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27 Nov 2018, 00:06
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C
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
45%
(medium)
Question Stats:
67% (01:29) correct
33%
(01:56)
wrong
based on 460
sessions
History
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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
A. 24
B. 25
C. 26
D. 27
E. 28
28 Nov 2018, 19:42
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ParthSanghavi
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.
General Discussion
27 Nov 2018, 00:16
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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.
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.
