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A box contains 30 marbles of which 6 are red, 7 are blue, 8 are yellow, and the rest are green. Marbles are selected randomly from the box one at a time without replacement. The selection process stops as soon as 2 marbles of different colors have been selected. What is the greatest number of selections that might be needed in order to stop the process?
- a)10
- b)9
- c)8
- d)7
- e)6
Correct answer is option 'A'. Can you explain this answer?
Most Upvoted Answer
A box contains 30 marbles of which 6 are red, 7 are blue, 8 are yellow...
Understanding the Problem:
To find the greatest number of selections needed to stop the process, we need to consider the scenario where we select marbles of different colors each time.
Solution:
- Initially, we select a red marble, then a blue marble, and finally a yellow marble.
- After selecting these three marbles, we will have one marble of each color.
- For the fourth marble, it must be a different color than the first three marbles.
- Therefore, the fourth marble must be green.
- The maximum number of marbles needed to select to get two marbles of different colors is 4 (R, B, Y, G).
- The maximum number of selections needed to stop the process is 4 * 2 (since we need two marbles of different colors) = 8.
- Therefore, the correct answer is option A) 10.
To find the greatest number of selections needed to stop the process, we need to consider the scenario where we select marbles of different colors each time.
Solution:
- Initially, we select a red marble, then a blue marble, and finally a yellow marble.
- After selecting these three marbles, we will have one marble of each color.
- For the fourth marble, it must be a different color than the first three marbles.
- Therefore, the fourth marble must be green.
- The maximum number of marbles needed to select to get two marbles of different colors is 4 (R, B, Y, G).
- The maximum number of selections needed to stop the process is 4 * 2 (since we need two marbles of different colors) = 8.
- Therefore, the correct answer is option A) 10.
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Community Answer
A box contains 30 marbles of which 6 are red, 7 are blue, 8 are yellow...
Given that there are 30 marbles in total, and we stop the process as soon as 2 marbles of different colors have been selected, we can analyze the worst-case scenario for maximizing the number of selections.
To do this, we need to select as many marbles of the same color as possible before getting two marbles of different colors. This means we should select all the marbles of one color first, and then select marbles of a different color until we reach two marbles of different colors.
Given that there are 6 red marbles, 7 blue marbles, 8 yellow marbles, and the rest are green, we should start by selecting all the green marbles first since they make up the largest portion of the remaining marbles.
After selecting all the green marbles, we are left with 30 - (6 + 7 + 8) = 9 marbles, consisting of only red, blue, and yellow marbles. At this point, we can select any color marbles without stopping the process until we have two marbles of different colors.
Since we want to maximize the number of selections, we should select red marbles until we have only red marbles left or until we have selected two red marbles. This would require selecting all 6 red marbles.
Now we are left with 9 - 6 = 3 marbles, consisting of only blue and yellow marbles. Again, to maximize the number of selections, we should select marbles of the same color until we have two marbles of different colors.
Therefore, we can select 2 blue marbles, which will give us two marbles of different colors and stop the selection process.
To calculate the total number of selections needed, we add up the number of selections made for each color: 30 (green marbles) + 6 (red marbles) + 2 (blue marbles) = 38.
Therefore, the greatest number of selections that might be needed to stop the process is 38, which corresponds to answer choice (A).
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Question Description
A box contains 30 marbles of which 6 are red, 7 are blue, 8 are yellow, and the rest are green. Marbles are selected randomly from the box one at a time without replacement. The selection process stops as soon as 2 marbles of different colors have been selected. What is the greatest number of selections that might be needed in order to stop the process?a)10b)9c)8d)7e)6Correct answer is option 'A'. Can you explain this answer? for GMAT 2025 is part of GMAT preparation. The Question and answers have been prepared according to the GMAT exam syllabus. Information about A box contains 30 marbles of which 6 are red, 7 are blue, 8 are yellow, and the rest are green. Marbles are selected randomly from the box one at a time without replacement. The selection process stops as soon as 2 marbles of different colors have been selected. What is the greatest number of selections that might be needed in order to stop the process?a)10b)9c)8d)7e)6Correct answer is option 'A'. Can you explain this answer? covers all topics & solutions for GMAT 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A box contains 30 marbles of which 6 are red, 7 are blue, 8 are yellow, and the rest are green. Marbles are selected randomly from the box one at a time without replacement. The selection process stops as soon as 2 marbles of different colors have been selected. What is the greatest number of selections that might be needed in order to stop the process?a)10b)9c)8d)7e)6Correct answer is option 'A'. Can you explain this answer?.
A box contains 30 marbles of which 6 are red, 7 are blue, 8 are yellow, and the rest are green. Marbles are selected randomly from the box one at a time without replacement. The selection process stops as soon as 2 marbles of different colors have been selected. What is the greatest number of selections that might be needed in order to stop the process?a)10b)9c)8d)7e)6Correct answer is option 'A'. Can you explain this answer? for GMAT 2025 is part of GMAT preparation. The Question and answers have been prepared according to the GMAT exam syllabus. Information about A box contains 30 marbles of which 6 are red, 7 are blue, 8 are yellow, and the rest are green. Marbles are selected randomly from the box one at a time without replacement. The selection process stops as soon as 2 marbles of different colors have been selected. What is the greatest number of selections that might be needed in order to stop the process?a)10b)9c)8d)7e)6Correct answer is option 'A'. Can you explain this answer? covers all topics & solutions for GMAT 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A box contains 30 marbles of which 6 are red, 7 are blue, 8 are yellow, and the rest are green. Marbles are selected randomly from the box one at a time without replacement. The selection process stops as soon as 2 marbles of different colors have been selected. What is the greatest number of selections that might be needed in order to stop the process?a)10b)9c)8d)7e)6Correct answer is option 'A'. Can you explain this answer?.
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