Multiple choice

Passage

The following questions are accompanied by two statements or three statements A, B and C. You have to determine which statement(s) is/are necessary/sufficient to answer the question.

There are x Red, y Blue and 7 Green balls in the bag . What will be the value of yWhen a ball is drawn out of the bag then its probability being Red is 5/18When a ball is drawn out of the bag then its probability being Blue is 3/9

  1. (a)Statement A alone is sufficient

  2. (b)Statement B alone is sufficient

  3. (c)Both statement A and B together are required

  4. (d)Either statement A alone or statement B alone is sufficient

  5. (e)Statement A and B together are not sufficient
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Total balls = x + y + 7. P(Red) = x/(x+y+7) = 5/18. P(Blue) = y/(x+y+7) = 3/9 = 1/3 = 6/18. From these, x/(x+y+7) = 5/18 and y/(x+y+7) = 6/18. Thus x+y+7 must be a multiple of 18. Both statements are needed to solve for x and y.

AI explanation

Statement A gives the probability of red as 5/18, meaning x divided by the total balls equals 5/18, but we still need the total to find x or y. Statement B gives the probability of blue as 3/9, meaning y divided by the total balls equals 1/3, which gives another equation but still leaves two variables. By setting the total balls as x plus y plus 7, you must combine both probability equations to solve for the total number of balls, allowing you to subsequently find y.

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