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# A jar contains 20 marbles: 4 red, 6 white and 10 blue. If you remove

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Math Expert
Joined: 02 Sep 2009
Posts: 58464
A jar contains 20 marbles: 4 red, 6 white and 10 blue. If you remove  [#permalink]

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23 Aug 2018, 04:54
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Difficulty:

55% (hard)

Question Stats:

55% (01:22) correct 45% (01:49) wrong based on 80 sessions

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A jar contains 20 marbles: 4 red, 6 white and 10 blue. If you remove marbles one at a time, randomly, what is the minimum number that must be removed to be certain that you have at least 2 marbles of each colour?

A. 6
B. 10
C. 12
D. 16
E. 18

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Math Expert
Joined: 02 Aug 2009
Posts: 8023
Re: A jar contains 20 marbles: 4 red, 6 white and 10 blue. If you remove  [#permalink]

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23 Aug 2018, 05:56
Bunuel wrote:
A jar contains 20 marbles: 4 red, 6 white and 10 blue. If you remove marbles one at a time, randomly, what is the minimum number that must be removed to be certain that you have at least 2 marbles of each colour?

A. 6
B. 10
C. 12
D. 16
E. 18

Since we are looking at ' minimum number to be CERTAIN', take the extreme case
4 Red, 6 White and 10 Blue
let us remove the max first - 10 Blue gone
then next higher 6 White - 6 white gone
and then we have to pick 2 of Red as nothing else left..
so 10+6+2=18

E
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A jar contains 20 marbles: 4 red, 6 white and 10 blue. If you remove  [#permalink]

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Updated on: 23 Aug 2018, 06:13
Bunuel wrote:
A jar contains 20 marbles: 4 red, 6 white and 10 blue. If you remove marbles one at a time, randomly, what is the minimum number that must be removed to be certain that you have at least 2 marbles of each colour?

A. 6
B. 10
C. 12
D. 16
E. 18

Corrected .

Minimum required to be sure = 10 blue + 6 white + 2 red = 18

Originally posted by CounterSniper on 23 Aug 2018, 05:08.
Last edited by CounterSniper on 23 Aug 2018, 06:13, edited 2 times in total.
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Re: A jar contains 20 marbles: 4 red, 6 white and 10 blue. If you remove  [#permalink]

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23 Aug 2018, 05:36
Bunuel wrote:
A jar contains 20 marbles: 4 red, 6 white and 10 blue. If you remove marbles one at a time, randomly, what is the minimum number that must be removed to be certain that you have at least 2 marbles of each colour?

A. 6
B. 10
C. 12
D. 16
E. 18

We have 10 Blue, 6 White, and 4 Red marbles.
We have to certainly remove a minimum of 2 numbers of marbles of each color.
I will go by options:-
A. Remove 6: Chances are there, you may choose 6 whites. --->No Red ,No Blue.......... DISCARD
B. Remove 10: Chances are there, you may choose 10 blue.--->No Red ,No White.......... DISCARD
C. Remove 12: Chances are there, you may choose 10 blue & 2 White.--->No Red.......... DISCARD
D. Remove 16: Chances are there, you may choose 10 blue & 6 White.--->No Red.......... DISCARD
E. Remove 18: Chances are there, you may choose 10 blue(fully taken), 6 White(fully taken), and 2 Red(its automatic).--->Each marbles at a minimum of 2 numbers.......... (This is the answer)

Ans. (E)
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Re: A jar contains 20 marbles: 4 red, 6 white and 10 blue. If you remove  [#permalink]

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23 Aug 2018, 12:22
Bunuel wrote:
A jar contains 20 marbles: 4 red, 6 white and 10 blue. If you remove marbles one at a time, randomly, what is the minimum number that must be removed to be certain that you have at least 2 marbles of each colour?

A. 6
B. 10
C. 12
D. 16
E. 18

Total Marble : 20

Red: 4

White: 6

Blue: 10

Note: 2 Marbles of each color ( At least )

For this kinda question Back solving Strategy is the best.

A) 6.........................All 6 can be white

B) 10.............All 10 can be blue

C) 12............( 10 blue + 2 white). Here no red.

D) 16............(10 blue + 6 white) Here no red.

E) 18............( 10 + 6 + 2). This is the option where we are compelled to pick up All the marbles and minimum 2 marbles of each color.

The best answer is E.
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Re: A jar contains 20 marbles: 4 red, 6 white and 10 blue. If you remove  [#permalink]

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26 Aug 2018, 19:25
Bunuel wrote:
A jar contains 20 marbles: 4 red, 6 white and 10 blue. If you remove marbles one at a time, randomly, what is the minimum number that must be removed to be certain that you have at least 2 marbles of each colour?

A. 6
B. 10
C. 12
D. 16
E. 18

We must remove at least 18 marbles to guarantee we have at least 2 marbles of each colour. That is because if we remove 17 marbles, it’s possible that we have 10 blue, 6 white and 1 red marbles, and we don’t have 2 marbles of each colour. However, if we remove one more marble and since that marble must be red, we have (at least) 2 marbles of each colour.

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Re: A jar contains 20 marbles: 4 red, 6 white and 10 blue. If you remove  [#permalink]

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27 Aug 2018, 10:21
chetan2u wrote:
Bunuel wrote:
A jar contains 20 marbles: 4 red, 6 white and 10 blue. If you remove marbles one at a time, randomly, what is the minimum number that must be removed to be certain that you have at least 2 marbles of each colour?

A. 6
B. 10
C. 12
D. 16
E. 18

Since we are looking at ' minimum number to be CERTAIN', take the extreme case
4 Red, 6 White and 10 Blue
let us remove the max first - 10 Blue gone
then next higher 6 White - 6 white gone
and then we have to pick 2 of Red as nothing else left..
so 10+6+2=18

E

chetan2u I did not even understand what the question wants us to do?
It went up above my head.!!
How does removing 18 marbles leave 2 marbles of each color as asked in the question? (highlighted in the red color)
Math Expert
Joined: 02 Aug 2009
Posts: 8023
Re: A jar contains 20 marbles: 4 red, 6 white and 10 blue. If you remove  [#permalink]

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27 Aug 2018, 18:36
1
siddreal wrote:
chetan2u wrote:
Bunuel wrote:
A jar contains 20 marbles: 4 red, 6 white and 10 blue. If you remove marbles one at a time, randomly, what is the minimum number that must be removed to be certain that you have at least 2 marbles of each colour?

A. 6
B. 10
C. 12
D. 16
E. 18

Since we are looking at ' minimum number to be CERTAIN', take the extreme case
4 Red, 6 White and 10 Blue
let us remove the max first - 10 Blue gone
then next higher 6 White - 6 white gone
and then we have to pick 2 of Red as nothing else left..
so 10+6+2=18

E

chetan2u I did not even understand what the question wants us to do?
It went up above my head.!!
How does removing 18 marbles leave 2 marbles of each color as asked in the question? (highlighted in the red color)

Hi

The question means that you start picking these marble such that you have 2 of each colour in your hand.
Now if you are lucky you may pick up RRBBWW so in 6 you have two of each colour.
But there may be another guy who picks up WWWWWW , so now he doesn't have two of each colour.

So how does one be certain that he has two of each. You take the worst scenario, wherein you keep picking the same colour till that colour gets over
So it will be BBB...10times and then WW...6 times and then RR
Now the moment you pick the two R you have two of each colour. Thus 10+6+2=18
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Re: A jar contains 20 marbles: 4 red, 6 white and 10 blue. If you remove   [#permalink] 27 Aug 2018, 18:36
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# A jar contains 20 marbles: 4 red, 6 white and 10 blue. If you remove

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