Author 
Message 
TAGS:

Hide Tags

Math Expert
Joined: 02 Sep 2009
Posts: 49303

Three positive integers a, b, and c are such that their average is 20
[#permalink]
Show Tags
30 Jan 2016, 02:58
Question Stats:
56% (02:10) correct 44% (02:51) wrong based on 133 sessions
HideShow timer Statistics




Manhattan Prep Instructor
Joined: 22 Mar 2011
Posts: 1302

Re: Three positive integers a, b, and c are such that their average is 20
[#permalink]
Show Tags
31 Jan 2016, 00:38
We can solve algebraically without testing values: a+b+c=60 a ≤ b ≤ c b=a+11 c=60(2a+11) b ≤ c a+11 ≤ 60(2a+11) 3a ≤ 38 a ≤ 12 (since it must be an integer) So the maximum values of a & b are 12 and 23, making the minimum value of c 25.
_________________
Dmitry Farber  Manhattan GMAT Instructor  New York
Manhattan GMAT Discount  Manhattan GMAT Course Reviews  View Instructor Profile  Manhattan GMAT Reviews




Current Student
Joined: 18 Sep 2014
Posts: 230

Re: Three positive integers a, b, and c are such that their average is 20
[#permalink]
Show Tags
30 Jan 2016, 03:55
a+b+c=60 & a<b<c By hit and trial, c=25 gives b=23 and a = 12 Hence C=25.
_________________
Kindly press the Kudos to appreciate my post !!



Manager
Joined: 22 Feb 2015
Posts: 56
Location: United States
Concentration: Finance, Operations
GMAT Date: 04012015
GPA: 3.98

Re: Three positive integers a, b, and c are such that their average is 20
[#permalink]
Show Tags
31 Jan 2016, 00:02
Three positive integers a, b, and c are such that their average is 20 and a ≤ b ≤ c. If the median is (a + 11), what is the least possible value of c? A. 23 B. 21 C. 25 D. 26 E. 24 Solution: (a+b+c)/3 = 20 so a+b+c=60  (1) a<=b<=c median = a+11 b is the middle value so median is b we have b = a + 11 (2) the least value of c is when c=b so we get c= a+ 11 (3) putting values in (1) we get a+a+11+a+11=60 i.e a = 38/3 a non integer let take c=b+1 from (2) we get c=a+12 putting values in (1) we get a + (a + 11) + (a + 12) = 60 i.e a= 37/3 again a non integer let take c= b+2 putting values in (1) we get a + (a + 11) + (a + 13) = 60 i.e. a=36/3 = 12 b = 23 c = 25 so C must be the correct answer
_________________
Click +1 KUDOS , You can make me happy with just one click! Thanks



EMPOWERgmat Instructor
Status: GMAT Assassin/CoFounder
Affiliations: EMPOWERgmat
Joined: 19 Dec 2014
Posts: 12432
Location: United States (CA)

Re: Three positive integers a, b, and c are such that their average is 20
[#permalink]
Show Tags
01 Feb 2016, 11:28
Hi All, As 'thick' as this question might appear, it can be solved with a bit of 'brute force' and a combination of basic arithmetic skills. We can use the answer choices and TEST THE ANSWERS, but we'll also need to 'play around' a bit with the information that we're given (so we can determine what answers are possible and what answers are not). We're given a number of facts about the variables A, B and C: 1) They're POSITIVE INTEGERS 2) Their average is 20 3) A ≤ B ≤ C 4) The median is (A + 11) We're asked for the LEAST possible value of C. To start, since there are 3 variables, we know that B is the median. So we can think of the three variables as A, (A+11) and C. By extension, we know that A is NOT 'close' to C; this means that A is probably a lot less than the average and C is well ABOVE the average. The average of the variables is 20, so their sum is 60. Let's TEST 23... IF.... C = 23 A+A+11 = 37 2A = 26 A = 13 The numbers would be 13, 24 and 23... This is NOT possible (B ≤ C is not true in this case) ELIMINATE 23. Let's TEST 24... IF.... C = 24 A+A+11 = 36 2A = 25 A = 12.5 This is NOT possible (the variables have to be INTEGERS) ELIMINATE 24. Let's TEST 25... IF.... C = 25 A+A+11 = 35 2A = 24 A = 12 The numbers would be 12, 23 and 25... This MATCHES everything we were told, so this MUST be the answer. Final Answer: GMAT assassins aren't born, they're made, Rich
_________________
760+: Learn What GMAT Assassins Do to Score at the Highest Levels Contact Rich at: Rich.C@empowergmat.com
Rich Cohen
CoFounder & GMAT Assassin
Special Offer: Save $75 + GMAT Club Tests Free
Official GMAT Exam Packs + 70 Pt. Improvement Guarantee www.empowergmat.com/
***********************Select EMPOWERgmat Courses now include ALL 6 Official GMAC CATs!***********************



Manager
Joined: 04 Jan 2014
Posts: 120
GMAT 1: 660 Q48 V32 GMAT 2: 630 Q48 V28 GMAT 3: 680 Q48 V35

Re: Three positive integers a, b, and c are such that their average is 20
[#permalink]
Show Tags
02 Feb 2016, 23:33
According to the condition, a, b and c can be equal to each other so let them be. They will form an equidistant set whose average = median = b = 20.
a + 11 = 20 a = 9
Then, form a grid and list down possible values.
a b c 9 20 31 10 21 29 11 22 27 12 23 25 > bingo! 13 24 23 > rejected because it will violate main condition (a <= b <= c). We can stop here.
Answer (C).



Board of Directors
Joined: 17 Jul 2014
Posts: 2683
Location: United States (IL)
Concentration: Finance, Economics
GPA: 3.92
WE: General Management (Transportation)

Re: Three positive integers a, b, and c are such that their average is 20
[#permalink]
Show Tags
04 May 2016, 19:41
Bunuel wrote: Three positive integers a, b, and c are such that their average is 20 and a ≤ b ≤ c. If the median is (a + 11), what is the least possible value of c?
A. 23 B. 21 C. 25 D. 26 E. 24 to minimize c, we have to maximize a we can suppose that we have: a+a+11+a+11=20*3 3a+22=60 3a=38 38/3 is not an integer, thus, minimum value of c must be greater than a+11 a+12  doesn't work (37/3) a+13  works (36/3=12) a=12, b=23, c=25. minimum value of c is 25.



Veritas Prep GMAT Instructor
Joined: 16 Oct 2010
Posts: 8288
Location: Pune, India

Re: Three positive integers a, b, and c are such that their average is 20
[#permalink]
Show Tags
04 May 2016, 22:28
mvictor wrote: Bunuel wrote: Three positive integers a, b, and c are such that their average is 20 and a ≤ b ≤ c. If the median is (a + 11), what is the least possible value of c?
A. 23 B. 21 C. 25 D. 26 E. 24 to minimize c, we have to maximize a we can suppose that we have: a+a+11+a+11=20*3 3a+22=60 3a=38 38/3 is not an integer, thus, minimum value of c must be greater than a+11 a+12  doesn't work (37/3) a+13  works (36/3=12) a=12, b=23, c=25. minimum value of c is 25. Good logic. Assume the numbers are a, a+11 and a+11 (to minimize the greatest value c) You get a = 38/3 = 12.67 Here itself, you see that a cannot be 13 since that will add up to a higher value than 60. So a must be 12  the highest integer value it can take. This gives c = 60  12  12  11 = 25
_________________
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: 8150

Re: Three positive integers a, b, and c are such that their average is 20
[#permalink]
Show Tags
17 Aug 2018, 16:38
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: Three positive integers a, b, and c are such that their average is 20 &nbs
[#permalink]
17 Aug 2018, 16:38






