BREAKING: Target Test Prep releases Brand New 2026 On Demand GMAT prep course

Redeem
TTP OnDemand GMAT Video Course
Featured Course

Target Test Prep GMAT OnDemand

Scott Woodbury-Stewart’s private virtual classroom — 400 hours of master-class video lessons for the GMAT Focus Edition.

  • 715+ score guarantee — highest in the industry (99th percentile)
  • 52 chapters · 1,500+ lessons · 4,000+ practice questions
  • 400 hours of video · 1,500+ instructor-led HD smartboard lessons
  • 300,000+ students accepted to Harvard, Stanford, Wharton, Booth & Sloan & more
  • 24/7 live support + weekly Zoom office hours with GMAT instructors
  • TTP AI Assist — 24/7 AI-powered virtual tutor for instant help
  • 1,200+ flashcards + AI-powered study assistant & daily calendar
  • OnDemand, LiveTeach & GMAT Bootcamp formats available
  • Also: GRE, SAT Math & Executive Assessment courses
  • MBA Admissions Consulting now available
  • 🏆 2025 EdTech Breakthrough Award: Test Prep Solution Provider of the Year
  • 200,000+ students served
  • 5-day free trial — $0 to start, no auto-billing, cancel anytime
★★★★★ 5.0 (559 reviews)
130-pt guarantee
$0 to start then $127/mo
Start Free 5-Day Trial Read 559 Reviews →

Probability Problem

Expert replies
Post new topic Post Reply
Previous Topic Next Topic
Master | Next Rank: 500 Posts
Posts: 458
Joined: Sun Aug 31, 2008 10:44 amFollowed by: 1 member
Thanked: 3 times
by gmat009 » Thu Oct 02, 2008 8:25 am
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

This is the way I did:
Blue cards= 9 Red cards=x Total cards=9+x
9C2/(9+x)C2 =6/11
Calculating this I am getting x=20,-3.
I am not sure my method is wrong or I am making calculation mistake.
OA is C
Top
Join the discussion
Log in to postLogin with Googleuse password
QUOTE IN REPLY
Source: — Problem Solving |
Master | Next Rank: 500 Posts
Posts: 145
Joined: Mon Sep 29, 2008 1:14 am
Thanked: 13 times

by mental » Thu Oct 02, 2008 9:00 am
Let total number of cards be x
9 are blue

probability of two cards = 9/x*8/x-1 = 72/x(x-1)
this is given as 6/11

72/ x(x-1) = 6/11

x^2 -x -132=0

solving we get, x=12, x=-11

Ans 12.
Top
Join the discussion
Log in to postLogin with Googleuse password
QUOTE IN REPLY
Master | Next Rank: 500 Posts
Posts: 145
Joined: Mon Sep 29, 2008 1:14 am
Thanked: 13 times

by mental » Thu Oct 02, 2008 9:03 am
your equation was correct, probably some sign mistake

(9C2)/(9+x)c2 = 9*8/(9+x)(8+x) = 6/11

132 = 72+17x+x^2

or x^2 + 17x -60 = 0

gives factors as (x +20)(x-3)=0
x=3, -20

total cards = 3+9=12
Top
Join the discussion
Log in to postLogin with Googleuse password
QUOTE IN REPLY
Master | Next Rank: 500 Posts
Posts: 458
Joined: Sun Aug 31, 2008 10:44 amFollowed by: 1 member
Thanked: 3 times

by gmat009 » Thu Oct 02, 2008 9:07 am
mental wrote:your equation was correct, probably some sign mistake

(9C2)/(9+x)c2 = 9*8/(9+x)(8+x) = 6/11

132 = 72+17x+x^2

or x^2 + 17x -60 = 0

gives factors as (x +20)(x-3)=0
x=3, -20

total cards = 3+9=12
Thanks.........
I got x=3,-20 but forgot to add 9 and 3
Top
Join the discussion
Log in to postLogin with Googleuse password
QUOTE IN REPLY
Post new topic Post Reply
• Page 1 of 1