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 →

DS - Prob. difficult question

Expert replies
Post new topic Post Reply
Previous Topic Next Topic
User avatar
Legendary Member
Posts: 1665
Joined: Thu Nov 03, 2011 7:04 pmFollowed by: 70 members
Thanked: 165 times
by karthikpandian19 » Sun May 27, 2012 6:18 pm
Every passenger on a certain airplane is from either Japan or Australia; no one is from both. Every passenger is reading either a novel or a biography; no one is reading both. If a passenger is to be selected at random, is the probability that the passenger is both from Japan and reading a novel greater than the probability that the passenger is both from Australia and reading a biography.

(1) The probability that a randomly selected passenger is either from Japan or reading a novel or both is 208/251.

(2) The probability that a randomly selected passenger is either from Australia or reading a biography or both is 172/251.
Regards,
Karthik
The source of the questions that i post from JUNE 2013 is from KNEWTON

---If you find my post useful, click "Thank" :) :)---
---Never stop until cracking GMAT---
Top
Join the discussion
Log in to postLogin with Googleuse password
QUOTE IN REPLY
Source: — Data Sufficiency |
User avatar
Legendary Member
Posts: 520
Joined: Sat Apr 28, 2012 9:12 pmFollowed by: 49 members
Thanked: 339 times
GMAT Score:770

by eagleeye » Sun May 27, 2012 6:58 pm
Hi karthikpandian19:

This is how I did it:
Let the probability that a person is from Japan be J. Similarly for Australia be A
Let the probability that a person is reading a novel be N. Similarly for Biography be A.
Since no one is from both countries and no one reads both ; we have AJ = 0 ; NB = 0.

Then A+J = 1; N+B =1 (Since P(AuB) = P(A)+P(B)-P(AB)

Now we need to find out whether JN > AB

1) We are given that we select either someone from Japan, or someone who reads a novel or does both.
In other words we need to find J or N or both.
Now we know that:
J = J(N+B) = JN + JB (Note that we could also have arrived at this statement since people from Japan includes both novel readers and biography readers).
similarly, N = N(A+J) = NA + NJ

We are given to find probability of people either from Japan or Novel people or both.

In other words we have JN + JB + NA (note that since Japanese Novel readers are in both sets, we count it only once). We then have JN + JB + NA = 208/251;
Now JN+ JB + NA+ (BA) = J + A = 1
Then, BA = 1 - (JN+JB+NA) = 1-208/251 = 43/251. We don't know what JN is. Hence not sufficient.

2) With similar reasoning as above; we have AB+AN + JB = 172/251 and JN = 1 - (AB + AN + JB) = 1 -172/251 = 79/251; We only know JN from this statement; we don't know AB; Hence not sufficient.

However from both 1 and 2, we have JN = 79/251 and AB = 43/251, Clearly we can see that JN>AB. Hence, C is the correct choice.

Let me know if I got it right, and if this helps :)
Top
Join the discussion
Log in to postLogin with Googleuse password
QUOTE IN REPLY
User avatar
Master | Next Rank: 500 Posts
Posts: 385
Joined: Mon Apr 16, 2012 8:40 amFollowed by: 29 members
Location: Pune, India
Thanked: 186 times

by aneesh.kg » Sun May 27, 2012 9:29 pm
Statement(1):

Image

Statement(2):

Image

Combining the two statements,

Image

[spoiler](C)[/spoiler] is the correct answer.
Aneesh Bangia
GMAT Math Coach
[email protected]

GMATPad:
Facebook Page: https://www.facebook.com/GMATPad
Top
Join the discussion
Log in to postLogin with Googleuse password
QUOTE IN REPLY
User avatar
Legendary Member
Posts: 1665
Joined: Thu Nov 03, 2011 7:04 pmFollowed by: 70 members
Thanked: 165 times

by karthikpandian19 » Sun May 27, 2012 10:27 pm
eagleeye wrote:........We then have JN + JB + NA = 208/251;
Now JN+ JB + NA+ (BA) = J + A = 1
Then, BA = 1 - (JN+JB+NA) = 1-208/251 = 43/251. We don't know what JN is. Hence not sufficient.
Here how u r adding BA? can you explain pls???
Regards,
Karthik
The source of the questions that i post from JUNE 2013 is from KNEWTON

---If you find my post useful, click "Thank" :) :)---
---Never stop until cracking GMAT---
Top
Join the discussion
Log in to postLogin with Googleuse password
QUOTE IN REPLY
Post new topic Post Reply
• Page 1 of 1