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

Question

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

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

chetan2u · Accepted Answer

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

CounterSniper · Answer

Corrected .

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

PKN · Answer

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)

KSBGC · Answer

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.

ScottTargetTestPrep · Answer

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.

Answer: E

targetbusiness · Answer

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)

chetan2u · Answer

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

chs123 · Answer

The wording confused me. I thought that 'you have at least' means that marbles are in the jar (the ones that are not removed).
I think it would be best to write something like: "If you COLLECT marbles one at a time..." instead of "REMOVE".

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

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

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