GMAT Question of the Day: Daily via email | Daily via Instagram New to GMAT Club? Watch this Video

 It is currently 09 Apr 2020, 16:31

### 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

# What is the value of n if the sum of the consecutive odd

Author Message
TAGS:

### Hide Tags

Intern
Joined: 13 Apr 2013
Posts: 3
What is the value of n if the sum of the consecutive odd  [#permalink]

### Show Tags

Updated on: 05 Nov 2013, 05:42
4
17
00:00

Difficulty:

35% (medium)

Question Stats:

71% (02:08) correct 29% (02:27) wrong based on 246 sessions

### HideShow timer Statistics

What is the value of n if the sum of the consecutive odd intergers from 1 to n equals 169?

A) 47
B) 25
C) 37
D) 33
E) 29

Originally posted by MaddieGMAT on 05 Nov 2013, 03:15.
Last edited by Bunuel on 05 Nov 2013, 05:42, edited 1 time in total.
Renamed the topic and edited the question.
EMPOWERgmat Instructor
Status: GMAT Assassin/Co-Founder
Affiliations: EMPOWERgmat
Joined: 19 Dec 2014
Posts: 16381
Location: United States (CA)
GMAT 1: 800 Q51 V49
GRE 1: Q170 V170
Re: What is the value of n if the sum of the consecutive odd  [#permalink]

### Show Tags

10 Jan 2015, 12:21
7
1
Hi All,

The GMAT is based heavily on patterns; your ability to recognize (or discover) patterns will help you to speed up and score at a higher level on Test Day. In "sequence" questions, at least one pattern will exist (the sequence has to based on a pattern; it's called a "sequence" because there's some "rule" that governs the sequence). In a prompt such as this, if you don't immediately see the pattern, then you can figure it out with a bit of experimentation.

Here, we're told to take the SUM of the positive ODD integers from 1 to N..... There's a pattern to this sequence; let's figure out what it is....

If N = 3
2 terms
1 + 3 = 4

If N = 5
3 terms
1 + 3 + 5 = 9

If N = 7
4 terms
1 + 3 + 5 + 7 = 16

Look at the sums. Do you recognize a pattern?
4....9......16......they're all PERFECT SQUARES!!!!

The next part of the question tells us the SUM of the terms in this sequence = 169 which is ALSO a perfect square (it's 13^2), so we can use this deduction along with the existing pattern we discovered to figure out the answer to the question.

169 = 13^2 = 13 terms

So we need the first 13 positive ODD integers starting with 1. We can physically list them out, if necessary...
1 3 5 7 9
11 13 15 17 19
21 23 25

B: 25

GMAT assassins aren't born, they're made,
Rich
_________________
Contact Rich at: Rich.C@empowergmat.com

The Course Used By GMAT Club Moderators To Earn 750+

souvik101990 Score: 760 Q50 V42 ★★★★★
ENGRTOMBA2018 Score: 750 Q49 V44 ★★★★★
Verbal Forum Moderator
Joined: 10 Oct 2012
Posts: 568
Re: What is the value of n  [#permalink]

### Show Tags

05 Nov 2013, 03:24
2
4
What is the value of n if the sum of the consecutive odd intergers from 1 to n equals 169?

A) 47 B) 25 C) 37 D) 33 E) 29

Sum of the odd consecutive integers from 1 to n, where the # of terms is N : $$N^2$$.

Thus, $$N^2 = 169$$: N=13.

Thus, there are 13 terms in the series, and 13th term :First term+(# of terms-1)*Common difference : 1+(13-1)*2 = 25

B.
_________________
##### General Discussion
Manager
Joined: 21 Aug 2013
Posts: 72
Schools: ISB '15
Re: What is the value of n if the sum of the consecutive odd  [#permalink]

### Show Tags

08 May 2014, 06:29
2
Ans: 25

# of terms = (n-1/2)+1 {(last term - first term)/2+1|
Sum = (1+n)/2 * # of terms
= (n+1)^2/4= 169
n+1 = 13*2
n+1 = 26
n=25.
Intern
Joined: 02 May 2012
Posts: 10
What is the value of n if the sum of the consecutive odd  [#permalink]

### Show Tags

10 Jan 2015, 11:31
3
1
Before you tackle this question you must first understand that the question is comprised of two key parts, 1st is finding out how many terms is in that sequence and 2nd what actual number value that term is. In an arithmetic progression, in this case consecutive odd integers 1, 3, 5, ...., there are two set of rules.

Rule #1 (Arithmetic Sequence): xn = a + d(n-1) Identifies what the actual # in the sequence would be. Each number in the sequence has a term such as 1(is the first term), 3(is the second term) and so on. So if I were to ask you to find out what the 10th term is of that sequence you would use that formula to find that value.
a=1 (first term)
d=2 (the common difference) remember in the sequence 1, 3, 5, 7 the common difference is always 2

*On a side note we use n-1 because we don't have d in the first term, therefore if we were solving for the first term we would get 0 as n-1 and 0 times d would give us 0, leaving only the first term. This works regardless what your first term is in any sequence.

But remember the question asks " What is the value of n if the sum of the consecutive odd integers from 1 to n equals 169?" which means we first need a consecutive sequence that sums up to 169 and than find what the value of the n is, in this case it would be the last number in that sequence. In order to find that we first need to know how many terms (how many of the n there is) in order to be able to plug n in this formula given we know what the sum is. For that to happen we need to use Rule #2.

Rule #2 (Summing an arithmetic series): 169 = n/2(2a+(n-1)d). Given the question gives us what the sum is (169 in this case) we would simply use this formula to solve for n. Once we solve for n (13 in this case) we can simply plug n into the first formula (rule 1) and find the value.

It feels very confusing and difficult at first, but once you identify the steps all you need to do is plug and play. We have the sum (169) of a sequence, the number of terms in that sequence is (unknown). Rule #2 tells us how many numbers there are in that sequence and Rule #1 gives us what that last term is.
SVP
Status: The Best Or Nothing
Joined: 27 Dec 2012
Posts: 1712
Location: India
Concentration: General Management, Technology
WE: Information Technology (Computer Software)
Re: What is the value of n if the sum of the consecutive odd  [#permalink]

### Show Tags

12 Jan 2015, 20:48
4

Addition of consecutive odd integers is a perfect square, it means $$\sqrt{169} = 13$$ consecutive odd numbers are added.

$$13 = \frac{n-1}{2} + 1$$

n = 25
Target Test Prep Representative
Status: Founder & CEO
Affiliations: Target Test Prep
Joined: 14 Oct 2015
Posts: 9984
Location: United States (CA)
Re: What is the value of n if the sum of the consecutive odd  [#permalink]

### Show Tags

09 Feb 2020, 04:14
What is the value of n if the sum of the consecutive odd intergers from 1 to n equals 169?

A) 47
B) 25
C) 37
D) 33
E) 29

Since sum = average x quantity:

169 = (n + 1)/2 x [(n -1)/2 + 1]

169 = (n^2 - 1)/4 + (n + 1)/2

Multiplying the equation by 4, we have:

676 = n^2 - 1 + 2(n + 1)

676 = n^2 - 1 + 2n + 2

n^2 + 2n - 675 = 0

(n - 25)(n + 27) = 0

n = 25 or n = -27

Since n can’t be negative, n = 25.

_________________

# Scott Woodbury-Stewart

Founder and CEO

Scott@TargetTestPrep.com
202 Reviews

5-star rated online GMAT quant
self study course

See why Target Test Prep is the top rated GMAT quant course on GMAT Club. Read Our Reviews

If you find one of my posts helpful, please take a moment to click on the "Kudos" button.

Re: What is the value of n if the sum of the consecutive odd   [#permalink] 09 Feb 2020, 04:14
Display posts from previous: Sort by