?


Statement 1:
y<=8
INSUFFICIENT

Statement 2:
y>=4
SUFFICIENT

Answer [spoiler]{B}[/spoiler]
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by [email protected] » Sun Oct 06, 2013 12:56 am
Hi rakesh347,

You can approach this question with either "probability math" or TESTing Values.

We're told that there are 8 red marbles and Y white marbles. We're asked is it more likely to randomly pull 2 reds OR 1 red and 1 white. This is essentially a Yes/No question. We're looking to prove if the "answer" to the question is consistent or inconsistent.

Fact 1: Y <= 8

If Y = 8
Probability of RedRed = (8/16)(7/15)
Probability of 1Red1White in either order = 1(8/15)
The answer to the question is REDWHITE is greater.

If Y = 0
Probability of RedRed is 100%
Probability of 1Red1White = 0%
The answer to the question is REDRED is greater

Fact 1 is INSUFFICIENT

Fact 2: Y > = 4

Here, we can use Y = 8 (from Fact 1), which says REDWHITE is greater

If Y = 4
Probability of RedRed = (8/12)(7/11) = 56/132
Probability of RedWhite + WhiteRed = (8/12)(4/11)(2) = 64/132
The answer to the question is REDWHITE is greater

If Y = 92
Probability of RedRed = (8/100)(7/99) = 56/9900
Probability of RedWhite + WhiteRed = (8/100)(92/99)(2) = 1472/9900
The answer to the question is REDWHITE is greater

Although I've done the calculations in Fact 2, if you can spot the "big numbers" involved, then you don't have to do all of the math.
Fact 2 is SUFFICIENT

Final Answer: B

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Rich
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