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A certain box contains only blue (b), green (g) and red(r) m

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by Nina1987 » Sun Feb 14, 2016 12:43 pm
A certain box contains only blue (b), green (g) and red(r) marbles. If one marble is to be picked out from the box at random, which color marble is most likely to be picked?

(1) b/(g+r) > r/(g+b)

(2) g > b
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Source: — Data Sufficiency |
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by Nina1987 » Sun Feb 14, 2016 12:45 pm
Let b, g and r be fraction of blue, green and red marbles in the box. so b+g+r=1

st1) b/(g+r) > r/(g+b)
--> b/(1-b) > r/(1-r)
--> (1-b)/b < (1-r)/r
--> (1/b -1) < (1/r - 1)
--> 1/b < 1/r
--> b>r. INSUF
St2) g > b INSUF

1+2--> g>b>r we know g is most likely to be picked. SUFF Ans:C
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by Matt@VeritasPrep » Sun Feb 14, 2016 9:47 pm
S2 is very friendly: either red or green is most likely.

S1 is trickier.

b/(g + r) - r/(g + b) > 0

(bg + b² - rg - r²)/((g + r)(g + b)) > 0

bg + b² - rg - r² > 0

(b + r)(b - r) + g(b - r) > 0

(b - r)(b + r + g) > 0

So b > r, and either blue or green is most likely.

Together, green is the only common answer, so it must be the likeliest color!
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