A certain jar of jelly beans contains 50 black jelly beans, 50 red

Question

﻿A certain jar of jelly beans contains 50 black jelly beans, 50 red jelly beans, 50 green jelly beans, and no other jelly beans. What is the minimum number of jelly beans that must be removed from the jar to ensure that at least 14 of the jelly beans that are removed have the same color?

(A) 30
(B) 40
(C) 50
(D) 64
(E) 114

Bunuel · Accepted Answer

It's important to recognize that the beans can be removed in many different orders. Ideally, the best case scenario to meet the requirement of removing at least 14 jelly beans of the same color would involve immediately removing 14 beans of the same color. However, this specific order of removal is not guaranteed. What we need to determine is a number of draws that, regardless of the order of removal, will always ensure that at least 14 of the jelly beans of the same color are extracted. Hence, to guarantee this under any sequence, it becomes necessary to consider the worst-case scenario, which would be the most unfavorable order of removal.

The most unfavorable order would be to remove 13 black beans, 13 red beans, and 13 green beans, totaling 39 beans, and we'd still not have 14 beans of the same color. However, the next jelly bean, regardless of its color, will match with one of the already extracted 13 beans, making 14 of the same color. Therefore, the answer is 39 + 1 = 40 jelly beans.

Answer: B.

Check other  Worst Case Scenario Questions  from our  Special Questions Directory  to practice.

gmatophobia · Answer

We have to consider the worst possible situation. Suppose we take out three jelly beans, all the jelly beans can be of different colors. If we perform this step, i.e. remove three jelly beans at a time, 13 times, we would have taken out  13*3 = 39  jelly beans.

In this case, at worst, we have  13  jelly beans of each color with us. The next jelly bean, whatever color that may be, when taken out, will ensure that we have at least 14 jelly beans of the same color.

Hence,  (13*3) + 1 = 40

Option B

uCS2020 · Answer

What I did for this question is,
I first checked all the answer choices and thought of ways in each answer choice if I can use 13 or less jelly beans to make up the answer choice
For example

A:30
I can have 10 black,10 green and 10 red 
They are less than 14 so this is not my answer

B:40
Let’s check with 13 for each colour as it’s the highest we can go
13+13+13 = 39
This is smaller than 40 and I would HAVE to use 14 or more for at least one of them,so answer is B

Answer = B

Posted from my mobile device

ad_la · Answer

Why isnt the answer for this question E? Isn't it possible for me to pick up 50 black jelly beans in a row before grabbing another color?

Bunuel · Answer

The answer 114 would be correct if the question were "What is the minimum number of jelly beans that must be removed from the jar to ensure that at least 14 of the jelly beans of  each color  are removed?" However, the original question asks for 14 jelly beans of any one of the colors. Hope you see the difference.

nisen20 · Answer

it is asking us  to make sure  that the removed 39 beans are evenly comprised of 13 beans for each color and then the 40th undisputedly becomes the savior of this question.

edit: i made a mistake.

Bunuel · Answer

No, that's not the case at all. It seems that you did not read either the question or the solutions above carefully. Please review the discussion above more thoroughly. It also seems that you are not familiar with this type of question, so it would be prudent to follow the link given in my post.

Hope this helps.

P.S. Please also note that this is a question from official mocks, so its quality is as good as it gets. Studying them diligently is advisable, while ridiculing them will get you nowhere.

nisen20 · Answer

hi  Bunuel

finally i got the concept of the worst case scenario and what the question wants.
 
 What is the  maximum  number of jelly beans that can be removed from the jar to ensure that 14 of the jelly beans that are removed have the same color?

test makers are normally not so generous to make questions straightforward, and in this particular one "at least" changes the game.
 
with this "at least" added, "the maximum number" has to be replaced by "the minimum number", a totally opposite direction making me confused.

thank you for your help.

ShilpiAgnihotrii · Answer

Why is the answer not 64? First 50 are picked of any kind and then 14 of the next kind so that worst case scenario is covered, at least 14 of 2 kinds are picked in this case .
Pls help with my understanding.

Bunuel · Answer

The reason the answer is not 64 is that the requirement is to ensure that at least 14 jelly beans of just one color are removed, not two or more colors. When you remove 50 jelly beans of any specific color, you'd already have 14 of the same color.

Please read the solution  here  carefully and follow the links to similar questions.

ShilpiAgnihotrii · Answer

Oh yes!!! thank you, Bunuel.

NetOrb · Answer

is this logic correct? 
every colour has equal probability of being picked, so if i pick 42 jelly beans, its can be assumed that there are equal number of jelly beans in the mix that is 14, and even if one colour is less it means other would be more so we have at-least 14 of one colour, closest to that is 40. so ans is 40

Bunuel · Answer

No. Equal probability does  not  mean that 42 draws will contain exactly 14 beans of each color.

Also, you cannot choose 40 merely because it is the closest option to 42. The  guarantee  comes from the worst-case distribution: after 39 draws, you could have 13 of each color, so the 40th bean must make 14 of one color.

Please review the complete solution above and follow the links to similar questions for additional practice and a better understanding of the concept.

A certain jar of jelly beans contains 50 black jelly beans, 50 red

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A certain jar of jelly beans contains 50 black jelly beans, 50 red

Prep Toolkit

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