Multiple choice

There are 21 balls in a bag, out of which 20 are black and 1 is blue. The average of black balls is x kg and total weight of all the 21 balls is 61 kg. If none of the balls is more than 3 kg and weights of all balls are integers, find the weight of the blue ball.

  1. 1

  2. 2

  3. 3

  4. Data inadequate

  5. None of these
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

The total weight is 61 kg for 21 balls. The average of 20 black balls is x, so their total weight is 20x. Thus, 20x + weight_blue = 61. Since weights are integers and max weight is 3, 20x must be 60 (if x=3) or 40 (if x=2). If 20x=60, blue=1. If 20x=40, blue=21 (impossible). However, the problem does not provide enough constraints to uniquely determine x.

AI explanation

The total weight is 61 kg and all weights are integers, meaning the weights of the balls could theoretically be 2 kg and 3 kg. However, the specific weight of the blue ball could be 1, 2, or 3 kg, as there are multiple valid integer distributions of weights for the 21 balls that sum to 61 kg without violating the maximum weight rule. Because we cannot uniquely determine the exact weight of the blue ball, the data is inadequate.

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