January 21, 2019 January 21, 2019 10:00 PM PST 11:00 PM PST Mark your calendars  All GMAT Club Tests are free and open January 21st for celebrate Martin Luther King Jr.'s Birthday. January 22, 2019 January 22, 2019 10:00 PM PST 11:00 PM PST In case you didn’t notice, we recently held the 1st ever GMAT game show and it was awesome! See who won a full GMAT course, and register to the next one.
Author 
Message 
TAGS:

Hide Tags

Manager
Joined: 26 Mar 2007
Posts: 64
Concentration: General Management, Leadership

In an arithmetic progression the difference between the any
[#permalink]
Show Tags
19 Jul 2011, 04:36
Question Stats:
66% (02:05) correct 34% (02:13) wrong based on 374 sessions
HideShow timer Statistics
In an arithmetic progression the difference between the any two consecutive terms is a constant. What is the arithmetic mean of all of the terms from the first to the 23rd in an arithmetic progression if the sum of the 10th and 14th terms of the sequence is 94? A. 47 B. 63 C. 55 D. 94 E. It can't be determined
Official Answer and Stats are available only to registered users. Register/ Login.




Senior Manager
Joined: 24 Aug 2009
Posts: 469
Schools: Harvard, Columbia, Stern, Booth, LSB,

Re: Arithmetic Progression
[#permalink]
Show Tags
20 Aug 2012, 04:23
The problem focuses upon concepts rather than formula i.e. There is no need to use any formula for this question. In order to solve this , we must know one property of AP which is 1) Any term is equal to half the sum of the terms which are equidistant from it. or 2) The sum of terms equidistant from the beginning & end is always same and is equal to the sum of the first & last term. Now back to the problem: As the series contain 23 terms, the mean of the series will the middle term of the series which is 12th term. 12th term is equal distance from both 10th & 12th term Thus 12th term = average of 10th & 14th term = 94/2 = 47
_________________
If you like my Question/Explanation or the contribution, Kindly appreciate by pressing KUDOS. Kudos always maximizes GMATCLUB worth Game Theory
If you have any question regarding my post, kindly pm me or else I won't be able to reply




Retired Moderator
Joined: 16 Nov 2010
Posts: 1419
Location: United States (IN)
Concentration: Strategy, Technology

Re: Arithmetic Progression
[#permalink]
Show Tags
19 Jul 2011, 04:51
kannn wrote: In an arithmetic progression the difference between the any two consecutive terms is a constant. What is the arithmetic mean of all of the terms from the first to the 23rd in an arithmetic progression if the sum of the 10th and 14th terms of the sequence is 94?
A. 47 B. 63 C. 55 D. 94 E. It can't be determined a10 = a1 + 9d
a14 = a1 + 13d
=> a10 + a14 = 2 * a1 + 22d = 94
Now, a1 + a23 = a1 + [a1 + (231)d]
=> a1 + a23 = a1 + a1 + 22d
=> a1 + a23 = 2 * a1 + 22d = 94
So AM from a1 to a23 = 94/2 = 47 (Because it's an AP)
Answer  A
_________________
Formula of Life > Achievement/Potential = k * Happiness (where k is a constant)
GMAT Club Premium Membership  big benefits and savings



Senior Manager
Joined: 03 Mar 2010
Posts: 374

Re: Arithmetic Progression
[#permalink]
Show Tags
19 Jul 2011, 04:52
10th term: t10 = a1 + (101)d t10 = a1 + 9d 14th term: t14 = a1 +13d t10+t14=94 2a1+22d=94 Sum of 23 terms of sequence= 23/2 [2a1+(231)d] =23/2 [2a1+22d] =23/2 * 94 =1081 Arithmetic mean = sum of 23 terms / 23 = 1081/23 =47
_________________
My dad once said to me: Son, nothing succeeds like success.



VP
Status: There is always something new !!
Affiliations: PMI,QAI Global,eXampleCG
Joined: 08 May 2009
Posts: 1013

Re: Arithmetic Progression
[#permalink]
Show Tags
19 Jul 2011, 08:27
mean = (first term + last term)/2
first term = a
last term = 23rd = a + (n1)d where d is the common difference.
thus 23rd term = a + 22d
now sum given is a+9d + a+ 13d = 2a + 22d = 94
thus mean = [a + (a+(n1)d) ]/2 = (2a+ 22d)/2 = 94/2 = 47



Retired Moderator
Joined: 20 Dec 2010
Posts: 1810

Re: Arithmetic Progression
[#permalink]
Show Tags
19 Jul 2011, 08:44
kannn wrote: In an arithmetic progression the difference between the any two consecutive terms is a constant. What is the arithmetic mean of all of the terms from the first to the 23rd in an arithmetic progression if the sum of the 10th and 14th terms of the sequence is 94?
A. 47 B. 63 C. 55 D. 94 E. It can't be determined Arithmetic mean from 1st to 23rd term would be the number in 12th term: (23+1)/2=12 We just need to find the 12th term. 10,11,12,13,14 We know that the 12th term is midway from 10th and 14th. And 12th term would be (10th+14th)/2=94/2=47 Ans: "A"
_________________
~fluke
GMAT Club Premium Membership  big benefits and savings



SVP
Joined: 06 Sep 2013
Posts: 1705
Concentration: Finance

Re: In an arithmetic progression the difference between the any
[#permalink]
Show Tags
11 Dec 2013, 10:17
kannn wrote: In an arithmetic progression the difference between the any two consecutive terms is a constant. What is the arithmetic mean of all of the terms from the first to the 23rd in an arithmetic progression if the sum of the 10th and 14th terms of the sequence is 94?
A. 47 B. 63 C. 55 D. 94 E. It can't be determined OK this is how you solve this question in under a minute. We are asked what is (s1+s23)/2 s23 = s1+22k, where k is a constant So we need to find (2s1+22k)/2 or s1+11k We are given s10+s14=94 So s1+9k+s1+13k=94 2s1+22k=94 s1+11k=47 So 47 is our answer Hence, (A) Hope it helps Cheers! J



Manager
Joined: 28 Dec 2013
Posts: 68

Re: In an arithmetic progression the difference between the any
[#permalink]
Show Tags
04 Jul 2014, 08:30
jlgdr wrote: kannn wrote: In an arithmetic progression the difference between the any two consecutive terms is a constant. What is the arithmetic mean of all of the terms from the first to the 23rd in an arithmetic progression if the sum of the 10th and 14th terms of the sequence is 94?
A. 47 B. 63 C. 55 D. 94 E. It can't be determined OK this is how you solve this question in under a minute. We are asked what is (s1+s23)/2 s23 = s1+22k, where k is a constant So we need to find (2s1+22k)/2 or s1+11k We are given s10+s14=94 So s1+9k+s1+13k=94 2s1+22k=94 s1+11k=47 So 47 is our answer Hence, (A) Hope it helps Cheers! J QUESTION : HOW DO WE KNOW WE NEED TO FIND (2S1 + 22K ) / 2 , what manipulation was done to figure this out?



Intern
Joined: 18 Jul 2013
Posts: 34

In an arithmetic progression the difference between the any
[#permalink]
Show Tags
07 Oct 2014, 17:35
We can directly predicate it as question mention difference is constant so mean = median let see adding the value of first and last term/2 ,second first and second last/2.......  we can get mean. so Values of any  1+23/2, 2+22/2, 3+21/2, 4+20/2, 5+19/2, 6+18/2, 7+17/2, 8+16/2, 9+15/2, 10+14 = 94/2(given)=47(mean) mean =median =47 so answer is 47.



SVP
Status: The Best Or Nothing
Joined: 27 Dec 2012
Posts: 1823
Location: India
Concentration: General Management, Technology
WE: Information Technology (Computer Software)

Re: In an arithmetic progression the difference between the any
[#permalink]
Show Tags
07 Oct 2014, 23:28
Let the numbers be as follows: x, x+y, x+2y, x+3y....................................................... x+22y 1st, 2nd ..............................................................................23rd 10th number = x+9y 14th number = x+13y Given that x+9y+x+13y = 94 2x + 22y = 94 x + 11y = 47Note that x+11y is the middle term of the series which will also be the mean of the series. Answer = A
_________________
Kindly press "+1 Kudos" to appreciate



Intern
Joined: 28 Oct 2015
Posts: 23
Location: United States
Concentration: Entrepreneurship, Technology
WE: Research (Computer Software)

Re: In an arithmetic progression the difference between the any
[#permalink]
Show Tags
09 Mar 2016, 09:10
Most of the previous analyses seem way too complicated.
Here's mine:  we're given that members of the set are evenly spaced, so it's an evenlyspaced set.  in an evenlyspaced (ordered) set the mean of any two members that are equidistant from the center is equal to the mean value of all members of the set.  the 10th and 14th members are equidistant from the center, which is the 12th member.  the mean of member 10 and member 14 = 47 = mean of the set. > A.



Intern
Joined: 03 Mar 2016
Posts: 15
Location: India

Re: In an arithmetic progression the difference between the any
[#permalink]
Show Tags
09 Mar 2016, 10:09
Very simple one to explain. Sum of 10 th term and 14 th term is a+9d + a+13d= 2a+ 22 d = 94. Therefore a + 11d = t(12 term)=47. Mean of arithmetic progression is sum of first and last term /2. Therefore sum of 1st and 23 rd /2= 12 term = 47.



Current Student
Joined: 12 Aug 2015
Posts: 2626

Re: In an arithmetic progression the difference between the any
[#permalink]
Show Tags
05 Aug 2016, 23:42
Superb Question Here we need to use the basic principle involving mean and AP series Mean of any AP series = Median Here N=23 Median = 12th term = A+11D fro first term being A and D being the common Difference Now Given A10 + A14 =94 => A+9D+A+13D = 2A+22D=94 => A+11D=47 Hence Median = 47 So the mean = 47 Smash that A
_________________
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!



Manager
Joined: 18 Jun 2017
Posts: 59

Re: In an arithmetic progression the difference between the any
[#permalink]
Show Tags
06 Aug 2017, 23:53
Average of 23 terms should be the 13th term in the series. Now to find the 13th term we can either add t1+t23 or as given in problem statement t10+t14 are also equi distant to LHS & RHS respectively of the t13. Hence avg of t10+t14=47 which should also be the 13th term and hence the avg of Sum of 1st 23 terms in the series. Option A.



VP
Joined: 07 Dec 2014
Posts: 1152

In an arithmetic progression the difference between the any
[#permalink]
Show Tags
07 Aug 2017, 12:00
kannn wrote: In an arithmetic progression the difference between the any two consecutive terms is a constant. What is the arithmetic mean of all of the terms from the first to the 23rd in an arithmetic progression if the sum of the 10th and 14th terms of the sequence is 94?
A. 47 B. 63 C. 55 D. 94 E. It can't be determined the sum of any two terms in an arithmetic progression will equal twice the term exactly between them thus the 12th term=94/2=47=mean in a 23 term progression A



NonHuman User
Joined: 09 Sep 2013
Posts: 9462

Re: In an arithmetic progression the difference between the any
[#permalink]
Show Tags
22 Sep 2018, 06:32
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: In an arithmetic progression the difference between the any &nbs
[#permalink]
22 Sep 2018, 06:32






