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There are 15 marbles in a jar consisting of

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There are 15 marbles in a jar consisting of  [#permalink]

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New post 19 Jan 2019, 00:58
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A
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Difficulty:

  35% (medium)

Question Stats:

72% (02:10) correct 28% (01:34) wrong based on 34 sessions

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There are 15 marbles in a jar consisting of only yellow and white marbles. The probability of choosing 2 white marbles, one after the other, is \(\frac{2}{21}\). How many yellow marbles are in the jar?

(A) 2
(B) 5
(C) 7
(D) 9
(E) 10
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Re: There are 15 marbles in a jar consisting of  [#permalink]

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New post 19 Jan 2019, 04:23
blitzkriegxX wrote:
There are 15 marbles in a jar consisting of only yellow and white marbles. The probability of choosing 2 white marbles, one after the other, is \(\frac{2}{21}\). How many yellow marbles are in the jar?

(A) 2
(B) 5
(C) 7
(D) 9
(E) 10


Where i went wrong, went too fast to solve this question.

Most important tip -> write in

what you want to calculate



To find -> Yellow marbles Y

Choosing 2 White Marbles, one after the other, will mean

n = number of white marbles

n /15 * (n-1)/14 = 2/21

n^2 - n - 20=0
n^2 - 5n + 4n - 20 =0
( n - 5 ) (n + 4 ) = 0
n =5

Number of Yellow marbles = 15 - n = 15 - 5 = 10
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Re: There are 15 marbles in a jar consisting of  [#permalink]

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New post 19 Jan 2019, 04:24
blitzkriegxX wrote:
There are 15 marbles in a jar consisting of only yellow and white marbles. The probability of choosing 2 white marbles, one after the other, is \(\frac{2}{21}\). How many yellow marbles are in the jar?

(A) 2
(B) 5
(C) 7
(D) 9
(E) 10


Let number of white balls be W

Probability of picking White on first try is W/15
Probability of picking White on second try is W-1/14

Multiplying both the events -

W/15 * W-1/15 = 2/21


Solving for W, we get 5 or -4.

The number of balls cannot be negative.

15-5 = 10
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Re: There are 15 marbles in a jar consisting of  [#permalink]

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New post 19 Jan 2019, 16:43
What is the source?
Quite convoluted for a sub-600 question. I managed to complete it in under 2 minutes, but it was a rush.
Is there a quicker method than x/15·(x-1)/14 etc?
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There are 15 marbles in a jar consisting of  [#permalink]

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New post 19 Jan 2019, 17:14
1
Since there are 15 marbles in the jar to start, we know that calculating the probability of choosing two white marbles involves multiplying two fractions, the first of which will have a denominator of 15 and the second of which will have a denominator of 14.

15 x 14 = 210.

The probability given by the question is 2/21.

So, to get to the number of white marbles, convert 2/21 so that it has the denominator 210. We get 20/210.

Now, since the number of white marbles will decrease by 1 when the first one is removed, we know that the we need to multiply two numbers that differ by 1 to arrive at the numerator of our fraction.

The numerator is 20. The two numbers that differ by 1 must be 5 and 4.

The number of white marbles in the jar before any were removed is 5.

Check the question to see what it is asking for, the number of yellow marbles.

The number of yellow marbles = 15 - 5 = 10

The correct answer is E.
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New post 19 Jan 2019, 18:34
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philipssonicare wrote:
What is the source?
Quite convoluted for a sub-600 question. I managed to complete it in under 2 minutes, but it was a rush.
Is there a quicker method than x/15·(x-1)/14 etc?


Hey philipssonicare !

Did you solve the final equation completely?
You don't have to solve it completely. It's a PS question, so we can try picking the numbers from the options!
Because we are finding yellow and not red marbles, remember to subtract the number in the option from the total.
(If you pick to try option D for instance, pick 15-10 = 5 )

After you write this -
x/15 * x-1/14 = 2/21
x(x-1) = 2/21 * 210
X(x-1) = 20

Now all you have to do is pick numbers from the options and put into the above equation.
This will save you a lot of time and you can solve the question well within 2 minutes.
This can be done in most of the PS questions. Always try to use the options.

Hope this helps!

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Re: There are 15 marbles in a jar consisting of  [#permalink]

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New post 20 Jan 2019, 11:51
Can this question be solved using favorable outcomes / all outcomes?

Let X be the number of white balls in the jar
(XC2)/(15C2)=2/21
21[(X)(X-1)]/2=15*14
(X)(X-1)=20
X=5

15-5=10 yellow balls.

Please let me know if my solution is flawed!
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Re: There are 15 marbles in a jar consisting of   [#permalink] 20 Jan 2019, 11:51
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