Data Sufficiency

way2ashish wrote:Q) A bag contains some red and some blue marbles.How many red marbles are in the bag?
(1) If two marbles are selected from the bag, the probability of selecting one red and one blue marble is 1/4
(2) There are a total of 8 marbles in the bag.

Statement 1: Say the total number of marbles in the bag is N and there are R red marbles. Hence, there are (N - R) blue marbles.

Number of ways to select two marbles from N marbles = NC2 = N(N - 1)/2
Number of ways to select one red marble from R marbles and one blue marbles from (N - R) marbles = (RC1)*((N - R)C1) = R*(N - R)

Hence, the probability of selecting one red and one blue marble = [R*(N - R)]/[N(N - 1)/2]
Hence, [R*(N - R)]/[N(N - 1)/2] = 1/4

As we have two unknowns N and R we cannot find the value of them from only one equation.

Statement 2: Clearly this statement is not sufficient

1 & 2 Together: N = 8
Now we have only one unknown R and we can solve the equation we obtained from statement 1 and find the value of R.

Sufficient

The correct answer is C.