The Answer is C:

Question Stem: The stem does not provide much information, only that there is a Jar with white balls in it (probably more colors as well) and we are asked to determine whether we have enough information to calculate the probability of selecting a white ball. To calculate the probability we therefore need to know the ratio of white balls to balls of any other color.

Statement 1: We learn that there are twice as many white balls as balls of any other color. This is insufficient, as we don't know how many other colors are there. We might for example have 10 white balls and 5 red balls, which would give a ratio of 10:5 and a probability of \(\frac{10}{(10+5)}=\frac{10}{15}=\frac{2}{3}\). We might also have 10 white balls, 5 red balls and 5 blue balls, which leads to 10:5:5 and \(\frac{10}{(10+5+5)}=\frac{1}{2}\).

Statement 2: This is also insufficient, as we only know about absolute values, not about ratios. There could be for example 40 white balls and 10 red balls. This leads to 4:1 or \(\frac{40}{(40+10)}=\frac{4}{5}\). Or we have 90 white balls and 60 red balls, which leads to \(\frac{90}{(90+60)}=\frac{4}{5}\).

Combined: This is sufficient. If we have twice as many white balls as balls of any other color and 30 white balls more than all other balls combined, these two statements contradict each other for more than 1 other color: If there are two other colors, red and blue, and we have double the amount of white balls, the sum of red and blue balls must equal the number of white balls, which contradicts statement 2. We can therefore conclude that there is only 1 other color and the two equations:

\(number of white balls = 2 * number of red balls\)

\(number of white balls = 30 + number of red balls\).

If you don't see the answer directly, you can plug one equation into the other and get 60 white balls and 30 red balls. From that we can derive the probability of selecting a white ball: \(\frac{60}{(60+30)}=\frac{2}{3}\). Answer C is sufficient.

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\(\sqrt{-1}\) \(2^3\) \(\Sigma\) \(\pi\) ... and it was delicious!

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