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In a jar there are balls in different colors: blue, red, green and yel

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In a jar there are balls in different colors: blue, red, green and yel  [#permalink]

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New post Updated on: 12 Sep 2014, 13:50
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In a jar there are balls in different colors: blue, red, green and yellow.
The probability of drawing a blue ball is 1/8.
The probability of drawing a red ball is 1/5.
The probability of drawing a green ball is 1/10.
If a jar cannot contain more than 50 balls, how many yellow balls are in the Jar?

A. 23
B. 20
C. 24
D. 17
E. 25

Originally posted by mohana on 07 Oct 2009, 17:48.
Last edited by Bunuel on 12 Sep 2014, 13:50, edited 1 time in total.
Renamed the topic, edited the question and added the OA.
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Re: In a jar there are balls in different colors: blue, red, green and yel  [#permalink]

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New post 07 Oct 2009, 18:30
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The answer is A: 23.

First step: determine how many balls are in the jar. Essentially, since the number of balls can't be a decimal number, it must be a multiple of 5, 8 and 10. The LCM of those three numbers is 40.

The probability of drawing a blue ball is 1/8. -> 5 blue balls
The probability of drawing a red ball is 1/5. -> 8 red balls
The probability of drawing a green ball is 1/10. -> 4 green balls

Number of yellow balls = 40 - 5 - 8 - 4 = 23
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Re: In a jar there are balls in different colors: blue, red, green and yel  [#permalink]

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New post 07 Oct 2009, 18:33
mohana wrote:
In a jar there are balls in different colors: blue, red, green and yellow.
The probability of drawing a blue ball is 1/8.
The probability of drawing a red ball is 1/5.
The probability of drawing a green ball is 1/10.
If a jar cannot contain more than 50 balls, how many yellow balls are in the Jar?

a) 23.
b) 20.
c) 24.
d) 17.
e) 25.


The probability of drawing a blue ball is 1/8 = 5/40
The probability of drawing a red ball is 1/5 = 8/40
The probability of drawing a green ball is 1/10 = 4/40
Yellow balls = 40-(5+8+4) = 23

Answer is A.
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Re: In a jar there are balls in different colors: blue, red, green and yel  [#permalink]

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New post 07 Oct 2009, 18:49
thanks. This is very helpful. I didnt know how to get that 40.

I am facing challenges with this one too.

In Rwanda, the chance for rain on any given day is 50%. What is the probability that it rains on 4 out of 7 consecutive days in Rwanda?

a) 4/7
b) 3/7
c) 35/128
d) 4/28
e) 28/135
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Re: In a jar there are balls in different colors: blue, red, green and yel  [#permalink]

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New post 07 Oct 2009, 18:59
1
Basically you can approach the problem this way:

You choose one specific scenario: R R R R N N N (R = Rain, N = No Rain). The probability for this scenario is (0.5)^7.

You can arrange the R's in 7C4 ways.

\(\frac{1}{2}^7 * 7C4\)

\(= \frac{1}{128} * 35\)

\(= \frac{35}{128}\)

The correct answer is C.
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Re: In a jar there are balls in different colors: blue, red, green and yel  [#permalink]

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New post 07 Oct 2009, 19:12
thanks,

this is really helpful, and explained in a simple way.


Do you know of any online resource that can be of help for probability questions.
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Re: In a jar there are balls in different colors: blue, red, green and yel  [#permalink]

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New post 07 Oct 2009, 19:33
mohana wrote:
thanks,

this is really helpful, and explained in a simple way.


Do you know of any online resource that can be of help for probability questions.


Check this out: http://gmatclub.com/forum/combinations-permutations-and-probability-references-56486.html#p402561
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Re: In a jar there are balls in different colors: blue, red, green and yel  [#permalink]

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New post 08 Oct 2009, 02:36
1
LCM of (8,5,10) < 50 ....i.e. 40 balls

The probability of drawing a blue ball is Pb = 1/8 : B/40 thus B = 5
The probability of drawing a red ball is Pr = 1/5 : R/40 thus R = 8
The probability of drawing a green ball is Pg = 1/10 : G/40 thus G = 4

Thus Yellow balls = 40-(5+8+4) = 23....OA A
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Re: In a jar there are balls in different colors: blue, red, green and yel  [#permalink]

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New post 08 Oct 2009, 06:24
answer of 1st

just add the given probabilities p(blue)+p(red)+p(green) i.e

1/8+1/5+1/10=17/40

now we know p(blue)+p(red)+p(green)+p(yellow)=1

17/40+p(yellow)=1

p(yellow)=23/40

i.e why yellow balls are 23.

if it has been given that that no of balls are more than 50 and less than 100 then it would have been 46.


answer of 2nd.

to select 4 days out of 7=7c4=(7*6*5*4)/(1*2*3*4)=35

now given that there is 50% chance of rain

probability of rain everyday is 1/2

for 7 days=1/2*1/2*1/2*1/2*1/2*1/2*1/2=1/128

so probability of rains on 4 out of 7 consecutive days is 35/128




hope this will help
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Re: In a jar there are balls in different colors: blue, red, green and yel  [#permalink]

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New post 03 May 2011, 08:50
total number of balls will have factors 8,5 and 10.Hence the number will be multiple of 40.
total balls = 40
yellow ball = 40- (5+8+4) = 23
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Re: In a jar there are balls in different colors: blue, red, green and yel  [#permalink]

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New post 19 Sep 2014, 22:14
mohana wrote:
In a jar there are balls in different colors: blue, red, green and yellow.
The probability of drawing a blue ball is 1/8.
The probability of drawing a red ball is 1/5.
The probability of drawing a green ball is 1/10.
If a jar cannot contain more than 50 balls, how many yellow balls are in the Jar?

A. 23
B. 20
C. 24
D. 17
E. 25


# Blue Balls = Total Balls / 8, similarly #Red Balls = TB/5; #Green Balls = TB/10

# Yellow Balls= TB- #blue-#Red-#Green = (TB*23)/40

SInce y has to be a integer, TB has to be 40. And therefore # Yellow balls =23

ps: i hate questions pertaining to balls.
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In a jar there are balls in different colors: blue, red, green and yel  [#permalink]

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New post 19 Aug 2018, 10:36
mohana wrote:
In a jar there are balls in different colors: blue, red, green and yellow.
The probability of drawing a blue ball is 1/8.
The probability of drawing a red ball is 1/5.
The probability of drawing a green ball is 1/10.
If a jar cannot contain more than 50 balls, how many yellow balls are in the Jar?

A. 23
B. 20
C. 24
D. 17
E. 25


OA:A
Total number of balls will be multiple of L.C.M of \(8,5,10\) ie multiple of \(40\).
Also given in the question, Total number of ball \(≤ 50\).
As 0 and negative multiples of \(40\) are not possible, then Only option left for total number of balls is \(40\).

Number of blue ball :\(\frac{1}{8}*40 = 5\)

Number of red ball :\(\frac{1}{5}*40 = 8\)

Number of green ball :\(\frac{1}{10}*40 = 4\)

Number of Yellow ball \(= 40 - 5-8-4 =23\)
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Re: In a jar there are balls in different colors: blue, red, green and yel  [#permalink]

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New post 20 Aug 2018, 00:02
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LCM of 8,5 and 10= 40
therefore, number of blue balls-5, red-8 and green-4
Remaining balls(yellow)-40-17=23
Answer- A
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Re: In a jar there are balls in different colors: blue, red, green and yel  [#permalink]

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New post 23 Aug 2018, 15:39
mohana wrote:
In a jar there are balls in different colors: blue, red, green and yellow.
The probability of drawing a blue ball is 1/8.
The probability of drawing a red ball is 1/5.
The probability of drawing a green ball is 1/10.
If a jar cannot contain more than 50 balls, how many yellow balls are in the Jar?

A. 23
B. 20
C. 24
D. 17
E. 25


We can create the equation:

1/8 + 1/5 + 1/10 + y = 1

Multiplying by 40, we have:

5 + 8 + 4 + 40y = 40

40y = 23

y = 23/40, so there are 23 yellow balls.

Alternate Solution:

The number of balls of each color inside the jar must be a whole number. Moreover, the total number of balls must be divisible by 8, 5 and 10; so let’s first find the LCM of 8, 5 and 10:

LCM(8, 5, 10) = 40

So, the number of balls could be 40, 80, 120, etc. However, we are also given that there are no more than 50 balls in the jar; thus the total number of balls must be 40. Then, there are 40 x 1/8 = 5 blue balls, 40 x 1/5 = 8 red balls and 40 x 1/10 = 4 green balls. Thus, there are 40 - (5 + 8 + 4) = 23 yellow balls.

Answer: A
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Re: In a jar there are balls in different colors: blue, red, green and yel &nbs [#permalink] 23 Aug 2018, 15:39
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