GMAT Question of the Day - Daily to your Mailbox; hard ones only

It is currently 15 Oct 2018, 12:19

Close

GMAT Club Daily Prep

Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track
Your Progress

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History

Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.

Close

Request Expert Reply

Confirm Cancel

Four integers are randomly selected from the set {-1,0,1}, with

  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics  
Author Message
TAGS:

Hide Tags

Senior Manager
Senior Manager
User avatar
G
Joined: 02 Mar 2017
Posts: 264
Location: India
Concentration: Finance, Marketing
Four integers are randomly selected from the set {-1,0,1}, with  [#permalink]

Show Tags

New post Updated on: 23 Apr 2017, 02:57
1
7
00:00
A
B
C
D
E

Difficulty:

  65% (hard)

Question Stats:

63% (02:24) correct 37% (02:07) wrong based on 94 sessions

HideShow timer Statistics

Four integers are randomly selected from the set {-1,0,1},with repetitions allowed.What is the probability that the product of the four integers chosen will be its least value possible

A. 1/81
B. 4/81
C. 8/81
D. 10/81
E. 16/81

_________________

Kudos-----> If my post was Helpful


Originally posted by VyshakhR1995 on 23 Apr 2017, 00:20.
Last edited by Bunuel on 23 Apr 2017, 02:57, edited 1 time in total.
Renamed the topic and edited the question.
Manager
Manager
avatar
G
Joined: 18 Jan 2017
Posts: 81
Location: India
Concentration: Finance, Economics
GMAT 1: 700 Q50 V34
GMAT ToolKit User
Re: Four integers are randomly selected from the set {-1,0,1}, with  [#permalink]

Show Tags

New post 23 Apr 2017, 03:36
1
The total probability is selecting any of the 3 integers in the 4 turns= 3*3*3*3= 81

Minimum Product (Least Value) = -1

Case 1: Selecting three "-1" and one "1"
=4!/3!=4

Case 2:Selecting three "1" and one "-1"
=4!/3!=4

Required Probability= (4+4)/81= 8/81
Intern
Intern
avatar
S
Joined: 05 Dec 2016
Posts: 7
Re: Four integers are randomly selected from the set {-1,0,1}, with  [#permalink]

Show Tags

New post 30 Apr 2017, 07:39
Minimum Product of four items on the list = -1
Number of ways to achieve the result= 2 {(3 Nos -1 + 1 Nos 1) OR (3 Nos +1 + 1 Nos -1)}

Probability for case 1 (3 Nos -1 + 1 Nos 1)
Number of ways= 4 (+1,+1,+1,-1/+1,+1,-1,+1/.........)
Probability = 4x (1/3)^4 = 4/81

Probability for case 2 (3 Nos +1 + 1 Nos -1)
Number of ways= 4 Similar explanations as earlier
Probability = 4x (1/3)^4= 4/81

Hence total probability= 4/81 +4/81= 8/81
e-GMAT Representative
User avatar
P
Joined: 04 Jan 2015
Posts: 2063
Re: Four integers are randomly selected from the set {-1,0,1}, with  [#permalink]

Show Tags

New post 30 Apr 2017, 11:15
1
1
VyshakhR1995 wrote:
Four integers are randomly selected from the set {-1,0,1},with repetitions allowed.What is the probability that the product of the four integers chosen will be its least value possible

A. 1/81
B. 4/81
C. 8/81
D. 10/81
E. 16/81


Solution



    • We have a negative number in the set, so the least value will be possible, only when the product is negative.

    • If the product is least and negative, we cannot select 0, so we need to select a combination of -1 and 1 to get a product of -1.

    • Since 4 numbers are selected –

      o We get a product of -1 if we select one -1 and three 1s.

         We can do that in 4C3 ways = 4 ways

      o OR we can select three -1s and one 1.

         We can do that same in 4C3 = 4 ways.

    • Thus, the total ways to get a least value \(= 4 + 4 = 8\) ways

    • Now total ways of selecting a number \(= 3*3*3*3 = 81\)

      o Thus, the probability of choosing the 4 integers whose product has least value \(= \frac{8}{81}\)

    • Hence, the correct answer is Option C.


Thanks,
Saquib
Quant Expert
e-GMAT

Register for our Free Session on Number Properties (held every 3rd week) to solve exciting 700+ Level Questions in a classroom environment under the real-time guidance of our Experts :)

Image
_________________








Register for free sessions
Number Properties | Algebra |Quant Workshop

Success Stories
Guillermo's Success Story | Carrie's Success Story

Ace GMAT quant
Articles and Question to reach Q51 | Question of the week

Must Read Articles
Number Properties – Even Odd | LCM GCD | Statistics-1 | Statistics-2
Word Problems – Percentage 1 | Percentage 2 | Time and Work 1 | Time and Work 2 | Time, Speed and Distance 1 | Time, Speed and Distance 2
Advanced Topics- Permutation and Combination 1 | Permutation and Combination 2 | Permutation and Combination 3 | Probability
Geometry- Triangles 1 | Triangles 2 | Triangles 3 | Common Mistakes in Geometry
Algebra- Wavy line | Inequalities

Practice Questions
Number Properties 1 | Number Properties 2 | Algebra 1 | Geometry | Prime Numbers | Absolute value equations | Sets



| '4 out of Top 5' Instructors on gmatclub | 70 point improvement guarantee | www.e-gmat.com

Manager
Manager
avatar
S
Joined: 24 Jan 2017
Posts: 150
GMAT 1: 640 Q50 V25
GMAT 2: 710 Q50 V35
GPA: 3.48
Reviews Badge
Re: Four integers are randomly selected from the set {-1,0,1}, with  [#permalink]

Show Tags

New post 30 Jun 2017, 04:28
EgmatQuantExpert wrote:
VyshakhR1995 wrote:
Four integers are randomly selected from the set {-1,0,1},with repetitions allowed.What is the probability that the product of the four integers chosen will be its least value possible

A. 1/81
B. 4/81
C. 8/81
D. 10/81
E. 16/81


Solution



    • We have a negative number in the set, so the least value will be possible, only when the product is negative.

    • If the product is least and negative, we cannot select 0, so we need to select a combination of -1 and 1 to get a product of -1.

    • Since 4 numbers are selected –

      o We get a product of -1 if we select one -1 and three 1s.

         We can do that in 4C3 ways = 4 ways

      o OR we can select three -1s and one 1.

         We can do that same in 4C3 = 4 ways.

    • Thus, the total ways to get a least value \(= 4 + 4 = 8\) ways

    • Now total ways of selecting a number \(= 3*3*3*3 = 81\)

      o Thus, the probability of choosing the 4 integers whose product has least value \(= \frac{8}{81}\)

    • Hence, the correct answer is Option C.


Thanks,
Saquib
Quant Expert
e-GMAT

Register for our Free Session on Number Properties (held every 3rd week) to solve exciting 700+ Level Questions in a classroom environment under the real-time guidance of our Experts :)

Image


Thank you for your explanation, e-GMAT expert.

Btw I have a general question, hope that you will help me clear this concern:
How can we know whether order of selection matters in a probability question? In other words, what are the indicators of order of selection?

In the above question, initially I didn't consider the order of 4 numbers chosen, so I worked out an answer different from all 5 choices. But then I realized the denominator is very big, I thought I might overlook many cases... the selecting order could be the key... so I calculated again and figured out the correct answer.

Since the above question is not an official one, I cannot draw any conclusion as to whether there is any OG/GMATPrep question in which no indicator is provided, and we have to test each case. I believe that such an experience expert as you could give me a reliable answer.

Thank you in advance.
GMAT Club Bot
Re: Four integers are randomly selected from the set {-1,0,1}, with &nbs [#permalink] 30 Jun 2017, 04:28
Display posts from previous: Sort by

Four integers are randomly selected from the set {-1,0,1}, with

  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics  


Copyright

GMAT Club MBA Forum Home| About| Terms and Conditions and Privacy Policy| GMAT Club Rules| Contact| Sitemap

Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne

Kindly note that the GMAT® test is a registered trademark of the Graduate Management Admission Council®, and this site has neither been reviewed nor endorsed by GMAC®.