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Ben has 30 pencils in a box. Each of the pencils is one of 5 different
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26 Jul 2025, 09:42
26 Jul 2025, 09:42
Expert Reply
00:00
Question Stats:
25% (02:05) correct
75% (01:52) wrong based on 4 sessions
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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 to ensure that he selects at least 2 pencils of each color?
A. 24
B. 25
C. 26
D. 27
E. 28
the minimum number of pencils that he must select to ensure that he selects at least 2 pencils of each color?
A. 24
B. 25
C. 26
D. 27
E. 28
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Re: Ben has 30 pencils in a box. Each of the pencils is one of 5 different
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03 Aug 2025, 22:30
03 Aug 2025, 22:30
Expert Reply
- You want to ensure 2 pencils of each color.
- There are 5 colors, 6 pencils each $\rightarrow$ total 30 pencils.
- The worst case for not having 2 pencils of each color is picking all 6 pencils from 4 colors +1 pencil from the 5th color.
Total pencils picked in that case:
$$
\(4 \times 6+1=24+1=25\)
$$
Only then would the 5 th color have less than 2 pencils.
- So, to guarantee at least 2 pencils of each color, you must pick:
$$
\(25+1=26\)
$$
pencils.
Final answer:
26 (which corresponds to option C)
Summary:
- Maximum pencils without at least 2 pencils in each color $=25$.
- Therefore, minimum pencils to guarantee 2 pencils in each color $=26$.
Answer: (C) 26
- There are 5 colors, 6 pencils each $\rightarrow$ total 30 pencils.
- The worst case for not having 2 pencils of each color is picking all 6 pencils from 4 colors +1 pencil from the 5th color.
Total pencils picked in that case:
$$
\(4 \times 6+1=24+1=25\)
$$
Only then would the 5 th color have less than 2 pencils.
- So, to guarantee at least 2 pencils of each color, you must pick:
$$
\(25+1=26\)
$$
pencils.
Final answer:
26 (which corresponds to option C)
Summary:
- Maximum pencils without at least 2 pencils in each color $=25$.
- Therefore, minimum pencils to guarantee 2 pencils in each color $=26$.
Answer: (C) 26
gmatclubot
Re: Ben has 30 pencils in a box. Each of the pencils is one of 5 different [#permalink]
03 Aug 2025, 22:30
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