Multiple choice

A box contains identical balls in three different colors - Black, white and blue. There are 8-x blue balls and 2X+5 black balls. If a ball is picked at random from the box, what is the probability that the ball is either blue or black? 1) X=2 2) There are 3X+39 white balls in the box.

  1. Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient

  2. Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient

  3. BOTH statements (1) and (2) TOGETHER are sufficient to answer

  4. EACH statement ALONE is sufficient to answer the question asked

  5. Statements (1) and (2) TOGETHER are NOT sufficient to answer the question
Reveal answer Fill a bubble to check yourself
B Correct answer
AI explanation

The probability of picking either a blue or black ball requires the sum of blue and black balls divided by the total balls. Using statement 2 alone, the number of blue balls is 8 minus x, black balls is 2x plus 5, and white balls is 3x plus 39, making the total number of balls 6x plus 52. The sum of blue and black balls is x plus 13, which is exactly one-fourth of the total balls (6x plus 52), meaning the probability is 1/4 without needing the exact value of x. Statement 1 alone only gives x equals 2, which provides the individual quantities but no total number of balls, making it insufficient. Therefore, statement 2 alone is sufficient to answer the question.

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