Author 
Message 
TAGS:

Hide Tags

Math Expert
Joined: 02 Sep 2009
Posts: 47184

If the average (arithmetic mean) of five distinct positive integers is
[#permalink]
Show Tags
03 Jul 2017, 03:40
Question Stats:
61% (01:01) correct 39% (00:59) wrong based on 241 sessions
HideShow timer Statistics



BSchool Forum Moderator
Joined: 26 Feb 2016
Posts: 2961
Location: India
GPA: 3.12

Re: If the average (arithmetic mean) of five distinct positive integers is
[#permalink]
Show Tags
03 Jul 2017, 05:15
Since the average of 5 numbers is 10, the total must be 50. The numbers, must be consecutive for the greatest number to be least (8,9,10,11,12) The least possible value of the greatest number(as it has been given that the numbers are distinct) has to be 12(Option B)
_________________
You've got what it takes, but it will take everything you've got



Intern
Joined: 24 Sep 2016
Posts: 17

Re: If the average (arithmetic mean) of five distinct positive integers is
[#permalink]
Show Tags
03 Jul 2017, 06:15
Ans :A 9,10,10,10,11 Sent from my Mi 4i using GMAT Club Forum mobile app



BSchool Forum Moderator
Joined: 26 Feb 2016
Posts: 2961
Location: India
GPA: 3.12

Re: If the average (arithmetic mean) of five distinct positive integers is
[#permalink]
Show Tags
03 Jul 2017, 06:18
Anannt wrote: Ans :A 9,10,10,10,11 Sent from my Mi 4i using GMAT Club Forum mobile appIt cannot be 9,10,10,10,11 because it has been given that the integers are distinct.
_________________
You've got what it takes, but it will take everything you've got



Board of Directors
Status: QA & VA Forum Moderator
Joined: 11 Jun 2011
Posts: 3655
Location: India
GPA: 3.5
WE: Business Development (Commercial Banking)

Re: If the average (arithmetic mean) of five distinct positive integers is
[#permalink]
Show Tags
03 Jul 2017, 09:01
Bunuel wrote: If the average (arithmetic mean) of five distinct positive integers is 10, what is the least possible value of the greatest of the five numbers?
(A) 11 (B) 12 (C) 24 (D) 40 (E) 46 \(a + ( a + 1 ) + ( a + 2 ) + ( a + 3 ) + (a + 4) = 50\) ( As the numbers are distinct )Or, \(5a + 10 = 50\) Or, \(5a = 40\) Or, \(a = 8\) So, The least value of the greatest of the five numbers is 8 + 4 = 12, answer , must be (B) 12
_________________
Thanks and Regards
Abhishek....
PLEASE FOLLOW THE RULES FOR POSTING IN QA AND VA FORUM AND USE SEARCH FUNCTION BEFORE POSTING NEW QUESTIONS
How to use Search Function in GMAT Club  Rules for Posting in QA forum  Writing Mathematical Formulas Rules for Posting in VA forum  Request Expert's Reply ( VA Forum Only )



Intern
Joined: 07 Jun 2017
Posts: 2

Re: If the average (arithmetic mean) of five distinct positive integers is
[#permalink]
Show Tags
15 Nov 2017, 21:51
Hi,
I don't understand how to get the "least" possible value of the greatest. Could someone explain it please.
Thank you!



Math Expert
Joined: 02 Sep 2009
Posts: 47184

Re: If the average (arithmetic mean) of five distinct positive integers is
[#permalink]
Show Tags
15 Nov 2017, 23:31
shamsm wrote: Hi,
I don't understand how to get the "least" possible value of the greatest. Could someone explain it please.
Thank you! If the average (arithmetic mean) of five distinct positive integers is 10, what is the least possible value of the greatest of the five numbers?(A) 11 (B) 12 (C) 24 (D) 40 (E) 46 Given: \(0<a < b < c< d< e\) and \(a + b + c + d + e = 10*5\). We want to minimise e. General rule for such kind of problems, when the sum is fixed: to maximize one quantity, minimize the others; to minimize one quantity, maximize the others.So, here we should maximize a, b, c, and d. Since the integers are distinct, then the max value of d is e  1, the max value of c is e  2, the max value of b is e  3 and the max value of a is e  4. Thus, \((e  4) + (e  3) + (e  2) + (e  1) + e = 50\); e = 12. Answer: B. 14. Min/Max Problems
_________________
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



Intern
Joined: 16 May 2017
Posts: 27
Location: India
WE: General Management (Retail Banking)

Re: If the average (arithmetic mean) of five distinct positive integers is
[#permalink]
Show Tags
30 Mar 2018, 00:04
Bunuel wrote: shamsm wrote: Hi,
I don't understand how to get the "least" possible value of the greatest. Could someone explain it please.
Thank you! If the average (arithmetic mean) of five distinct positive integers is 10, what is the least possible value of the greatest of the five numbers?(A) 11 (B) 12 (C) 24 (D) 40 (E) 46 Given: \(0<a < b < c< d< e\) and \(a + b + c + d + e = 10*5\). We want to minimise e. General rule for such kind of problems, when the sum is fixed: to maximize one quantity, minimize the others; to minimize one quantity, maximize the others.So, here we should maximize a, b, c, and d. Since the integers are distinct, then the max value of d is e  1, the max value of c is e  2, the max value of b is e  3 and the max value of a is e  4. Thus, \((e  4) + (e  3) + (e  2) + (e  1) + e = 50\); e = 12. Answer: B. 14. Min/Max Problems Why 0<a<b<c<d<e? Sent from my Redmi 4 using GMAT Club Forum mobile app
_________________
"The harder you work the luckier you get"



Intern
Joined: 03 Mar 2018
Posts: 1

Re: If the average (arithmetic mean) of five distinct positive integers is
[#permalink]
Show Tags
02 Apr 2018, 06:15
I don't understand the word "distinct". In my opinion, this word does not mean "consecutive". So, why do we should calculate
Thus, (e−4)+(e−3)+(e−2)+(e−1)+e=50. ?



Board of Directors
Status: QA & VA Forum Moderator
Joined: 11 Jun 2011
Posts: 3655
Location: India
GPA: 3.5
WE: Business Development (Commercial Banking)

Re: If the average (arithmetic mean) of five distinct positive integers is
[#permalink]
Show Tags
04 Apr 2018, 07:56
AQHER wrote: I don't understand the word "distinct". The word distinct means that the numbers must not be same, (Say) All the numbers are 2 Or Say, the sequence be 2, 2 , 1, 3 , 2 Thus distinct means that the numbers must not be equal. AQHER wrote: In my opinion, this word does not mean "consecutive". So, why do we should calculate
Thus, (e−4)+(e−3)+(e−2)+(e−1)+e=50. ? Since the question stem asks " least possible value of the greatest of the five numbers " , we have assumed that the numbers are consecutive.. Hope this helps !!
_________________
Thanks and Regards
Abhishek....
PLEASE FOLLOW THE RULES FOR POSTING IN QA AND VA FORUM AND USE SEARCH FUNCTION BEFORE POSTING NEW QUESTIONS
How to use Search Function in GMAT Club  Rules for Posting in QA forum  Writing Mathematical Formulas Rules for Posting in VA forum  Request Expert's Reply ( VA Forum Only )



VP
Joined: 07 Dec 2014
Posts: 1039

If the average (arithmetic mean) of five distinct positive integers is
[#permalink]
Show Tags
Updated on: 04 Apr 2018, 10:16
Bunuel wrote: If the average (arithmetic mean) of five distinct positive integers is 10, what is the least possible value of the greatest of the five numbers?
(A) 11 (B) 12 (C) 24 (D) 40 (E) 46 because sum (50) is multiple of 5, and integers are distinct, assume consecutive integers checking options, A: 4x+6=(5011) no, x not integer B: 4x+6=(5012) yes x=8 8,9,10,11,12 B
Originally posted by gracie on 04 Apr 2018, 09:58.
Last edited by gracie on 04 Apr 2018, 10:16, edited 3 times in total.



Intern
Joined: 22 Aug 2017
Posts: 14

Re: If the average (arithmetic mean) of five distinct positive integers is
[#permalink]
Show Tags
04 Apr 2018, 10:09
pushpitkc wrote: Since the average of 5 numbers is 10, the total must be 50. The numbers, must be consecutive for the greatest number to be least (8,9,10,11,12)
The least possible value of the greatest number(as it has been given that the numbers are distinct) has to be 12(Option B) Why does the set have to be consecutive numbers? I understand everything up until the necessity to have a consecutive set since the question read distinct numbers. Thank you in advance.




Re: If the average (arithmetic mean) of five distinct positive integers is &nbs
[#permalink]
04 Apr 2018, 10:09






