GMAT Changed on April 16th - Read about the latest changes here

It is currently 23 May 2018, 08:10

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

Events & Promotions

Events & Promotions in June
Open Detailed Calendar

Set A = {-5, -4, -3, -2, -1, 0, 1, 2, 3, 4, 5}. If 10 integers are ran

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

Hide Tags

Expert Post
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 45302
Set A = {-5, -4, -3, -2, -1, 0, 1, 2, 3, 4, 5}. If 10 integers are ran [#permalink]

Show Tags

New post 25 Apr 2018, 21:48
Expert's post
3
This post was
BOOKMARKED
00:00
A
B
C
D
E

Difficulty:

  55% (hard)

Question Stats:

58% (01:16) correct 42% (01:04) wrong based on 52 sessions

HideShow timer Statistics

Set A = {-5, -4, -3, -2, -1, 0, 1, 2, 3, 4, 5}. If 10 integers are randomly chosen from A, with repetitions allowed, how many different ways, can the least possible value of the product of the 10 integers be obtained?

(A) One
(B) Two
(C) Three
(D) Four
(E) Five

_________________

New to the Math Forum?
Please read this: Ultimate GMAT Quantitative Megathread | All You Need for Quant | PLEASE READ AND FOLLOW: 12 Rules for Posting!!!

Resources:
GMAT Math Book | Triangles | Polygons | Coordinate Geometry | Factorials | Circles | Number Theory | Remainders; 8. Overlapping Sets | PDF of Math Book; 10. Remainders | GMAT Prep Software Analysis | SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) | Tricky questions from previous years.

Collection of Questions:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


What are GMAT Club Tests?
Extra-hard Quant Tests with Brilliant Analytics

1 KUDOS received
DS Forum Moderator
avatar
G
Joined: 22 Aug 2013
Posts: 1145
Location: India
Premium Member CAT Tests
Re: Set A = {-5, -4, -3, -2, -1, 0, 1, 2, 3, 4, 5}. If 10 integers are ran [#permalink]

Show Tags

New post 25 Apr 2018, 22:49
1
This post received
KUDOS
Bunuel wrote:
Set A = {-5, -4, -3, -2, -1, 0, 1, 2, 3, 4, 5}. If 10 integers are randomly chosen from A, with repetitions allowed, how many different ways, can the least possible value of the product of the 10 integers be obtained?

(A) One
(B) Two
(C) Three
(D) Four
(E) Five


So here numbers can be repeated. We can choose all 0's or five 1's and five -4's etc. But the product has to be least. The way to make it least would be to make it negative and as far away from 0 on the number line as possible.

So the product should be a number with highest possible magnitude (absolute value) but with a negative sign before it. Out of given numbers, 5 or -5 have the highest magnitudes. So we need to make the product with all ten 5's, but sign should be negative. So this can be done in following ways:
Nine -5's, One 5
Seven -5's, Three 5's
Five -5's, Five 5's
Three -5's, Seven 5's
One -5, Nine 5's

(We are taking only odd number of negatives here because if we take even number of negative integers, then our product will be positive which we dont want)

So in total, there are five ways as explained.

Hence E answer
1 KUDOS received
Intern
Intern
User avatar
B
Joined: 19 Dec 2017
Posts: 5
Location: Kuwait
GMAT 1: 640 Q48 V31
GPA: 3.64
CAT Tests
Re: Set A = {-5, -4, -3, -2, -1, 0, 1, 2, 3, 4, 5}. If 10 integers are ran [#permalink]

Show Tags

New post 25 Apr 2018, 23:01
1
This post received
KUDOS
Set A = {-5, -4, -3, -2, -1, 0, 1, 2, 3, 4, 5}. If 10 integers are randomly chosen from A, with repetitions allowed, how many different ways, can the least possible value of the product of the 10 integers be obtained?

(A) One
(B) Two
(C) Three
(D) Four
(E) Five

Lets consider 10 boxes, we need to fill these boxes with numbers so that the product of all numbers is minimum.
X X X X X X X X X X
We can't have all the 10 numbers as negative (as product of 10 negative numbers will become positive)

As repetitions are allowed, the lowest product will be when all numbers are a combination of 5 and -5

So we need to fill these 10 boxes with 5 and -5 so that product is negative. That is, we need odd number of -5s.

There are 5 ways of doing this :
one (-5), nine (5s)
three (-5s), seven (5s)
five (-5s), five (5s)
seven (-5s), three (5s)
nine (-5s), one (5)

So answer is 5. Option (E)
Senior Manager
Senior Manager
avatar
S
Joined: 02 Oct 2017
Posts: 481
Re: Set A = {-5, -4, -3, -2, -1, 0, 1, 2, 3, 4, 5}. If 10 integers are ran [#permalink]

Show Tags

New post 13 May 2018, 09:51
Product will be least when it has negative and highest number

Highest number is 5 so cases

One(-5) nine 5
Three(-5) seven 5
Five(-5) five (5)
Nine(-5) one (5)
Seven (-5) three (5)

So five cases

Give kudos if it helps

Posted from my mobile device
Re: Set A = {-5, -4, -3, -2, -1, 0, 1, 2, 3, 4, 5}. If 10 integers are ran   [#permalink] 13 May 2018, 09:51
Display posts from previous: Sort by

Set A = {-5, -4, -3, -2, -1, 0, 1, 2, 3, 4, 5}. If 10 integers are ran

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


GMAT Club MBA Forum Home| About| Terms and Conditions| 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®.