ISEE Mathematics Achievement Question 20: Answer and Explanation
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Question: 20
6. Use the chart below to answer the question.
| MARBLES IN A BAG | |
| Color | Number |
| White | 20 |
| Black | 30 |
| Beige | 40 |
There are also purple marbles in the bag. Which of the following can NOT be the probability of randomly selecting a purple marble from the bag?
- A.
- B.
- C.
- D.
Correct Answer: D
Explanation:
D
Let x represent the number of purple marbles in the bag. Thus, there are 90 + x marbles in the bag. Set up an expression for the probability of selecting a purple marble: 
. Set this fraction equal to the value of each answer, cross multiply, and solve for x. For choice (A), x = 10. For choice (B), x = 30. For choice (C), x = 60. Choice (D) does not yield an integer value.
You can guess and check possible numbers of purple marbles, but this may be too time consuming. As an example, if you guess that there are 10 purple marbles, that would mean there are 100 marbles, and choice (A) would represent the probability of picking one of those 10 purple marbles.