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Attend this FREE session to learn how to Define your GMAT Strategy, Create your Study Plan and Master the Core Skills to excel on the GMAT. # In a stack of cards, 9 cards are blue and the rest are red  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics Author Message TAGS: ### Hide Tags Manager Joined: 10 Oct 2008 Posts: 56 In a stack of cards, 9 cards are blue and the rest are red [#permalink] ### Show Tags 10 Oct 2008, 10:05 2 6 00:00 Difficulty: 25% (medium) Question Stats: 81% (02:25) correct 19% (02:51) wrong based on 367 sessions ### HideShow timer Statistics 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: 75 Re: In a stack of cards, 9 cards are blue and the rest are red [#permalink] ### Show Tags 10 Oct 2008, 10:42 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 the answer is (C) Senior Manager Joined: 04 Aug 2008 Posts: 360 Re: In a stack of cards, 9 cards are blue and the rest are red [#permalink] ### Show Tags 10 Oct 2008, 10:43 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 lets start with C probability to get first blue is 9/12 x second blue 8/11 bingo! that turns out to be 6/11 IMO C _________________ The one who flies is worthy. The one who is worthy flies. The one who doesn't fly isn't worthy Director Status: No dream is too large, no dreamer is too small Joined: 14 Jul 2010 Posts: 532 Re: In a stack of cards, 9 cards are blue and the rest are red [#permalink] ### Show Tags 13 Jan 2012, 11:58 2 Total card x so, 9/x*8/x-1 = 6/11 x^2 - x -132= 0 x = 12 Ans. C _________________ Collections:- PSof OG solved by GC members: http://gmatclub.com/forum/collection-ps-with-solution-from-gmatclub-110005.html DS of OG solved by GC members: http://gmatclub.com/forum/collection-ds-with-solution-from-gmatclub-110004.html 100 GMAT PREP Quantitative collection http://gmatclub.com/forum/gmat-prep-problem-collections-114358.html Collections of work/rate problems with solutions http://gmatclub.com/forum/collections-of-work-rate-problem-with-solutions-118919.html Mixture problems in a file with best solutions: http://gmatclub.com/forum/mixture-problems-with-best-and-easy-solutions-all-together-124644.html Manager Joined: 03 Oct 2009 Posts: 51 Re: In a stack of cards, 9 cards are blue and the rest are red [#permalink] ### Show Tags 17 Jan 2012, 19:04 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 EMPOWERgmat Instructor Status: GMAT Assassin/Co-Founder Affiliations: EMPOWERgmat Joined: 19 Dec 2014 Posts: 12853 Location: United States (CA) GMAT 1: 800 Q51 V49 GRE 1: Q170 V170 Re: In a stack of cards, 9 cards are blue and the rest are red [#permalink] ### Show Tags 10 Dec 2015, 17:37 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. Normally, when TESTing THE ANSWERS, we should start with either B or D. Answer B looks easier, so let's start there. Answer B: 11 total 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...). Answer C: 12 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. Final Answer: GMAT assassins aren't born, they're made, Rich _________________ 760+: Learn What GMAT Assassins Do to Score at the Highest Levels Contact Rich at: Rich.C@empowergmat.com # Rich Cohen Co-Founder & GMAT Assassin Special Offer: Save$75 + GMAT Club Tests Free
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Senior Manager
Joined: 20 Aug 2015
Posts: 389
Location: India
GMAT 1: 760 Q50 V44
Re: In a stack of cards, 9 cards are blue and the rest are red  [#permalink]

### Show Tags

11 Dec 2015, 03:38
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]

### Show Tags

30 Apr 2016, 03:35
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

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

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

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

$$x=12$$

Non-Human User
Joined: 09 Sep 2013
Posts: 8767
Re: In a stack of cards, 9 cards are blue and the rest are red  [#permalink]

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