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
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A jar contains 8 red marbles and y white marbles
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rakeshd347
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Last edited by rakeshd347 on Sat Oct 05, 2013 10:54 pm, edited 1 time in total.
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theCodeToGMAT
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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]
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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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
GMAT assassins aren't born, they're made,
Rich
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
GMAT assassins aren't born, they're made,
Rich
