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There are 100 black balls, 100 red balls and 100 green balls evenly mi

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There are 100 black balls, 100 red balls and 100 green balls evenly mi [#permalink]

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New post Updated on: 06 Sep 2017, 20:27
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[GMAT math practice question]

There are 100 black balls, 100 red balls and 100 green balls evenly mixed in a jar. What is the minimum number of balls to ensure that at least 15 balls selected are the same color?

A. 40
B. 41
C. 42
D. 43
E. 44

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Originally posted by MathRevolution on 06 Sep 2017, 01:34.
Last edited by MathRevolution on 06 Sep 2017, 20:27, edited 1 time in total.
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Re: There are 100 black balls, 100 red balls and 100 green balls evenly mi [#permalink]

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New post 06 Sep 2017, 02:27
MathRevolution wrote:
[GMAT math practice question]

There are 100 black balls, 100 red balls and 100 green balls evenly mixed in a jar. What is the minimum number of balls to ensure that at least 15 beans selected are the same color?

A. 40
B. 41
C. 42
D. 43
E. 44


Not able to get the question.. What does the word "beans" mean here?. Also if we consider Balls instead of bean then also we can't arrive at any of the options.
Is there some kind of trick involved in the question ?
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Re: There are 100 black balls, 100 red balls and 100 green balls evenly mi [#permalink]

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New post 06 Sep 2017, 02:30
Hi,

Please clarify what do you mean by beans here?
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Re: There are 100 black balls, 100 red balls and 100 green balls evenly mi [#permalink]

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New post 06 Sep 2017, 02:33
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Re: There are 100 black balls, 100 red balls and 100 green balls evenly mi [#permalink]

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New post 06 Sep 2017, 02:51
Luckisnoexcuse wrote:
MathRevolution wrote:
[GMAT math practice question]

There are 100 black balls, 100 red balls and 100 green balls evenly mixed in a jar. What is the minimum number of balls to ensure that at least 15 beans selected are the same color?

A. 40
B. 41
C. 42
D. 43
E. 44


14*3 + 1 = 43
D


How can we say that.. The minimum number of balls to ensure at least 15 balls of same color is 15 and not 43..
If all the selected 15 balls are RED
or say if all the selected balls are GREEN
or say if all the selected balls are BLACK

So, the answer should be 15.
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Re: There are 100 black balls, 100 red balls and 100 green balls evenly mi [#permalink]

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New post 06 Sep 2017, 03:02
Luckisnoexcuse wrote:
MathRevolution wrote:
[GMAT math practice question]

There are 100 black balls, 100 red balls and 100 green balls evenly mixed in a jar. What is the minimum number of balls to ensure that at least 15 beans selected are the same color?

A. 40
B. 41
C. 42
D. 43
E. 44


14*3 + 1 = 43
D


can u please explain how you reached this solution
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Re: There are 100 black balls, 100 red balls and 100 green balls evenly mi [#permalink]

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New post 06 Sep 2017, 03:03
Bunuel wrote:
jatin0705 wrote:
Hi,

Please clarify what do you mean by beans here?


It's a typo should be "balls" instead.


Can you help us solve this, please?
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Re: There are 100 black balls, 100 red balls and 100 green balls evenly mi [#permalink]

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New post Updated on: 06 Sep 2017, 03:50
1
shashankism wrote:
Luckisnoexcuse wrote:
MathRevolution wrote:
[GMAT math practice question]

There are 100 black balls, 100 red balls and 100 green balls evenly mixed in a jar. What is the minimum number of balls to ensure that at least 15 beans selected are the same color?

A. 40
B. 41
C. 42
D. 43
E. 44


14*3 + 1 = 43
D


How can we say that.. The minimum number of balls to ensure at least 15 balls of same color is 15 and not 43..
If all the selected 15 balls are RED
or say if all the selected balls are GREEN
or say if all the selected balls are BLACK

So, the answer should be 15.


I can explain more.

Maybe we can use real world scenario like this :
- Suppose we have 5 pairs of red socks and 5 pairs of black socks in our drawer.
- We want to pick randomly to get one pair of the same color, maybe we in a hurry so we cannot take a closer look at the socks color.
- How do we want to make sure that we can get one pair?
- If we only take 2 - as your answer - so we MAY get 2 black socks, 2 red socks OR one black plus one red. There is no certainty we get one pair of same color.
- But, if we take 3 - as Luckisnoexcuse answer - we DEFINITELY get at least one pair of the same color.

Hope it helps.
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Originally posted by septwibowo on 06 Sep 2017, 03:07.
Last edited by septwibowo on 06 Sep 2017, 03:50, edited 2 times in total.
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Re: There are 100 black balls, 100 red balls and 100 green balls evenly mi [#permalink]

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New post 06 Sep 2017, 03:19
rahulkashyap wrote:
Luckisnoexcuse wrote:
MathRevolution wrote:
[GMAT math practice question]

There are 100 black balls, 100 red balls and 100 green balls evenly mixed in a jar. What is the minimum number of balls to ensure that at least 15 beans selected are the same color?

A. 40
B. 41
C. 42
D. 43
E. 44


14*3 + 1 = 43
D


can u please explain how you reached this solution


In order to to ensure that at least 15 balls selected are the same color...

if we choose 14 balls of each color first (14*3 = 42) and then one ball of any color..we will be certain that atleast 15 balls of one color are selected.
Hope it helps
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Re: There are 100 black balls, 100 red balls and 100 green balls evenly mi [#permalink]

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New post 06 Sep 2017, 03:45
septwibowo wrote:

Maybe we can use real world scenario like this :
- Suppose we have 5 pairs of red socks and 5 pairs of black socks in our drawer.
- We want to pick randomly to get one pair of the same color, maybe we in a hurry so we cannot take a closer look at the socks color.
- How do we want to make sure that we can get one pair?
- If we only take 2 - as your answer - so we MAY get 2 black socks, 2 red socks OR one black plus one red. There is no certainty we get one pair of same color.
- But, if we take 3 - as chetan2u answer - we DEFINITELY get at least one pair of the same color.

Hope it helps.


I got your answer.. Nice Explanation.. I actually got confused with the word minimum.. But Now I understand why it is 14*3 +1 = 43.. Thanks..
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Expert Post
Math Revolution GMAT Instructor
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Joined: 16 Aug 2015
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Re: There are 100 black balls, 100 red balls and 100 green balls evenly mi [#permalink]

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New post 08 Sep 2017, 01:03
=>
We can assume we have 14 black balls, 14 red balls and 14 green balls. After that, if we have just one more ball, it ensures we have 15 balls with a same color.

Thus we need 43 ( = (15-1) + (15-1) + (15-1) + 1 = 14 + 14 + 14 + 1 ) balls.40 balls ensure there are 15 balls that have a same color.

Ans: D
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Re: There are 100 black balls, 100 red balls and 100 green balls evenly mi   [#permalink] 08 Sep 2017, 01:03
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