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Ben has 30 pencils in a box. Each of the pencils is one of 5 different
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27 Nov 2018, 00:06
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56% (01:24) correct 44% (01:50) wrong based on 112 sessions
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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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27 Nov 2018, 00:16
Answer: C. 26 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.
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Ben has 30 pencils in a box. Each of the pencils is one of 5 different
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Updated on: 09 Jan 2019, 01:31
Bunuel wrote: 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 GMATinsight : for each color we have 6 pencils each so incase of worst 4 colors 6 pencils 4*6;24 after which the next set of 26 would be the min no pencils would be 26 IMO 26
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Originally posted by Archit3110 on 27 Nov 2018, 08:58.
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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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28 Nov 2018, 04:25
Bunuel wrote: 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 chetan2uPls Weigh in on this



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Ben has 30 pencils in a box. Each of the pencils is one of 5 different
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28 Nov 2018, 19:42
ParthSanghavi wrote: Bunuel wrote: 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 chetan2uPls Weigh in on this Hi ParthSanghavi, The question is a simple one if we understand what is happening in this question. Say there were 7 red balls and 3 blue balls. You have to pick balls one by one such that you MUST have one ball of each. Now, this is MUST, so take the worst scenario  you keep picking the larger color, red, one after another. So you pick up 7 red and now three blue ball are left. Now, when you pick a ball, it has to be blue. Thus, you MUST pick up 8 balls to be sure that you have a ball of each color. Let us apply the same to this question. We have 5 colors and 6 ball of each. There MUST be 2 of each. So, we take worst scenario again. We keep getting all other colors except one color, so you pick up 4*6=24 balls and there are 6 balls of same color. Now the next two will surely give you two of this left over color, so 24+2 are a MUST to be sure to pick up two of each. thus our answer is 26.
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1) Absolute modulus : http://gmatclub.com/forum/absolutemodulusabetterunderstanding210849.html#p1622372 2)Combination of similar and dissimilar things : http://gmatclub.com/forum/topic215915.html 3) effects of arithmetic operations : https://gmatclub.com/forum/effectsofarithmeticoperationsonfractions269413.html 4) Base while finding % increase and % decrease : https://gmatclub.com/forum/percentageincreasedecreasewhatshouldbethedenominator287528.html
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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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08 Jan 2019, 06:04
chetan2u wrote: ParthSanghavi wrote: Bunuel wrote: 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 chetan2uPls Weigh in on this Hi ParthSanghavi, The question is a simple one if we understand what is happening in this question. Say there were 7 red balls and 3 blue balls. You have to pick balls one by one such that you MUST have one ball of each. Now, this is MUST, so take the worst scenario  you keep picking the larger color, red, one after another. So you pick up 7 red and now three blue ball are left. Now, when you pick a ball, it has to be blue. Thus, you MUST pick up 8 balls to be sure that you have a ball of each color. Let us apply the same to this question. We have 5 colors and 6 ball of each. There MUST be 2 of each. So, we take worst scenario again. We keep getting all other colors except one color, so you pick up 5*5=25 balls and there are 6 balls of same color. Now the next two will surely give you two of this left over color, so 5*5+2 are a MUST to be sure to pick up two of each. thus our answer is 27. Hi Chetan, Is the answer 27  D, or 26  C?



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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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08 Jan 2019, 07:06
nausherwan wrote: chetan2u wrote: ParthSanghavi wrote: chetan2uPls Weigh in on this Hi ParthSanghavi, The question is a simple one if we understand what is happening in this question. Say there were 7 red balls and 3 blue balls. You have to pick balls one by one such that you MUST have one ball of each. Now, this is MUST, so take the worst scenario  you keep picking the larger color, red, one after another. So you pick up 7 red and now three blue ball are left. Now, when you pick a ball, it has to be blue. Thus, you MUST pick up 8 balls to be sure that you have a ball of each color. Let us apply the same to this question. We have 5 colors and 6 ball of each. There MUST be 2 of each. So, we take worst scenario again. We keep getting all other colors except one color, so you pick up 5*5=25 balls and there are 6 balls of same color. Now the next two will surely give you two of this left over color, so 5*5+2 are a MUST to be sure to pick up two of each. thus our answer is 27. Hi Chetan, Is the answer 27  D, or 26  C? Hi.. Answer will be 26. There was a typo, which I have corrected. Thanks
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1) Absolute modulus : http://gmatclub.com/forum/absolutemodulusabetterunderstanding210849.html#p1622372 2)Combination of similar and dissimilar things : http://gmatclub.com/forum/topic215915.html 3) effects of arithmetic operations : https://gmatclub.com/forum/effectsofarithmeticoperationsonfractions269413.html 4) Base while finding % increase and % decrease : https://gmatclub.com/forum/percentageincreasedecreasewhatshouldbethedenominator287528.html
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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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