A bag contains black and white marbles. How many white marbles are the

Let b-->black marbles and w-->white marbles
stmt1 : p(w)=1/2 -->this just says that there are 50% of white marbles, but we cannot deduce actual no. of marbles, hence not sufficient

stmt2 : black marbles = 10, no mention on white marbles, nor any relation mentioned between b & w, hence not sufficient.

stmt1+stmt2 : from 1, we know 50% are white marbles, hence remaining 50% are black marbles, which is 10 (from stmt2)
hence, white marbles should be 10 in number.

Ans. C


Thanks,
JJo

St 1: The prob is same, which means that the no. of black and white marbles are same. But we cannot find a distinct no with this information.
Hence Not sufficient.

St 2: 10 black marbles. No info on white marbles. Not sufficient.

Combining 1 and 2:

The no. of white marbles = 10. Sufficient.

Option C

800score Official Solution:

The probability equals to the number of favourable outcomes divided by the number of all possible outcomes. Let’s denote the number of white marbles by w and the number of black marbles by b.

Statement (1) means w/(w + b) = 1/2. It yields w = b. So we can tell that white marbles make exactly half of all marbles in the bag. But we do NOT know how many black marbles or marbles in total there are. Therefore statement (1) by itself is NOT sufficient to answer the question.

Statement (2) means b = 10. But we do NOT know anything about white marbles. Statement (2) by itself is NOT sufficient.

If we use the both statements together, statement (1) implies w = b, while statement (2) is b = 10. Therefore w = 10. So statements (1) and (2) taken together are sufficient to answer the question, even though neither statement by itself is sufficient.

The correct answer is C.

(1) The probability of picking a white marble at random is 1/2
so the number of white marble is equal to the number of black marbles.
but we dont know the number of black marbles in the bag.
(1) itsefl is not sufficient

(2 )There are 10 black marbles in the bag
but we dont know the ratio of white marbles and black marbles
(2) itsefl is not sufficient.
combine (1) and (2), we can get- the number of white marbles is 10

ans: C

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