January 17, 2019 January 17, 2019 08:00 AM PST 09:00 AM PST Learn the winning strategy for a high GRE score — what do people who reach a high score do differently? We're going to share insights, tips and strategies from data we've collected from over 50,000 students who used examPAL. January 19, 2019 January 19, 2019 07:00 AM PST 09:00 AM PST Aiming to score 760+? 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.
Author 
Message 
TAGS:

Hide Tags

Math Expert
Joined: 02 Sep 2009
Posts: 52161

Set A = {5, 4, 3, 2, 1, 0, 1, 2, 3, 4, 5}. If 10 integers are ran
[#permalink]
Show Tags
25 Apr 2018, 20:48
Question Stats:
60% (01:39) correct 40% (01:32) wrong based on 62 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
Official Answer and Stats are available only to registered users. Register/ Login.
_________________
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? Extrahard Quant Tests with Brilliant Analytics



DS Forum Moderator
Joined: 21 Aug 2013
Posts: 1428
Location: India

Re: Set A = {5, 4, 3, 2, 1, 0, 1, 2, 3, 4, 5}. If 10 integers are ran
[#permalink]
Show Tags
25 Apr 2018, 21:49
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



Intern
Joined: 19 Dec 2017
Posts: 5
Location: Kuwait
GMAT 1: 640 Q48 V31 GMAT 2: 710 Q49 V37
GPA: 3.64

Re: Set A = {5, 4, 3, 2, 1, 0, 1, 2, 3, 4, 5}. If 10 integers are ran
[#permalink]
Show Tags
25 Apr 2018, 22:01
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)



Director
Joined: 02 Oct 2017
Posts: 735

Re: Set A = {5, 4, 3, 2, 1, 0, 1, 2, 3, 4, 5}. If 10 integers are ran
[#permalink]
Show Tags
13 May 2018, 08:51
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
_________________
Give kudos if you like the post




Re: Set A = {5, 4, 3, 2, 1, 0, 1, 2, 3, 4, 5}. If 10 integers are ran &nbs
[#permalink]
13 May 2018, 08:51






