Author 
Message 
TAGS:

Hide Tags

Math Expert
Joined: 02 Sep 2009
Posts: 46214

If the average (arithmetic mean) of n consecutive odd intege [#permalink]
Show Tags
30 Jan 2014, 23:40
Question Stats:
64% (01:26) correct 36% (01:53) wrong based on 514 sessions
HideShow timer Statistics
The Official Guide For GMAT® Quantitative Review, 2ND EditionIf the average (arithmetic mean) of n consecutive odd integers is 10, what is the least of the integers? (1) The range of the n integers is 14. (2) The greatest of the n integers is 17. Data Sufficiency Question: 66 Category: Arithmetic Statistics Page: 157 Difficulty: 600 GMAT Club is introducing a new project: The Official Guide For GMAT® Quantitative Review, 2ND Edition  Quantitative Questions ProjectEach week we'll be posting several questions from The Official Guide For GMAT® Quantitative Review, 2ND Edition and then after couple of days we'll provide Official Answer (OA) to them along with a slution. We'll be glad if you participate in development of this project: 1. Please provide your solutions to the questions; 2. Please vote for the best solutions by pressing Kudos button; 3. Please vote for the questions themselves by pressing Kudos button; 4. Please share your views on difficulty level of the questions, so that we have most precise evaluation. Thank you!
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



Math Expert
Joined: 02 Sep 2009
Posts: 46214

Re: If the average (arithmetic mean) of n consecutive odd intege [#permalink]
Show Tags
30 Jan 2014, 23:40



Manager
Joined: 23 Jun 2008
Posts: 85
Location: Australia
GMAT Date: 04012014

Re: If the average (arithmetic mean) of n consecutive odd intege [#permalink]
Show Tags
31 Jan 2014, 00:35
What we know: If n consecutive integers have arithmetic mean of 10; those numbers are distributed either side of 10 perfectly symmetrically. Statement (1) Range is the difference between the greatest and the least numbers in the series. If the range is known the least of these integers must be less than the mean, i.e. 10  (14/2) = 3 (Note we don't really need to calculate this... to know we can is sufficient.) Statement (2) Similarly, the distance from the greatest number to mean equals to the distance from mean to the least number. So knowing the greatest number also sufficient to calculate the least number. (in this case 10  (17  10) = 3) The answer is D : Both Statement 1 and Statement 2 are sufficient ALONE . Bunuel wrote: The Official Guide For GMAT® Quantitative Review, 2ND EditionIf the average (arithmetic mean) of n consecutive odd integers is 10, what is the least of the integers? (1) The range of the n integers is 14. (2) The greatest of the n integers is 17. Data Sufficiency Question: 66 Category: Arithmetic Statistics Page: 157 Difficulty: 600 GMAT Club is introducing a new project: The Official Guide For GMAT® Quantitative Review, 2ND Edition  Quantitative Questions ProjectEach week we'll be posting several questions from The Official Guide For GMAT® Quantitative Review, 2ND Edition and then after couple of days we'll provide Official Answer (OA) to them along with a slution. We'll be glad if you participate in development of this project: 1. Please provide your solutions to the questions; 2. Please vote for the best solutions by pressing Kudos button; 3. Please vote for the questions themselves by pressing Kudos button; 4. Please share your views on difficulty level of the questions, so that we have most precise evaluation. Thank you!
_________________
Kudos (+1) if you find this post helpful.



Senior Manager
Joined: 20 Dec 2013
Posts: 250
Location: India

Re: If the average (arithmetic mean) of n consecutive odd intege [#permalink]
Show Tags
31 Jan 2014, 02:34
Ans. D Let the series start from x=>x,(x+2),(x+4),...(x+k) id the series. Average=[x+(x+k)]/2=10(1) x+(x+k)=20=>2x+k=20
Given in S1, x+kx=14=>k=14.We can find out x,the smallest integer.Sufficient
From S2: x+k=17 By putting this value in (1),we can get x,the answer. Sufficient.



Math Expert
Joined: 02 Sep 2009
Posts: 46214

Re: If the average (arithmetic mean) of n consecutive odd intege [#permalink]
Show Tags
01 Feb 2014, 10:14



Intern
Joined: 24 Jul 2014
Posts: 1

If the average (arithmetic mean) of n consecutive odd intege [#permalink]
Show Tags
15 Aug 2014, 08:52
I did it this way.
Since consecutive odd integers are evenly spaced then avg = median = 10
Since median is even (10) for a set of consecutive odd integers, set must have even number of integers Ex: if set has 3,5,7 then median 5 (odd) if set has 3,5,7,9 then median = 5+7/2 = 6 (even)
so we can say (x+ (x+2))/2 = 10 => 2x+2=20 => x=9. So middle terms of the set are 9 & 11. If I know one more thing like range or first/last term I can create full list.
Hence both statements are sufficient. Ans: D



Director
Joined: 10 Mar 2013
Posts: 562
Location: Germany
Concentration: Finance, Entrepreneurship
GPA: 3.88
WE: Information Technology (Consulting)

Re: If the average (arithmetic mean) of n consecutive odd intege [#permalink]
Show Tags
13 Jun 2015, 05:47
(Min + Max)/2 = 10 > Min + Max=20 1)Range means Max  Min=14, sow we have two equations and two unknowns > can be solved Min = 3 2)Max=17, Plug it here Min+Max=20 > Min=3
_________________
When you’re up, your friends know who you are. When you’re down, you know who your friends are.
Share some Kudos, if my posts help you. Thank you !
800Score ONLY QUANT CAT1 51, CAT2 50, CAT3 50 GMAT PREP 670 MGMAT CAT 630 KAPLAN CAT 660



BSchool Forum Moderator
Joined: 12 Aug 2015
Posts: 2642
GRE 1: 323 Q169 V154

Re: If the average (arithmetic mean) of n consecutive odd intege [#permalink]
Show Tags
20 Dec 2016, 17:05
Great Official Question. Here is what i did in this one =>
Given data => N consecutive odds Mean =Median (For any evenly spaced set)=10 AS medan 10 => N must be even Sum of deviations around the mean is always zero. E.g => 9,11 OR 7,9,11,13
Hence we are adding elements in pair around the mean 10. We need to get the least element now
Statement 1> Range =14 Series => 3,5,7,9,11,13,15,17=> Least Integer will be 3 Hence Sufficient
Statement 2> Greasers integer =17
Number of terms tot he right of the median = Number of terms to the left of median Median =10 11,13,15,17 => 4 terms to the right of it=> 4 terms must be there t the left of it. Series => 3,5,7,9.. Hence least term =3 Hence Sufficient
Hence D
_________________
MBA Financing: INDIAN PUBLIC BANKS vs PRODIGY FINANCE! Getting into HOLLYWOOD with an MBA! The MOST AFFORDABLE MBA programs!STONECOLD's BRUTAL Mock Tests for GMATQuant(700+)AVERAGE GRE Scores At The Top Business Schools!



Senior Manager
Joined: 05 Jan 2017
Posts: 427
Location: India

Re: If the average (arithmetic mean) of n consecutive odd intege [#permalink]
Show Tags
23 Feb 2017, 04:53
PROMPT ANALYSIS Let a, a+2, a+4, a+6…...n terms have average as 10 Sum of all values = na +n(n1) = 10n or a +n1 =10
SUPERSET a can be any odd number.
TRANSLATION In order to find a: 1# we need exact value of a 2# another equation with a and n as variable.
STATEMENT ANALYSIS
St 1: a +2n2  a =14 or n=8 therefore a =3 ANSWER. Option B, C, E eliminated. St 2: a+2n2 = 17.Solving with the equation in PROMPT, we get a =3 and n= 8. ANSWER. OptionA eliminated.
Option D.



NonHuman User
Joined: 09 Sep 2013
Posts: 7010

Re: If the average (arithmetic mean) of n consecutive odd intege [#permalink]
Show Tags
08 May 2018, 01:08
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: If the average (arithmetic mean) of n consecutive odd intege
[#permalink]
08 May 2018, 01:08






