Official Solution:

There are 15 black chips and 5 white chips in a jar. What is the least number of chips we should pick to guarantee that we have 2 chips of the same color?

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

Worst case scenario would be if the first two chips we pick will be of the different colors. But the next chip must match with either of two, so 3 is the answer.

Answer: E
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imagine we pick any chip first and put it on the table - no matter what color. next we drag the second and put it next to the first. if we are lucky these 2 chips will be either black or white (less probable) but if not we need to pick another one because we have a combination of black and white:

BL WH

So what happens next? We drag out whatever chip it is and place it on the table - voila we guarantee we will have a pair: either a pair of 2 blacks or a pair of 2 whites

That's a simple one. If we take three , at least two will be of same type. Hence, answer is 3.

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.

What is the least number of chips we should pick to guarantee that we have 2 chips of the same color? So, we need to have tow white or two black chips.

The worst case would be if for the first two pick we'll get one black and one white chips: BW or WB. The next (3rd) chip will be B or W in any case we'll have two chips of the same color: BW - W or BW - B.

You should check other worst case scenario questions. Link is in the post above.
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Hmm, I guess i understood the question incorrectly; i had inferred how many picks till we guarantee two colors same in a ROW. Thanks Bunuel.

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.

I think you misunderstood the question. The question asks about the number of picks to guarantee that we have either two black or two white chips.

The worst case would be if we pick one black and one white for the first two picks. The next one will be either black or white. So, after three picks we for sure 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.
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Hi

Can someone explain how this question is different from the one below:

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?
(source: GMAT Club forums)

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

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.

In this question, we want to ensure, to guarantee that we have 2 chips of the same color? So, we need to have tow white or two black chips. The worst case would be if for the first two pick we'll get one black and one white chips: BW or WB. The next (3rd) chip will be B or W in any case we'll have two chips of the same color: BW - W or BW - B.



In this question, we want to ensure, to guarantee that we have at least two tablets of each kind are among the extracted. So, we need AABB. The worst case would be if we pick all 15 tablets of medicine B first: BBBBBBBBBBBBBBB. We will be left with 10 tablets of of medicine A. So, the next 2 tablets we remove have to be of medicine A, so we'd have BBBBBBBBBBBBBBBAA. This gives us 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.
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If you have 15 of one color, and 5 of another color, then there is a possibility that drawing 15 chips will still only yield chips of a SINGLE color.

Thus, you need to draw 16 chips.

WORST CASE SCENARIO is the one that I just described. This question is worded poorly or your solution is false.

Please read the question carefully!

There are 15 black chips and 5 white chips in a jar. What is the least number of chips we should pick to guarantee that we have 2 chips of the same color?

A. 19
B. 16
C. 6
D. 5
E. 3
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So obvious, so easy. Still got it WRONG

What can be easier? we have got two colors, of course after picking two chips there is no way to pick the third color, so you have to pick already picked color.

frustrated

There are 15 black chips and 5 white chips in a jar. What is the least number of chips we should pick to guarantee that we have 2 chips of the DIFFERENT color?

In this case the answer will be 16 i guess.
Bunnel can you confirm.

Bunuel chetan2u
Hello,
After reading all the above questions/answers I still have trouble understanding this problem.
The way I see it, is that in order to guarantee that we will pick 2 chips of the same color then we should pick 17 pieces (worst scenario would be picking all 15 blacks) so the correct answer, as per my understanding would be A , so what is the flaw of my approach?

Hi,
There are only two colours and that is the thing which is important. How many each colour really does not affect the answer.
You pick W, next has to be B or W. worst case it is B, so W, B, _.
Now the next has to be B or W, so whatever it is, we will surely have 2 of some colour, W or B.
Say there were 15 colours and we were to talk of this answer, then answer would be 16.
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I agree with chetan2u, why is it the worst case if we pick 1black and 1white?

Why isn't the worst case when all that we pick is of the SAME color ? This is why the question is referring to the "least" number in order to avoid such scenario in which all we pick is of the SAME color.

It is not?

Bunuel

hi Bunuel can you provide a link for more questions like this?
Thanks.