Author 
Message 
TAGS:

Hide Tags

Manager
Status: Current MBA Student
Joined: 19 Nov 2009
Posts: 127
Concentration: Finance, General Management

If the average (arithmetic mean) of n consecutive odd [#permalink]
Show Tags
09 Dec 2010, 14:43
5
This post received KUDOS
21
This post was BOOKMARKED
Question Stats:
63% (01:20) correct 37% (01:23) wrong based on 701 sessions
HideShow timer Statistics
If 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"
Official Answer and Stats are available only to registered users. Register/ Login.



Math Expert
Joined: 02 Sep 2009
Posts: 43887

Re: Quant Rev v.2, DS # 66: Consecutive Integer Problem [#permalink]
Show Tags
09 Dec 2010, 14:59
28
This post received KUDOS
Expert's post
12
This post was BOOKMARKED
tonebeeze wrote: Hello All,
I got this problem correct. I just would like to see a technical explanation of how to arrive at both occasions of sufficiency.
Thanks!
"If 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" Odd consecutive integers is an evenly spaced set. For any evenly spaced set the mean equals to the average of the first and the last terms, so in our case \(mean=10=\frac{x_1+x_{n}}{2}\) > \(x_1+x_{n}=20\). Question: \(x_1=?\) (1) The range of the n integers is 14 > the range of a set is the difference between the largest and smallest elements of a set, so \(x_{n}x_1=14\) > solving for \(x_1\) > \(x_1=3\). Sufficient. (2) The greatest of the n integers is 17 > \(x_n=17\) > \(x_1+17=20\) > \(x_1=3\). Sufficient. Answer: D.
_________________
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



Senior Manager
Status: Bring the Rain
Joined: 17 Aug 2010
Posts: 387
Location: United States (MD)
Concentration: Strategy, Marketing
Schools: Michigan (Ross)  Class of 2014
GPA: 3.13
WE: Corporate Finance (Aerospace and Defense)

Re: Quant Rev v.2, DS # 66: Consecutive Integer Problem [#permalink]
Show Tags
10 Dec 2010, 06:20
1
This post received KUDOS
I say D as well. Great explanation
_________________
Go Blue!
GMAT Club Premium Membership  big benefits and savings



Veritas Prep GMAT Instructor
Joined: 16 Oct 2010
Posts: 7951
Location: Pune, India

Re: Quant Rev v.2, DS # 66: Consecutive Integer Problem [#permalink]
Show Tags
12 Dec 2010, 04:24
tonebeeze wrote: Hello All,
I got this problem correct. I just would like to see a technical explanation of how to arrive at both occasions of sufficiency.
Thanks!
"If 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" If mean of consecutive odd integers is 10, the sequence of numbers will be something like this: 9, 11 or 7, 9, 11, 13 or 5, 7, 9, 11, 13, 15 or 3, 5, 7, 9, 11, 13, 15, 17 or 1, 3, 5, 7, 9, 11, 13, 15, 17, 19 etc Every time you add a number to the left, you need to add one to the right to keep the mean 10. The smallest sequence will have 2 numbers 9 and 11, the largest will have infinite numbers. Stmnt 1: Only one possible sequence: 3, 5, 7, 9, 11, 13, 15, 17 will have range 14. Least of the integers is 3. Sufficient. Stmnt 2: Only one possible sequence:3, 5, 7, 9, 11, 13, 15, 17 Least of the integers is 3. Sufficient. Answer (D). Note: You don't actually have to do all this. All such sequences will have distinct number of elements, greatest number, smallest number and range. So each statement alone will be sufficient.
_________________
Karishma Veritas Prep  GMAT Instructor My Blog
Get started with Veritas Prep GMAT On Demand for $199
Veritas Prep Reviews



TOEFL Forum Moderator
Joined: 16 Nov 2010
Posts: 1590
Location: United States (IN)
Concentration: Strategy, Technology

Re: Quant Rev v.2, DS # 66: Consecutive Integer Problem [#permalink]
Show Tags
06 Apr 2011, 07:28
2
This post received KUDOS
(1) so (a + a + 14)/2 = 10 => 2a = 20  14 = 6 => a =3 (2) (a+17)/2 = 10 => a = 3 Answer  D (a+17)
_________________
Formula of Life > Achievement/Potential = k * Happiness (where k is a constant)
GMAT Club Premium Membership  big benefits and savings



Manager
Joined: 15 Apr 2011
Posts: 66

Re: If the average (arithmetic mean) of n consecutive odd [#permalink]
Show Tags
14 Apr 2012, 10:11
Awesome explanation Bunuel!
_________________
http://mymbadreamz.blogspot.com



Intern
Joined: 05 Sep 2012
Posts: 1

Re: If the average (arithmetic mean) of n consecutive odd [#permalink]
Show Tags
29 Sep 2012, 22:27
I think solution D is wrong, what is numbers are : 5, 3, 1, 1, 3,5,7, 9 then range is 14 thus least value in set is : 5 However, if we consider numbers from 3 to 11 then least value is 3.



Veritas Prep GMAT Instructor
Joined: 16 Oct 2010
Posts: 7951
Location: Pune, India

Re: If the average (arithmetic mean) of n consecutive odd [#permalink]
Show Tags
29 Sep 2012, 22:41
bandgmat wrote: I think solution D is wrong, what is numbers are : 5, 3, 1, 1, 3,5,7, 9 then range is 14 thus least value in set is : 5 However, if we consider numbers from 3 to 11 then least value is 3. Yeah, but is the average of these numbers 10?
_________________
Karishma Veritas Prep  GMAT Instructor My Blog
Get started with Veritas Prep GMAT On Demand for $199
Veritas Prep Reviews



Manager
Joined: 11 Jul 2012
Posts: 55

Re: Quant Rev v.2, DS # 66: Consecutive Integer Problem [#permalink]
Show Tags
28 Oct 2012, 10:36
Bunuel wrote: tonebeeze wrote: Hello All,
I got this problem correct. I just would like to see a technical explanation of how to arrive at both occasions of sufficiency.
Thanks!
"If 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" Odd consecutive integers is an evenly spaced set. For any evenly spaced set the mean equals to the average of the first and the last terms, so in our case \(mean=10=\frac{x_1+x_{n}}{2}\) > \(x_1+x_{n}=20\). Question: \(x_1=?\) (1) The range of the n integers is 14 > the range of a set is the difference between the largest and smallest elements of a set, so \(x_{n}x_1=14\) > solving for \(x_1\) > \(x_1=3\). Sufficient. (2) The greatest of the n integers is 17 > \(x_n=17\) > \(x_1+17=20\) > \(x_1=3\). Sufficient. Answer: D. Doesn't the highlighted statement actually mean that the highest number in the series is 17??



Veritas Prep GMAT Instructor
Joined: 16 Oct 2010
Posts: 7951
Location: Pune, India

Re: Quant Rev v.2, DS # 66: Consecutive Integer Problem [#permalink]
Show Tags
29 Oct 2012, 01:26
avaneeshvyas wrote: Bunuel wrote: tonebeeze wrote: Hello All,
I got this problem correct. I just would like to see a technical explanation of how to arrive at both occasions of sufficiency.
Thanks!
"If 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" Odd consecutive integers is an evenly spaced set. For any evenly spaced set the mean equals to the average of the first and the last terms, so in our case \(mean=10=\frac{x_1+x_{n}}{2}\) > \(x_1+x_{n}=20\). Question: \(x_1=?\) (1) The range of the n integers is 14 > the range of a set is the difference between the largest and smallest elements of a set, so \(x_{n}x_1=14\) > solving for \(x_1\) > \(x_1=3\). Sufficient. (2) The greatest of the n integers is 17 > \(x_n=17\) > \(x_1+17=20\) > \(x_1=3\). Sufficient. Answer: D. Doesn't the highlighted statement actually mean that the highest number in the series is 17?? Yes. We generally use the terms greatest/largest.
_________________
Karishma Veritas Prep  GMAT Instructor My Blog
Get started with Veritas Prep GMAT On Demand for $199
Veritas Prep Reviews



Math Expert
Joined: 02 Sep 2009
Posts: 43887

Re: If the average (arithmetic mean) of n consecutive odd [#permalink]
Show Tags
07 Jul 2013, 23:54



Intern
Joined: 05 May 2013
Posts: 27
GRE 1: 1480 Q800 V680

Re: If the average (arithmetic mean) of n consecutive odd [#permalink]
Show Tags
09 Jul 2013, 06:30
1
This post received KUDOS
Let a be the first term. every term in this sequence can be expressed as a+ (i1) where i ranges from 1 to n. Thus sum of these terms is a*n +1+2+3+..+n1= an +n(n1)/2 = 10 n.
(1) We are given that a+n1 a =14. We have two eqns for the unkowns (a and n ) and thus (1) is sufficient. No need to actually solve for and and n.
(2) is also sufficient since it is given a+(n1) =17.
Answer is (D)



Intern
Joined: 24 Apr 2013
Posts: 1

Re: If the average (arithmetic mean) of n consecutive odd [#permalink]
Show Tags
09 Jul 2013, 20:57
Or, since this is DS, we can skip the math and use the fact that for a consecutive sequence we only need 2 pieces of information (among mean, smallest number, greatest number, and range) to determine it. So D is correct.



Manager
Joined: 24 Jun 2014
Posts: 52
Concentration: Social Entrepreneurship, Nonprofit

Re: If the average (arithmetic mean) of n consecutive odd [#permalink]
Show Tags
28 Feb 2015, 21:19
As per the question average of n consecutive integers is 10 ;Sum of n consecutive integers =10n or lets say lowest integer is k then k+ k+2+k+4...+ k+2(n1) =10n Simplifying further nk+2(1+2...+n1)=10n > A
lets go with option I
i) The range of n integers is 14
so we know highest integer  lowest integer =14 highest integer =k+2(n1) lowest integer =k
Hence we get 2(n1) =14 or n=8 ,Substituting we get value of k hence I is sufficient
ii) if greatest integer is 17, then sum would be 17 + 172 ...+(17 (n1)) = 10n Simplifying 17n  2(1+2...+(n1))=10n or 7n = 2(1+2+...+(n1))> B
From A and B we get K=3 ,this sufficient to get all numbers in series Hence II is sufficient



Intern
Joined: 10 Mar 2015
Posts: 2

Re: If the average (arithmetic mean) of n consecutive odd [#permalink]
Show Tags
09 Oct 2015, 04:43
Below is a very simple logical approach to the problem.
Set={consecutive odd integers} for eg:{3,5,7}Avg=5(an odd number;this is because number of integers in set= odd) Avg given=10 (even number) Thus, obviously the number of terms are even. For eg: {9;11} or {7,9,11,13} Avg:10 Thus; possible entries in set={1,3,5,7,9,11,13,15,17}
1) range=Greatestleast= 14 Check set above ;only 173=14 ; thus highest number is 17,lowest 3 Sufficient
2) Greatest =17 in consecutive integer set greatest+lowest/2= mean 17+Low/2=10 Low= 3 ~~ sufficient.
ANS= D Hope I was clear.



Current Student
Joined: 12 Jul 2013
Posts: 7

Re: If the average (arithmetic mean) of n consecutive odd [#permalink]
Show Tags
23 Oct 2016, 02:48
Bunuel wrote: tonebeeze wrote: Hello All,
I got this problem correct. I just would like to see a technical explanation of how to arrive at both occasions of sufficiency.
Thanks!
"If 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" Odd consecutive integers is an evenly spaced set. For any evenly spaced set the mean equals to the average of the first and the last terms, so in our case \(mean=10=\frac{x_1+x_{n}}{2}\) > \(x_1+x_{n}=20\). Question: \(x_1=?\) (1) The range of the n integers is 14 > the range of a set is the difference between the largest and smallest elements of a set, so \(x_{n}x_1=14\) > solving for \(x_1\) > \(x_1=3\). Sufficient. (2) The greatest of the n integers is 17 > \(x_n=17\) > \(x_1+17=20\) > \(x_1=3\). Sufficient. Answer: D. Bunuel , My question is from the problem statement itself only one solution is possible. [ 3,5,7,9,11,13,15,17]. Are there any chances to encounter such a question on actual exam



Math Expert
Joined: 02 Sep 2009
Posts: 43887

Re: If the average (arithmetic mean) of n consecutive odd [#permalink]
Show Tags
23 Oct 2016, 05:32
rt1601 wrote: Bunuel wrote: tonebeeze wrote: Hello All,
I got this problem correct. I just would like to see a technical explanation of how to arrive at both occasions of sufficiency.
Thanks!
"If 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" Odd consecutive integers is an evenly spaced set. For any evenly spaced set the mean equals to the average of the first and the last terms, so in our case \(mean=10=\frac{x_1+x_{n}}{2}\) > \(x_1+x_{n}=20\). Question: \(x_1=?\) (1) The range of the n integers is 14 > the range of a set is the difference between the largest and smallest elements of a set, so \(x_{n}x_1=14\) > solving for \(x_1\) > \(x_1=3\). Sufficient. (2) The greatest of the n integers is 17 > \(x_n=17\) > \(x_1+17=20\) > \(x_1=3\). Sufficient. Answer: D. Bunuel , My question is from the problem statement itself only one solution is possible. [ 3,5,7,9,11,13,15,17]. Are there any chances to encounter such a question on actual exam Unfiniftley many sets are possible: {9, 11} {7, 9, 11, 13} {5, 7, 9, 11, 13, 15} ...
_________________
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



Manager
Joined: 23 Dec 2013
Posts: 235
Location: United States (CA)
GMAT 1: 710 Q45 V41 GMAT 2: 760 Q49 V44
GPA: 3.76

Re: If the average (arithmetic mean) of n consecutive odd [#permalink]
Show Tags
02 Jun 2017, 08:43
tonebeeze wrote: If 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" The goal is to find the minimum value of the set of n consecutive odd integers whose average is 10. Statement 1) The range of n integers is 14. If you know the average and range of a set of consecutive integers, then you can determine its length and the value of each element in that set. So there is only one set of consecutive odd integers with an average of 10 and a range of 14. Sufficient. Statement 2) The max of n integers is 17. Once again, if we know the maximum value and the average of a set of evenly spaced integers, then we can determine all values of that set. Sufficient.



Manager
Joined: 19 Aug 2016
Posts: 72

Re: If the average (arithmetic mean) of n consecutive odd [#permalink]
Show Tags
07 Sep 2017, 18:19
Bunuel wrote: tonebeeze wrote: Hello All,
I got this problem correct. I just would like to see a technical explanation of how to arrive at both occasions of sufficiency.
Thanks!
"If 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" Odd consecutive integers is an evenly spaced set. For any evenly spaced set the mean equals to the average of the first and the last terms, so in our case \(mean=10=\frac{x_1+x_{n}}{2}\) > \(x_1+x_{n}=20\). Question: \(x_1=?\) (1) The range of the n integers is 14 > the range of a set is the difference between the largest and smallest elements of a set, so \(x_{n}x_1=14\) > solving for \(x_1\) > \(x_1=3\). Sufficient. (2) The greatest of the n integers is 17 > \(x_n=17\) > \(x_1+17=20\) > \(x_1=3\). Sufficient. Answer: D. Hi Bunuel Could you please explain what evenly spaced set means?



Math Expert
Joined: 02 Sep 2009
Posts: 43887

Re: If the average (arithmetic mean) of n consecutive odd [#permalink]
Show Tags
07 Sep 2017, 20:39
zanaik89 wrote: Bunuel wrote: tonebeeze wrote: Hello All,
I got this problem correct. I just would like to see a technical explanation of how to arrive at both occasions of sufficiency.
Thanks!
"If 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" Odd consecutive integers is an evenly spaced set. For any evenly spaced set the mean equals to the average of the first and the last terms, so in our case \(mean=10=\frac{x_1+x_{n}}{2}\) > \(x_1+x_{n}=20\). Question: \(x_1=?\) (1) The range of the n integers is 14 > the range of a set is the difference between the largest and smallest elements of a set, so \(x_{n}x_1=14\) > solving for \(x_1\) > \(x_1=3\). Sufficient. (2) The greatest of the n integers is 17 > \(x_n=17\) > \(x_1+17=20\) > \(x_1=3\). Sufficient. Answer: D. Hi Bunuel Could you please explain what evenly spaced set means? Evenly spaced set (aka arithmetic progression) is a special type of sequence in which the difference between successive terms is constant. Fore example, 1, 4, 7, 10, ... is an evenly spaced set. Check for more here: https://gmatclub.com/forum/mathsequenc ... 01891.htmlHope it helps.
_________________
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




Re: If the average (arithmetic mean) of n consecutive odd
[#permalink]
07 Sep 2017, 20:39






