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Ben has 30 pencils in a box. Each of the pencils is one of 5 different colors, and there are 6 pencils of each color. If Ben selects pencils one at a time from the box without being able to see the pencils, what is the minimum number of pencils that he must select in order to ensure that he selects at least 2 pencils of each color?
- a)24
- b)25
- c)26
- d)27
- e)28
Correct answer is option 'C'. Can you explain this answer?
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Most Upvoted Answer
Ben has 30 pencils in a box. Each of the pencils is one of 5 different...
Let me 5 color be C1, C2, C3, C4, C5
In the worst case scenario, Ben selects all 6 pencils of each of the 4 colors. Total ways = 6X4 = 24
Then Ben must select at least 2 pencil from the 5th color to ensure that he selects at least 2 pencils of each color.
Therefore, minimum number of ways = 24+2 = 26. Hence, option C is the correct choice.
In the worst case scenario, Ben selects all 6 pencils of each of the 4 colors. Total ways = 6X4 = 24
Then Ben must select at least 2 pencil from the 5th color to ensure that he selects at least 2 pencils of each color.
Therefore, minimum number of ways = 24+2 = 26. Hence, option C is the correct choice.
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Ben has 30 pencils in a box. Each of the pencils is one of 5 different...
Understanding the Problem
Ben has 30 pencils of 5 different colors, with 6 pencils of each color. The goal is to find the minimum number of pencils he must select to ensure he has at least 2 of each color.
Analyzing Worst-Case Scenario
To determine the minimum number of pencils needed, consider the worst-case scenario in selection:
- Ben could potentially select the maximum number of pencils without getting 2 of each color.
Calculating Worst-Case Selections
1. Select 1 Pencil of Each Color:
- Ben can pick 1 pencil from each of the 5 colors.
- Total pencils selected so far: 5
2. Select 1 Pencil from Each Color Again:
- He can pick another pencil from each of the 5 colors (totaling 2 pencils of each color).
- Total pencils selected so far: 10 (5 from the first selection + 5 from the second selection)
3. Now, To Ensure 2 of Each Color:
- To avoid having 2 of any specific color, he can only select 1 pencil of each color until he has 5 colors represented.
- If he continues picking just 1 pencil of each color, he would need to pick 10 pencils (5 colors x 2).
Final Selections for Guarantee
To ensure that there are at least 2 pencils of each color:
- After selecting 10 pencils, if he picks any additional pencil (the 11th), it must be from one of the colors he already has, resulting in at least one color having 2 pencils.
Conclusion
Therefore, to guarantee at least 2 pencils of each color, Ben must select a minimum of:
- Total pencils needed = 10 + 2 = 12
However, since there are 6 pencils of each color, to ensure this condition is met with maximum efficiency, he would need to select at least 26 pencils to ensure he has 2 of each color.
Thus, the final answer is option C: 26.
Ben has 30 pencils of 5 different colors, with 6 pencils of each color. The goal is to find the minimum number of pencils he must select to ensure he has at least 2 of each color.
Analyzing Worst-Case Scenario
To determine the minimum number of pencils needed, consider the worst-case scenario in selection:
- Ben could potentially select the maximum number of pencils without getting 2 of each color.
Calculating Worst-Case Selections
1. Select 1 Pencil of Each Color:
- Ben can pick 1 pencil from each of the 5 colors.
- Total pencils selected so far: 5
2. Select 1 Pencil from Each Color Again:
- He can pick another pencil from each of the 5 colors (totaling 2 pencils of each color).
- Total pencils selected so far: 10 (5 from the first selection + 5 from the second selection)
3. Now, To Ensure 2 of Each Color:
- To avoid having 2 of any specific color, he can only select 1 pencil of each color until he has 5 colors represented.
- If he continues picking just 1 pencil of each color, he would need to pick 10 pencils (5 colors x 2).
Final Selections for Guarantee
To ensure that there are at least 2 pencils of each color:
- After selecting 10 pencils, if he picks any additional pencil (the 11th), it must be from one of the colors he already has, resulting in at least one color having 2 pencils.
Conclusion
Therefore, to guarantee at least 2 pencils of each color, Ben must select a minimum of:
- Total pencils needed = 10 + 2 = 12
However, since there are 6 pencils of each color, to ensure this condition is met with maximum efficiency, he would need to select at least 26 pencils to ensure he has 2 of each color.
Thus, the final answer is option C: 26.
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Ben has 30 pencils in a box. Each of the pencils is one of 5 different colors, and there are 6 pencils of each color. If Ben selects pencils one at a time from the box without being able to see the pencils, what is the minimum number of pencils that he must select in order to ensure that he selects at least 2 pencils of each color?a)24b)25c)26d)27e)28Correct answer is option 'C'. Can you explain this answer?
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Ben has 30 pencils in a box. Each of the pencils is one of 5 different colors, and there are 6 pencils of each color. If Ben selects pencils one at a time from the box without being able to see the pencils, what is the minimum number of pencils that he must select in order to ensure that he selects at least 2 pencils of each color?a)24b)25c)26d)27e)28Correct answer is option 'C'. Can you explain this answer? for GMAT 2024 is part of GMAT preparation. The Question and answers have been prepared according to the GMAT exam syllabus. Information about Ben has 30 pencils in a box. Each of the pencils is one of 5 different colors, and there are 6 pencils of each color. If Ben selects pencils one at a time from the box without being able to see the pencils, what is the minimum number of pencils that he must select in order to ensure that he selects at least 2 pencils of each color?a)24b)25c)26d)27e)28Correct answer is option 'C'. Can you explain this answer? covers all topics & solutions for GMAT 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Ben has 30 pencils in a box. Each of the pencils is one of 5 different colors, and there are 6 pencils of each color. If Ben selects pencils one at a time from the box without being able to see the pencils, what is the minimum number of pencils that he must select in order to ensure that he selects at least 2 pencils of each color?a)24b)25c)26d)27e)28Correct answer is option 'C'. Can you explain this answer?.
Ben has 30 pencils in a box. Each of the pencils is one of 5 different colors, and there are 6 pencils of each color. If Ben selects pencils one at a time from the box without being able to see the pencils, what is the minimum number of pencils that he must select in order to ensure that he selects at least 2 pencils of each color?a)24b)25c)26d)27e)28Correct answer is option 'C'. Can you explain this answer? for GMAT 2024 is part of GMAT preparation. The Question and answers have been prepared according to the GMAT exam syllabus. Information about Ben has 30 pencils in a box. Each of the pencils is one of 5 different colors, and there are 6 pencils of each color. If Ben selects pencils one at a time from the box without being able to see the pencils, what is the minimum number of pencils that he must select in order to ensure that he selects at least 2 pencils of each color?a)24b)25c)26d)27e)28Correct answer is option 'C'. Can you explain this answer? covers all topics & solutions for GMAT 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Ben has 30 pencils in a box. Each of the pencils is one of 5 different colors, and there are 6 pencils of each color. If Ben selects pencils one at a time from the box without being able to see the pencils, what is the minimum number of pencils that he must select in order to ensure that he selects at least 2 pencils of each color?a)24b)25c)26d)27e)28Correct answer is option 'C'. Can you explain this answer?.
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