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# In a stack of cards, 9 cards are blue and the rest are red

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Manager
Joined: 10 Oct 2008
Posts: 56
In a stack of cards, 9 cards are blue and the rest are red  [#permalink]

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10 Oct 2008, 11:05
2
6
00:00

Difficulty:

25% (medium)

Question Stats:

80% (01:47) correct 20% (02:18) wrong based on 350 sessions

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In a stack of cards, 9 cards are blue and the rest are red. If 2 cards are to be chosen at random from the stack without replacement, the probability that the cards chosen will both be blue is 6/11. What is the number of cards in the stack?

A. 10
B. 11
C. 12
D. 15
E. 18
Manager
Joined: 27 Sep 2008
Posts: 76
Re: In a stack of cards, 9 cards are blue and the rest are red  [#permalink]

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10 Oct 2008, 11:42
1
1
$$9/(9+x)*8/(8+x) = 6/11$$

$$0 = 17x+x^2-60$$

$$0 = (x+20)(x-3)$$

x=3

9+3 = 12

Senior Manager
Joined: 04 Aug 2008
Posts: 362
Re: In a stack of cards, 9 cards are blue and the rest are red  [#permalink]

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10 Oct 2008, 11:43
2
Jcpenny wrote:
In a stack of cards, 9 cards are blue and the rest are red. If 2 cards are to be chosen at random from the stack without replacement, the probability that the cards chosen will both be blue is 6/11. What is the number of cards in the stack?

A. 10
B. 11
C. 12
D. 15
E. 18

Okay here is best bet to use plug in method

probability to get first blue is 9/12 x second blue 8/11

bingo! that turns out to be 6/11

IMO C
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Re: In a stack of cards, 9 cards are blue and the rest are red  [#permalink]

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13 Jan 2012, 12:58
2
Total card x
so,
9/x*8/x-1 = 6/11
x^2 - x -132= 0
x = 12
Ans. C
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Posts: 52
Re: In a stack of cards, 9 cards are blue and the rest are red  [#permalink]

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17 Jan 2012, 20:04
In a stack of cards, 9 cards are blue and the rest are red. If 2 cards are to be chosen at random from the stack without replacement, the probability that the cards chosen will both be blue is 6/11. What is the number of cards in the stack?

A. 10
B. 11
C. 12
D. 15
E. 18

9 - B
let total cards be n

(9/n) * (8/(n-1)) = 6/11
(72 * 11) / 6 = n (n-1)
12 * 11 = n (n-1)

n = 12
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Re: In a stack of cards, 9 cards are blue and the rest are red  [#permalink]

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10 Dec 2015, 18:37
Hi All,

This question can be solved by TESTing THE ANSWERS.

We're told that we have 9 blue cards and an unknown number of red cards. We're also told that if 2 cards are to be chosen at random from the stack WITHOUT replacement, then the probability that the cards chosen will BOTH be BLUE is 6/11. We're asked for the TOTAL number of cards.

With 11 total cards, and 9 blue cards, the probability of pulling two blue cards is...
(9/11)(8/10) = 36/55

Since 6/11 = 30/55, this is clearly NOT the answer. The probability that occurs with Answer B is a little TOO BIG, so we need an answer that lowers the probability (and thus, requires MORE total cards...).

With 12 total cards, and 9 blue cards, the probability of pulling two blue cards is...
(9/12)(8/11) = 24/44 = 6/11
This is an exact MATCH for what we were told, so this MUST be the answer.

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Rich
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Joined: 20 Aug 2015
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Re: In a stack of cards, 9 cards are blue and the rest are red  [#permalink]

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11 Dec 2015, 04:38
Jcpenny wrote:
In a stack of cards, 9 cards are blue and the rest are red. If 2 cards are to be chosen at random from the stack without replacement, the probability that the cards chosen will both be blue is 6/11. What is the number of cards in the stack?

A. 10
B. 11
C. 12
D. 15
E. 18

Assume the numbe rof red cards = x
Total cards = 9 + x

P(Both blue cards) = $$\frac{9}{{x+9}} * \frac{8}{{x + 8}}$$ = $$\frac{6}{11}$$

$$\frac{72}{{(x + 9)(x + 8)}}$$ = 6/11
132 =$$x^2$$ + 17x + 72
$$x^2$$ + 17x - 60 =0
(x + 20)(x - 3) = 0
x can take only positive values, hence x = 3

Total cards = 9 + 3 = 12
Option C
Intern
Joined: 05 Jul 2014
Posts: 6
In a stack of cards, 9 cards are blue and the rest are red  [#permalink]

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30 Apr 2016, 04:35
1
Jcpenny wrote:
In a stack of cards, 9 cards are blue and the rest are red. If 2 cards are to be chosen at random from the stack without replacement, the probability that the cards chosen will both be blue is 6/11. What is the number of cards in the stack?

A. 10
B. 11
C. 12
D. 15
E. 18

$$b=9$$
$$x=b+r$$

$$\frac{b}{x} *\frac{b-1}{x-1}=b/x$$
$$\frac{9}{x} *\frac{8}{x-1}=6/11$$
$$\frac{72}{x(x-1)}=\frac{6}{11}$$

$$12*11=x(x-1)$$

$$x=12$$

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Posts: 7780
Re: In a stack of cards, 9 cards are blue and the rest are red  [#permalink]

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28 Jul 2018, 04:03
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Re: In a stack of cards, 9 cards are blue and the rest are red &nbs [#permalink] 28 Jul 2018, 04:03
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