Author 
Message 
TAGS:

Hide Tags

Math Expert
Joined: 02 Sep 2009
Posts: 49300

The average of five integers is 63, and none of these integers is
[#permalink]
Show Tags
05 Nov 2015, 11:59
Question Stats:
51% (01:19) correct 49% (01:30) wrong based on 222 sessions
HideShow timer Statistics



Manager
Joined: 11 Sep 2013
Posts: 110

Re: The average of five integers is 63, and none of these integers is
[#permalink]
Show Tags
05 Nov 2015, 13:11
Bunuel wrote: The average of five integers is 63, and none of these integers is greater than 100. If the average of three of the integers is 65, what is the least possible value of one of the other two integers? A. 5 B. 15 C. 20 D. 21 E. 30 The sum of two other integers = 63*565*3 = 120 the least possible value of one integer when the other integer has the highest value of 100 =120  100 = 20 Ans C



CEO
Joined: 12 Sep 2015
Posts: 2872
Location: Canada

The average of five integers is 63, and none of these integers is
[#permalink]
Show Tags
05 Nov 2015, 17:08
Bunuel wrote: The average of five integers is 63, and none of these integers is greater than 100. If the average of three of the integers is 65, what is the least possible value of one of the other two integers? A. 5 B. 15 C. 20 D. 21 E. 30 When it comes to averages, we know that average value = (sum of n values)/nWe can rewrite this into a useful formula: sum of n values = (average value)(n)The average of five integers is 63 So, the sum of ALL 5 integers = (63)(5) = 315The average of three of the integers is 65So, the sum of the 3 integers = (65)(3) = 195So, the sum of the 2 REMAINING integers = 315  195 = 120If the sum of the 2 REMAINING integers = 120, and we want to minimize one value, we must MAXIMIZE the other value. 100 is the maximum value so let 1 integer = 100, which means the other must equal 20 Answer: C Cheers, Brent
_________________
Brent Hanneson – GMATPrepNow.com
Sign up for our free Question of the Day emails



Board of Directors
Status: QA & VA Forum Moderator
Joined: 11 Jun 2011
Posts: 4032
Location: India
GPA: 3.5
WE: Business Development (Commercial Banking)

Re: The average of five integers is 63, and none of these integers is
[#permalink]
Show Tags
06 Nov 2015, 12:52
Bunuel wrote: The average of five integers is 63 Σ5 = 315 Bunuel wrote: If the average of three of the integers is 65 Σ5 = 315 Bunuel wrote: none of these integers is greater than 100, what is the least possible value of one of the other two integers? Σ3 = 195 Σ2 = 120 x + y = 120 x & y < 100 Now the condition here is if we maximise one we will be minimuziing the other value. Lets check the options now  X + Y =>120 A. 5  Impossible , the other value is 115 B. 15 Impossible , the other value is 105 C. 20 , the other value is 100 D. 21, the other value is 115 E. 30 , the other value is 90 Now check for the maximimum possible value of the one integer, to mazimize the other Integer among the given options only (C) is the best.
_________________
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: 28 Dec 2010
Posts: 23

Re: The average of five integers is 63, and none of these integers is
[#permalink]
Show Tags
18 Aug 2016, 14:44
I selected option (d) also noticed that 40% of the folks who tried this question opted for the same option. The questions say's "none of these integers is greater than 100" i.e. they can be equal to 100 or less. Is this a fair assumption ? This is the part I missed and opted for (d).



Current Student
Joined: 18 Oct 2014
Posts: 872
Location: United States
GPA: 3.98

Re: The average of five integers is 63, and none of these integers is
[#permalink]
Show Tags
18 Aug 2016, 14:58
gary391 wrote: I selected option (d) also noticed that 40% of the folks who tried this question opted for the same option. The questions say's "none of these integers is greater than 100" i.e. they can be equal to 100 or less. Is this a fair assumption ? This is the part I missed and opted for (d). Hi! Gary, IMO, unless it is not written in the question that any of the number is not equal to or greater than 100, we must assume that number can be = 100
_________________
I welcome critical analysis of my post!! That will help me reach 700+



Current Student
Joined: 18 Oct 2014
Posts: 872
Location: United States
GPA: 3.98

Re: The average of five integers is 63, and none of these integers is
[#permalink]
Show Tags
18 Aug 2016, 15:04
Bunuel wrote: The average of five integers is 63, and none of these integers is greater than 100. If the average of three of the integers is 65, what is the least possible value of one of the other two integers? A. 5 B. 15 C. 20 D. 21 E. 30 This is how I solved it: Average of 5 integers is 63. That means five numbers are 63, 63, 63, 63, 63 Average of 3 integers is 65. That means three integers are 65, 65, 65 (if we notice that 65 is 2 greater than 63, and hence total 6 is more in this care compared to three integers in above scenario) Hence, we need to subtract 6 from the remaining two integers to have same total. We can write the remaining two integers as 60, 60 (Subtract 3 from each) Since out of these two numbers the largest number can be 100, the smallest can be 20 to get the same total. B is the answer
_________________
I welcome critical analysis of my post!! That will help me reach 700+



Veritas Prep GMAT Instructor
Joined: 16 Oct 2010
Posts: 8285
Location: Pune, India

Re: The average of five integers is 63, and none of these integers is
[#permalink]
Show Tags
18 Aug 2016, 21:58
Bunuel wrote: The average of five integers is 63, and none of these integers is greater than 100. If the average of three of the integers is 65, what is the least possible value of one of the other two integers? A. 5 B. 15 C. 20 D. 21 E. 30 You can use the method of deviations. The average of all number is 63 but of three is 65. So these three numbers give a positive deviation of 3*2 = 6 If the greatest number is 100 (maximum allowed), the smallest number will be the least. 100 is 37 more than 63. So the lest numbers can be 6 + 37 = 43 less than 63. The least number would be 20. Answer (C) For more, check: http://www.veritasprep.com/blog/2012/05 ... eviations/
_________________
Karishma Veritas Prep GMAT Instructor
Learn more about how Veritas Prep can help you achieve a great GMAT score by checking out their GMAT Prep Options >
GMAT selfstudy has never been more personalized or more fun. Try ORION Free!



NonHuman User
Joined: 09 Sep 2013
Posts: 8136

Re: The average of five integers is 63, and none of these integers is
[#permalink]
Show Tags
05 Jan 2018, 08:53
Hello from the GMAT Club BumpBot! Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up  doing my job. I think you may find it valuable (esp those replies with Kudos). Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
_________________
GMAT Books  GMAT Club Tests  Best Prices on GMAT Courses  GMAT Mobile App  Math Resources  Verbal Resources




Re: The average of five integers is 63, and none of these integers is &nbs
[#permalink]
05 Jan 2018, 08:53






