A bag contains a total of x 6 balls of three colors of Black White and Brown such that the ratio of ...........

Quantitative Aptitude ( CCS) Data Sufficiency

A bag contains a total of (x+6) balls of three colors of Black, White and Brown such that the ratio of number of White and Brown balls is 3:4 resp. and the probability of drawing a Black ball is 1/3. Find the number of balls in the bag.

Statement I: Probability of drawing a white ball is (2/7).

Statement II: The number of Black balls in the bag is 2 less than the number of Brown balls.

Both are necessary

Only Statement I

Only Statement II

Both are not sufficient

Either I or II

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Explanation:

Let the number of White and Brown color balls be 3k and 4k resp.
So, the number of Black balls = (x+6) – (3k+4k) = (x – 7k +6)
Probability of drawing Black balls = 1/3 (x – 7k +6)/(x+6) = 1/3
=> 21k = 2x+12 –(1)
From I: Probability of drawing a white ball = 2/7 3k/(x+6) = 2/7
=> 21k = 2x+12 –(2)
Both the equations are same.
So, this statement is not sufficient.
From II: (x – 7k + 6) = 4k – 2
=> x = 11k – 8 –(3)
From (1) and (3), we get
21k – 12 = 22k – 16
=> k = 4
So, x = 11*4 – 8 = 36
Therefore, the total number of balls = 36 + 6 = 42
Hence, this statement is sufficient alone.

Hence, option 3 is the correct answer.