GMAT Question of the Day - Daily to your Mailbox; hard ones only

 It is currently 17 Oct 2018, 02:39

### 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

# If the sum of the 4th term and the 12th term of an arithmetic progress

Author Message
TAGS:

### Hide Tags

Math Expert
Joined: 02 Sep 2009
Posts: 49948
If the sum of the 4th term and the 12th term of an arithmetic progress  [#permalink]

### Show Tags

30 Jul 2015, 11:11
1
13
00:00

Difficulty:

15% (low)

Question Stats:

81% (02:00) correct 19% (02:13) wrong based on 177 sessions

### HideShow timer Statistics

If the sum of the 4th term and the 12th term of an arithmetic progression is 8, what is the sum of the first 15 terms of the progression?

A. 60
B. 120
C. 160
D. 240
E. 840

Kudos for a correct solution.

_________________
CEO
Joined: 08 Jul 2010
Posts: 2537
Location: India
GMAT: INSIGHT
WE: Education (Education)
If the sum of the 4th term and the 12th term of an arithmetic progress  [#permalink]

### Show Tags

30 Jul 2015, 11:18
1
3
Bunuel wrote:
If the sum of the 4th term and the 12th term of an arithmetic progression is 8, what is the sum of the first 15 terms of the progression?

A. 60
B. 120
C. 160
D. 240
E. 840

Kudos for a correct solution.

nth Term of an Arithmetic Progression, $$T_n = a + (n-1)d$$

Sum of n terms, $$S_n = (n/2)*[2a + (n-1)*d$$

Where, a = first term of Progression, d = common difference (Second term - first term or Third - second term etc.)

4th Term, $$T_4 = a + (4-1)*d = a+3d$$
12th Term, $$T_{12} = a + (12-1)*d = a+11d$$

Given : (a+11d) + (a+3d) = 8
i.e. 2a + 14d = 8

Question : Sum of 15 terms, $$S_{15} = (15/2)*[2a + (15-1)*d = (15/2)*[2a+14d] = (15/2)*8 = 60$$

_________________

Prosper!!!
GMATinsight
Bhoopendra Singh and Dr.Sushma Jha
e-mail: info@GMATinsight.com I Call us : +91-9999687183 / 9891333772
Online One-on-One Skype based classes and Classroom Coaching in South and West Delhi
http://www.GMATinsight.com/testimonials.html

ACCESS FREE GMAT TESTS HERE:22 ONLINE FREE (FULL LENGTH) GMAT CAT (PRACTICE TESTS) LINK COLLECTION

##### General Discussion
Manager
Joined: 14 Mar 2014
Posts: 147
GMAT 1: 710 Q50 V34
Re: If the sum of the 4th term and the 12th term of an arithmetic progress  [#permalink]

### Show Tags

30 Jul 2015, 15:03
Bunuel wrote:
If the sum of the 4th term and the 12th term of an arithmetic progression is 8, what is the sum of the first 15 terms of the progression?

A. 60
B. 120
C. 160
D. 240
E. 840

Kudos for a correct solution.

IMO: A

nth term of an AP = a+(n-1)d
Let 1st term of AP = a+d
12th term of AP = a+11d
Sum of 1st & 12th = 8
a+d+a+11d =8
2a+14d=8
a+7d = 4 ---(i)

Sum of 1st 15 terms =
(a+d)+(a+2d)+(a+3d)+.....(a+14d)
=15a+(d+2d+3d+4d+..14d)
= 15a+d(1+2+3+..14)
Sum of 1st n natural numbers = $$\frac{n(n+1)}{2}$$
= 15a +d ($$\frac{14*15}{2}$$)
= 15a +d(7*15)
=15(a+7d) --(sub eq---(i))
=15*4=60
_________________

I'm happy, if I make math for you slightly clearer
And yes, I like kudos
¯\_(ツ)_/¯

Manager
Joined: 25 Nov 2014
Posts: 158
WE: Engineering (Manufacturing)
Re: If the sum of the 4th term and the 12th term of an arithmetic progress  [#permalink]

### Show Tags

31 Jul 2015, 02:08
1
Ans = A

4th term + 12th term = 8
i.e., (a+3d)+(a+11d) = 8
2a+14d = 8 -------------------------------- (1)

Now, Sum of first 15 terms = (15/2) * [2a + (15-1)d]
= (15/2) * [2a + 14d]
= (15/2) * 8 --------------- From (1)
= 60
Director
Joined: 21 May 2013
Posts: 651
Re: If the sum of the 4th term and the 12th term of an arithmetic progress  [#permalink]

### Show Tags

31 Jul 2015, 02:35
1
Bunuel wrote:
If the sum of the 4th term and the 12th term of an arithmetic progression is 8, what is the sum of the first 15 terms of the progression?

A. 60
B. 120
C. 160
D. 240
E. 840

Kudos for a correct solution.

First term=a, common difference=d
4th term=a+3d
12th term=a+11d
Sum=2a+14d=8

Now , sum upto first 15 terms= 15/2(2a+14d)=15/2(8)=60
Senior Manager
Joined: 28 Jun 2015
Posts: 293
Concentration: Finance
GPA: 3.5
Re: If the sum of the 4th term and the 12th term of an arithmetic progress  [#permalink]

### Show Tags

31 Jul 2015, 07:18
Let a = first term, d = common difference.

4th term = a+3d
12th term = a+11d

a+3d + a+11d = 8
2a + 14d = 8
a + 7d = 4.

Sum of the first 15 terms = 15/2 (2a + 14d) = 15 (a+7d) = 15 (4) = 60. Ans (A).
_________________

I used to think the brain was the most important organ. Then I thought, look what’s telling me that.

Senior Manager
Joined: 21 Jan 2015
Posts: 346
Location: India
Concentration: Strategy, Marketing
GMAT 1: 620 Q48 V28
GMAT 2: 690 Q49 V35
WE: Sales (Consumer Products)
Re: If the sum of the 4th term and the 12th term of an arithmetic progress  [#permalink]

### Show Tags

05 Aug 2015, 23:49
1
Bunuel wrote:
If the sum of the 4th term and the 12th term of an arithmetic progression is 8, what is the sum of the first 15 terms of the progression?

A. 60
B. 120
C. 160
D. 240
E. 840

Ans: A

solution: given that, lets say first term is a and common difference is d
then, a+3d+a+11d=8 = a+7d =4 ===this is the 8th term, which will be the median of the set of 15 terms in AP
so the sum of all the terms in AP= number of terms*median = 15*4 = 60
_________________

--------------------------------------------------------------------
The Mind is Everything, What we Think we Become.
Kudos will encourage many others, like me.
Thanks

Current Student
Joined: 12 Aug 2015
Posts: 2638
Schools: Boston U '20 (M)
GRE 1: Q169 V154
Re: If the sum of the 4th term and the 12th term of an arithmetic progress  [#permalink]

### Show Tags

06 Aug 2016, 00:47
VP
Joined: 07 Dec 2014
Posts: 1103
Re: If the sum of the 4th term and the 12th term of an arithmetic progress  [#permalink]

### Show Tags

06 Aug 2016, 14:54
t4+t12=8
in AP 1,2,3,4,5.., where a and d=1, t4+t12=2*8
if we assume a and d=1/2,
then ∑15=15/2*(1+14*1/2)=60
VP
Joined: 07 Dec 2014
Posts: 1103
If the sum of the 4th term and the 12th term of an arithmetic progress  [#permalink]

### Show Tags

24 Aug 2017, 12:20
Bunuel wrote:
If the sum of the 4th term and the 12th term of an arithmetic progression is 8, what is the sum of the first 15 terms of the progression?

A. 60
B. 120
C. 160
D. 240

the 8th term is the middle term between the 4th and 12th terms
the middle term is half the sum of equidistant terms on either side
the 8th term=4
because the 8th term is the middle term of a 15 term progression,
it is also the median
4*15=60
A
Target Test Prep Representative
Status: Founder & CEO
Affiliations: Target Test Prep
Joined: 14 Oct 2015
Posts: 3846
Location: United States (CA)
Re: If the sum of the 4th term and the 12th term of an arithmetic progress  [#permalink]

### Show Tags

29 Aug 2017, 16:15
1
Bunuel wrote:
If the sum of the 4th term and the 12th term of an arithmetic progression is 8, what is the sum of the first 15 terms of the progression?

A. 60
B. 120
C. 160
D. 240
E. 840

An arithmetic progression (sequence) is characterized by having each term separated from the next term by a common difference. We can let d = the common difference (i.e., the difference between each pair of consecutive terms) and let the first term = a.

Thus, the first term is a, second term is a + d, and third term is a +2d, so the 4th term is a + 3d and the 12th term is a + 11d. Thus:

(a + 3d) + (a + 11d) = 8

2a + 14d = 8

a + 7d = 4

We are asked to find the sum of the first 15 terms. Since this is an arithmetic progression, we can use the formula sum = quantity x average. The ‘quantity’ is 15 since there are 15 terms. The ‘average’ of a finite arithmetic progression is also the median, which in this case is the 8th term. The 8th term in terms of a and d is a + 7d, and we have found that to be 4. Thus:

Sum = 15 x 4 = 60

_________________

Scott Woodbury-Stewart
Founder and CEO

GMAT Quant Self-Study Course
500+ lessons 3000+ practice problems 800+ HD solutions

Intern
Joined: 14 Oct 2016
Posts: 30
Location: India
WE: Sales (Energy and Utilities)
Re: If the sum of the 4th term and the 12th term of an arithmetic progress  [#permalink]

### Show Tags

07 Sep 2017, 10:18
We can use the concept of corresponding pairs if the series is in AP.
here is what i mean
suppose there are 15 terms in AP
the sequence is given below is in AP

2 , 4, 6, 8, 10,12,14,16,18,20,22,24,26,28,30
Then the corresponding pairs are (2,30),(4,28), (6,26), (8,24), (10,22), (12,20),(14,18) (16,16).Then the average of any corresponding pairs will be equal to average of the seq.

Given that the series is in AP
hence
in given problem 4 pair corresponds to 12 pair in a sequence of 15 terms The sum of 4 pair and 12 pair is 8
So,
sum= 15(8/2)= 60
_________________

Abhimanyu

Non-Human User
Joined: 09 Sep 2013
Posts: 8426
Re: If the sum of the 4th term and the 12th term of an arithmetic progress  [#permalink]

### Show Tags

22 Sep 2018, 08:28
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.
_________________
Re: If the sum of the 4th term and the 12th term of an arithmetic progress &nbs [#permalink] 22 Sep 2018, 08:28
Display posts from previous: Sort by