List S consists of 10 consecutive odd integers, and list T : GMAT Problem Solving (PS)
Check GMAT Club Decision Tracker for the Latest School Decision Releases http://gmatclub.com/AppTrack

 It is currently 16 Jan 2017, 03:40

### GMAT Club Daily Prep

#### Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History

# Events & Promotions

###### Events & Promotions in June
Open Detailed Calendar

# List S consists of 10 consecutive odd integers, and list T

Author Message
TAGS:

### Hide Tags

Director
Status: No dream is too large, no dreamer is too small
Joined: 14 Jul 2010
Posts: 651
Followers: 42

Kudos [?]: 859 [1] , given: 39

List S consists of 10 consecutive odd integers, and list T [#permalink]

### Show Tags

16 Feb 2011, 08:42
1
KUDOS
17
This post was
BOOKMARKED
00:00

Difficulty:

55% (hard)

Question Stats:

67% (02:51) correct 33% (02:08) wrong based on 428 sessions

### HideShow timer Statistics

List S consists of 10 consecutive odd integers, and list T consists of 5 consecutive even integers. If the least integer in S is 7 more than the least integer in T, how much greater is the average (arithmetic mean) of the integers in S than the average of the integers in T?

A. 2
B. 7
C. 8
D. 12
E. 22
[Reveal] Spoiler: OA

_________________

Collections:-
PSof OG solved by GC members: http://gmatclub.com/forum/collection-ps-with-solution-from-gmatclub-110005.html
DS of OG solved by GC members: http://gmatclub.com/forum/collection-ds-with-solution-from-gmatclub-110004.html
100 GMAT PREP Quantitative collection http://gmatclub.com/forum/gmat-prep-problem-collections-114358.html
Collections of work/rate problems with solutions http://gmatclub.com/forum/collections-of-work-rate-problem-with-solutions-118919.html
Mixture problems in a file with best solutions: http://gmatclub.com/forum/mixture-problems-with-best-and-easy-solutions-all-together-124644.html

Math Expert
Joined: 02 Sep 2009
Posts: 36507
Followers: 7063

Kudos [?]: 92851 [8] , given: 10528

### Show Tags

16 Feb 2011, 08:59
8
KUDOS
Expert's post
7
This post was
BOOKMARKED
Baten80 wrote:
List S consists of 10 consecutive odd integers, and list T consists of 5 consecutive even integers. If the least integer in S is 7 more than the least integer in T, how much greater is the average (arithmetic mean) of the integers in S than the average of the integers in T?

a) 2
b) 7
c) 8
d) 12
e) 22

For any evenly spaced set median=mean=the average of the first and the last terms.

So the mean of S will be the average of the first and the last terms: mean=(x+x+9*2)/2=x+9, where x is the first term;
The mean of T will simply be the median or the third term: mean=(x-7)+2*2=x-3;

The difference will be (x+9)-(x-3)=12.

_________________
Current Student
Status: Up again.
Joined: 31 Oct 2010
Posts: 541
Concentration: Strategy, Operations
GMAT 1: 710 Q48 V40
GMAT 2: 740 Q49 V42
Followers: 21

Kudos [?]: 410 [3] , given: 75

### Show Tags

17 Feb 2011, 04:51
3
KUDOS
3
This post was
BOOKMARKED
If you didnt know the formula for evenly spaced sets, you can pick numbers and solve this question very easily.

Pick first number of set T=2. Since number of elements = 5, the mean will be the middle term ie the 3rd term, which will be 6.

From the question, you can infer that first number of the set T, will be 2+7= 9. Since this set consists of even number of terms,ie 10, the mean will be the average of the middle 2 terms, ie 5th and 6th term, which are 17 and 19 respectively and their average will be 18= mean of the set.

Therefore, the difference between the mean of two sets= 18-6= 12.

_________________

My GMAT debrief: http://gmatclub.com/forum/from-620-to-710-my-gmat-journey-114437.html

Math Forum Moderator
Joined: 20 Dec 2010
Posts: 2021
Followers: 161

Kudos [?]: 1701 [2] , given: 376

### Show Tags

16 Feb 2011, 08:56
2
KUDOS
2
This post was
BOOKMARKED
Sum of evenly spaced progression:
$$\frac{n}{2}(2a+(n-1)d)$$

$$Average = \frac{Sum}{n}$$
or
$$Average =\frac{1}{2}(2a+(n-1)d)$$

$$\frac{1}{2}(2a+(10-1)*2) - \frac{1}{2}(2(a-7)+(5-1)*2)$$

$$\frac{1}{2}(2a+(10-1)*2) - \frac{1}{2}(2(a-7)+(5-1)*2)$$

$$a+9-(a-7+4)$$

$$a+9-a+7-4$$

$$12$$

Ans: "D"
_________________
SVP
Status: The Best Or Nothing
Joined: 27 Dec 2012
Posts: 1858
Location: India
Concentration: General Management, Technology
WE: Information Technology (Computer Software)
Followers: 47

Kudos [?]: 1926 [2] , given: 193

Re: List S consists of 10 consecutive odd integers, and list T [#permalink]

### Show Tags

23 Jun 2014, 01:53
2
KUDOS
2
This post was
BOOKMARKED
Picked up numbers:

T = 2 , 4 , 6, 8 , 10 (Mean = 6)

S = 9, 11, 13, 15, 17, 19, 21, 23, 25, 27 (Mean $$= \frac{17+19}{2} = 18$$)

Difference = 18-6 = 12

_________________

Kindly press "+1 Kudos" to appreciate

EMPOWERgmat Instructor
Status: GMAT Assassin/Co-Founder
Affiliations: EMPOWERgmat
Joined: 19 Dec 2014
Posts: 8264
Location: United States (CA)
GMAT 1: 800 Q51 V49
GRE 1: 340 Q170 V170
Followers: 379

Kudos [?]: 2452 [2] , given: 163

Re: List S consists of 10 consecutive odd integers, and list T [#permalink]

### Show Tags

26 Aug 2015, 10:25
2
KUDOS
Expert's post
Hi All,

This question can be solved by using Number Property Rules or by TESTing VALUES:

Here's how TESTing VALUES works:

List S: 10 consecutive ODD integers
List T: 5 consecutive EVEN integers
The least integer is S is 7 more than the least integer in T.

Let's say that….
T = {2, 4, 6, 8, 10}
Since the least integers in S is 7 MORE than the least integer in T…
S = {9, 11, 13, 15, 17, 19, 21, 23, 25, 27}

The average of T = 6
The average of S = 18

So, the average of S is 18 - 6 = 12 more than the average of T.

[Reveal] Spoiler:
D

GMAT assassins aren't born, they're made,
Rich
_________________

# Rich Cohen

Co-Founder & GMAT Assassin

# Special Offer: Save \$75 + GMAT Club Tests

60-point improvement guarantee
www.empowergmat.com/

***********************Select EMPOWERgmat Courses now include ALL 6 Official GMAC CATs!***********************

Senior Manager
Joined: 08 Nov 2010
Posts: 417
Followers: 7

Kudos [?]: 105 [0], given: 161

### Show Tags

17 Feb 2011, 12:01
Fluke - when u say 2a - what do u mean?
shouldnt it be A1 (the first number in the series)?

thanks.
_________________
Manager
Joined: 17 Feb 2011
Posts: 200
Concentration: Real Estate, Finance
Schools: MIT (Sloan) - Class of 2014
GMAT 1: 760 Q50 V44
Followers: 44

Kudos [?]: 707 [0], given: 70

### Show Tags

17 Feb 2011, 17:24
Easy by picking numbers, but I didn't know that formula. Thanks.
Math Forum Moderator
Joined: 20 Dec 2010
Posts: 2021
Followers: 161

Kudos [?]: 1701 [0], given: 376

### Show Tags

17 Feb 2011, 23:46
144144 wrote:
Fluke - when u say 2a - what do u mean?
shouldnt it be A1 (the first number in the series)?

thanks.

You are half right;

It should be $$2*a_1$$ i.e. twice of the first term. "a" is another way of depicting $$a_1$$

The formula for Sum of n numbers in an evenly spaced progression is denoted by:
$$\frac{n}{2}(2*a_1+(n-1)d)$$

If the progression is: 2,4,6. Sum=12

Using formula:
$$a_1=2$$. First term of the series
$$n=3$$ Number of elements in the progression(series)
$$d=a_2-a_1=4-2=2$$

$$Sum=\frac{n}{2}(2a_1+(n-1)d)$$
$$Sum=\frac{3}{2}(2*2+(3-1)2)$$
$$Sum=\frac{3}{2}*8$$
$$Sum=12$$
_________________
Senior Manager
Joined: 08 Nov 2010
Posts: 417
Followers: 7

Kudos [?]: 105 [0], given: 161

### Show Tags

18 Feb 2011, 05:55
ye, i mixed with N formula. thanks.
_________________
VP
Status: There is always something new !!
Affiliations: PMI,QAI Global,eXampleCG
Joined: 08 May 2009
Posts: 1353
Followers: 17

Kudos [?]: 240 [0], given: 10

### Show Tags

18 May 2011, 22:43
(2a + 2a + 8) /2

(2a+7 + 2a + 25)/2

leaves 12 after subtracting.
_________________

Visit -- http://www.sustainable-sphere.com/
Promote Green Business,Sustainable Living and Green Earth !!

Senior Manager
Joined: 12 Oct 2009
Posts: 268
Followers: 4

Kudos [?]: 153 [0], given: 4

### Show Tags

19 May 2011, 18:57
I got 12 by solving but i think Bunuel's method is brilliant ( as always )
GMAT Club Legend
Joined: 09 Sep 2013
Posts: 13409
Followers: 575

Kudos [?]: 163 [0], given: 0

Re: List S consists of 10 consecutive odd integers, and list T [#permalink]

### Show Tags

23 Jun 2014, 00:53
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.
_________________
Intern
Joined: 26 Jan 2014
Posts: 2
Followers: 0

Kudos [?]: 0 [0], given: 0

Re: List S consists of 10 consecutive odd integers, and list T [#permalink]

### Show Tags

29 Jun 2014, 21:14
PareshGmat wrote:
Picked up numbers:

T = 2 , 4 , 6, 8 , 10 (Mean = 6)

S = 9, 11, 13, 15, 17, 19, 21, 23, 25, 27 (Mean $$= \frac{17+19}{2} = 18$$)

Difference = 18-6 = 12

PareshGmat's solution is the quickest way. Anyway, here is mine:
T=(t1+t2+t3+t4+t5)/5
=[t1+(t1+1*2)+(t1+2*2)+(t1+3*2)+(t1+4*2)]/5
=[5t1+2*(1+2+3+4)]/5
=[5t1+2*(4*(4+1)/2)]/5
=[5t1+20]/5=t1+4
S=(s1+...+s10)/10
=[s1+(s1+1*2)+...+(s1+9*2)]/10
=[10s1+2*(1+...+9)]/10
=[10s1+2*(9*(9+1)/2)]/10
=[10s1+90]/10=s1+9
We have s1=t1+7
S-T=s1+9-t1-4=t1+7+9-t1-4=12 =>D
P/S: Sum of n consecutive integers:
n(n+1)/2
GMAT Club Legend
Joined: 09 Sep 2013
Posts: 13409
Followers: 575

Kudos [?]: 163 [0], given: 0

Re: List S consists of 10 consecutive odd integers, and list T [#permalink]

### Show Tags

26 Aug 2015, 06:56
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.
_________________
Intern
Joined: 12 Apr 2014
Posts: 9
Followers: 0

Kudos [?]: 0 [0], given: 0

Re: List S consists of 10 consecutive odd integers, and list T [#permalink]

### Show Tags

18 Jun 2016, 00:21
the idea is to remember the rule for consecutive numbers whether even or odd that it will have median=mean=average(1st term+last term)....then for S and T series have a difference of 7 of first digit of series when creating hypothetical digits for series....this will result in exact solution
Senior Manager
Joined: 27 Mar 2016
Posts: 337
Location: United States (CO)
GMAT 1: 770 Q51 V44
GPA: 3.69
WE: Analyst (Consulting)
Followers: 17

Kudos [?]: 92 [0], given: 25

Re: List S consists of 10 consecutive odd integers, and list T [#permalink]

### Show Tags

19 Jun 2016, 01:21
Mean of 10 consecutive odd integers is 9 more than the least.
Mean of 5 consecutive even integers is 4 more than the least.

9 - 4 + 7 = 12.
Intern
Joined: 12 Apr 2014
Posts: 9
Followers: 0

Kudos [?]: 0 [0], given: 0

Re: List S consists of 10 consecutive odd integers, and list T [#permalink]

### Show Tags

20 Jun 2016, 01:02
when we read consecutive odd/even integers...that implies mean(average)=median=average(1st term+last term).....make series S and T with hypothetical numbers according to the condition given....on setting up the numbers.....find A.M according to the method described above leading to the right solution
Re: List S consists of 10 consecutive odd integers, and list T   [#permalink] 20 Jun 2016, 01:02
Similar topics Replies Last post
Similar
Topics:
M is a list of 12 consecutive integers and N is a list of 31 consecuti 1 30 Nov 2016, 01:55
If the sum of a list of consecutive odd integers is 5, which of the fo 1 16 Aug 2016, 05:08
2 List K consists of 12 consecutive integers. If -4 is the least integer 1 16 Aug 2016, 01:20
37 List S consists of 10 consecutive odd integers, and list T c 15 30 Jan 2014, 00:57
10 List K consists of 12 consecutive integers. If -4 is the 14 24 Feb 2013, 11:39
Display posts from previous: Sort by