M07-35

Question

In a jar, there are 15 black chips and 5 white chips. What is the minimum number of chips we need to draw to ensure that we have at least 2 chips of the same color?

A. 19
B. 16
C. 6
D. 5
E. 3

Bunuel · Answer

Official Solution:

In a jar, there are 15 black chips and 5 white chips. What is the minimum number of chips we need to draw to ensure that we have at least 2 chips of the same color?

A. 19
B. 16
C. 6
D. 5
E. 3

In the worst-case scenario, the first two chips we draw are of different colors. However, the third chip we pick must match one of the first two, ensuring that we have at least two chips of the same color. Therefore, the answer is 3.

Answer: E

OreoShake · Answer

shouldnt the least amount of chips needed to be picked be 5? this is because after we remove 5 black chips, we will only have white chips making it sure that any two chips are of same colour. Bunuel I was unable to understand your explanation; please elaborate. Thanks.

Bunuel · Answer

The goal is to determine the minimum number of chips we need to draw in order to guarantee that we have at least 2 chips of the same color. This means we need to have either two white or two black chips.

In the worst-case scenario, the first two chips we draw are one black and one white chip: BW or WB. Regardless of the outcome, the third chip drawn will either be black or white. In any case, this will ensure that we have at least two chips of the same color: BWW or BWB.

You might find it helpful to review other worst-case scenario questions:

Worst Case Scenario Questions  from our  Special Questions Directory  to understand the concept better.

Manas1212 · Answer

Hi  Bunuel

Please help me understand this.

IMO,

For a best scenario(Least no of picks) We should select minimum 6 to ensure that one color chips are exhausted. 
For a worst scenario(Max no of picks) we should select minimum 17 to ensure the same.

If we are picking 2, then why are we considering the third to be of the other color ? why not of the same color as we have picked before ?

Please help me evaluate my thought process.

Bunuel · Answer

I believe you may have misunderstood the question. The question is asking for the minimum number of chips we need to pick in order to guarantee that we have at least two chips of the same color, either black or white.

In the worst-case scenario, the first two chips we pick will be one black and one white. The next pick will be either black or white. So, after three picks, we can be sure that we will have at least two black or at least two white chips.

Does this make sense?

Check other  Worst Case Scenario Questions  from our  Special Questions Directory  to understand the concept better.

Rashed12 · Answer

Dear  Bunuel ,

I am really confused about the above question. I have understood the below question and solution.  what is the difference between the two questions? 
the above question answer is 3, but my understanding is that answer is 16 when I am comparing this to the below solution.

kindly make me clear about the confusion.

The below solution form GMAT CLUB TEST and it is your solution.

BELOW IS REVISED VERSION OF THIS QUESTION:

A box contains 10 tablets of medicine A and 15 tablets of medicine B. What is the least number of tablets that should be taken from the box to ensure that at least two tablets of each kind are among the extracted?

A. 12
B. 15
C. 17
D. 19
E. 21

A. 12
B. 15
C. 17
D. 19
E. 21

The worst case scenario will be if we remove all 15 tablets of medicine B first. The next 2 tablets we remove have to be of medicine A, so to guarantee that at least two tablets of each kind will be taken we should remove minimum of 15+2=17 tablets.

Answer: C.

Bunuel · Answer

In this question, we aim to guarantee that we have at least 2 chips of the same color, meaning we need to have either two white or two black chips. The worst-case scenario occurs if, for the first two picks, we draw one black and one white chip: BW or WB. Regardless of the outcome, the next (3rd) chip drawn will be either black or white, and in either case, we will have two chips of the same color: BW - W or BW - B.

In this question, we want to guarantee that we have at least two tablets of each kind among the extracted ones. So, we need AABB. The worst case would be if we pick all 15 tablets of medicine B first: BBBBBBBBBBBBBBB. We will then be left with 10 tablets of medicine A. The next 2 tablets we remove must be of medicine A, resulting in the sequence  BB BBBBBBBBBBBBB AA . This ensures that we have at least two tablets of each kind.

Check other  Worst Case Scenario Questions  from our  Special Questions Directory  to understand the concept better.

Hope it helps.

Bunuel · Answer

I have edited the question and the solution by adding more details to enhance its clarity. I hope it is now easier to understand.

r_putra_rp · Answer

Gosh darnit I got fooled cz most of the question I had has been about minimum number of draws for  to get different colors  while the question is actually about  minimum to get same color

A bit of my aproach
Let's say we take the first two draws, the possible results are
WW
BB
BW
WB

the first two combinations are OK since we have two of the same colors, they haven't answered the question stem just yet, since we  must  have 2 of the same colors and combo 3 and 4 do not, thus next we'll consider the latter two

for the 3rd combo, the resultant will be either BWW or BWB. in either case, we have two same-colored pills.
for the 4th combo, the resultant will be either WBW or WBB. in either case, we have two same-colored pills.

notice that, whatever we do, the third draw will include at least 2 same-colored pills.

bumpbot · Answer

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M07-35

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