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From a bag containing 12 identical blue balls, y identical

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From a bag containing 12 identical blue balls, y identical [#permalink] New post 06 Apr 2006, 14:32
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From a bag containing 12 identical blue balls, y identical yellow balls, and no other balls, one ball will be removed at random. If the probability is less than 2/5 that the removed ball will be blue, what is the least number of yellow balls that must be in the bag?

A. 17
B. 18
C. 19
D. 20
E. 21
[Reveal] Spoiler: OA

Last edited by Bunuel on 22 Sep 2013, 02:54, edited 1 time in total.
Renamed the topic, edited the question, added the answer choices and the OA.
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 [#permalink] New post 06 Apr 2006, 14:38
12/x = 2/5

x = 30 total number of balls.

There must be at least 18 yellow balls in the bag.
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 [#permalink] New post 07 Apr 2006, 07:18
Agree with NTLancer.

Since the prob of blue balls is LESS than 2/5, you need at least 19 yellow balls in the bag.
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 [#permalink] New post 07 Apr 2006, 15:54
Agree

The number of yellow balls is atleast 19.

Since yellow balls must be greater than 18...hence least number is 19
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 [#permalink] New post 07 Apr 2006, 22:19
Agree with 19 too.

Since 2/5=12/x, x = 30 so if probability is less than 2/5 that means x is >30, say 31 then 31-12=19 yellow balls.
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Re: PS - probability [#permalink] New post 09 Apr 2006, 11:38
(12 blue) / (12 blue + x yellow) = 2/5

12/30 = 2/5

The denominator must be 30. You have 12 already which means you need 18 yellow balls. This makes the equation equal to each other. However, you want less than 2/5 so add one ball to make it 19.
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Re: [#permalink] New post 21 Sep 2013, 22:46
It is 18
P(blue) = 12 / (12+Y)
P(blue) < 2/5
solving this: 12 /12+Y = 2/5
y = 18
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Re: Re: [#permalink] New post 22 Sep 2013, 02:57
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alexgomez2013 wrote:
It is 18
P(blue) = 12 / (12+Y)
P(blue) < 2/5
solving this: 12 /12+Y = 2/5
y = 18


The answer is 19, not 18. Notice that we have an inequality sign there.

From a bag containing 12 identical blue balls, y identical yellow balls, and no other balls, one ball will be removed at random. If the probability is less than 2/5 that the removed ball will be blue, what is the least number of yellow balls that must be in the bag?
A. 17
B. 18
C. 19
D. 20
E. 21

P(blue) = \frac{12}{12+y}<\frac{2}{5} --> y>18 --> y_{min}=19.

Answer: C.

Hope it's clear.
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Re: From a bag containing 12 identical blue balls, y identical [#permalink] New post 25 Nov 2013, 12:52
Matador wrote:
From a bag containing 12 identical blue balls, y identical yellow balls, and no other balls, one ball will be removed at random. If the probability is less than 2/5 that the removed ball will be blue, what is the least number of yellow balls that must be in the bag?

A. 17
B. 18
C. 19
D. 20
E. 21


It goes like this.

12 Blue
y yellow

12 + y total

12/x = 2/5

So x = 30, x being the total number of ballos
Then yellow> 30-12 = 18

Therefore, yellow must be at least 19

Cheers!
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Re: From a bag containing 12 identical blue balls, y identical   [#permalink] 25 Nov 2013, 12:52
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