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

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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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