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# M20-31

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Math Expert
Joined: 02 Sep 2009
Posts: 41884

Kudos [?]: 128710 [0], given: 12182

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16 Sep 2014, 01:09
Expert's post
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Difficulty:

45% (medium)

Question Stats:

70% (01:01) correct 30% (02:21) wrong based on 43 sessions

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The sum of first $$N$$ consecutive positive odd integers is $$N^2$$ . What is the sum of all odd integers between 13 and 39, inclusive?

A. 351
B. 364
C. 410
D. 424
E. 450
[Reveal] Spoiler: OA

_________________

Kudos [?]: 128710 [0], given: 12182

Math Expert
Joined: 02 Sep 2009
Posts: 41884

Kudos [?]: 128710 [1], given: 12182

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16 Sep 2014, 01:09
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Official Solution:

The sum of first $$N$$ consecutive positive odd integers is $$N^2$$ . What is the sum of all odd integers between 13 and 39, inclusive?

A. 351
B. 364
C. 410
D. 424
E. 450

The sum of all odd integers between 13 and 39, inclusive equals to the sum of all odd integers from 1 to 39, inclusive minus the sum of all odd integers from 1 to 11, inclusive.

Since there are 20 odd integers from 1 to 39, inclusive then the sum of all odd integers from 1 to 39, inclusive is $$20^2$$;

Since there are 6 odd integers from 1 to 11, inclusive then the sum of all odd integers from 1 to 11, inclusive is $$6^2$$;

So, the required sum is $$20^2-6^2=364$$.

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Kudos [?]: 128710 [1], given: 12182

Intern
Joined: 13 Oct 2014
Posts: 2

Kudos [?]: 3 [2], given: 13

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03 Jan 2016, 04:31
2
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HI.
we can restate the problem as : what is the summation of evenly spaced series (arithmatic progression) 13,15,17...,39
no. of terms of the series= (39-13)/2 +1=14 and avg of the series =(1st term+last term)/2=52/2=26. so summation =26*14=364

Kudos [?]: 3 [2], given: 13

Intern
Joined: 27 Jun 2017
Posts: 1

Kudos [?]: 0 [0], given: 2

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29 Jun 2017, 12:19
I think this is a high-quality question and I don't agree with the explanation. it says between 13 and 39 inclusive, not between 11 and 39.

Kudos [?]: 0 [0], given: 2

Math Expert
Joined: 02 Sep 2009
Posts: 41884

Kudos [?]: 128710 [0], given: 12182

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29 Jun 2017, 14:46
rer05 wrote:
I think this is a high-quality question and I don't agree with the explanation. it says between 13 and 39 inclusive, not between 11 and 39.

Please re-read the solution. It says that the sum of all odd integers between 13 and 39, inclusive equals to the sum of all odd integers from 1 to 39, inclusive minus the sum of all odd integers from 1 to 11, inclusive.
_________________

Kudos [?]: 128710 [0], given: 12182

Intern
Joined: 01 Jul 2017
Posts: 7

Kudos [?]: 0 [0], given: 167

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07 Aug 2017, 03:06
Why are we taking 'the sum of all odd integers from 1 to 39, inclusive ' even though the question asks for odd numbers 'BETWEEN' 13 and 39?

Kudos [?]: 0 [0], given: 167

Math Expert
Joined: 02 Sep 2009
Posts: 41884

Kudos [?]: 128710 [0], given: 12182

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07 Aug 2017, 16:38
chaitalip wrote:
Why are we taking 'the sum of all odd integers from 1 to 39, inclusive ' even though the question asks for odd numbers 'BETWEEN' 13 and 39?

Please re-read the solution. It says that the sum of all odd integers between 13 and 39, inclusive equals to the sum of all odd integers from 1 to 39, inclusive minus the sum of all odd integers from 1 to 11, inclusive.
_________________

Kudos [?]: 128710 [0], given: 12182

Intern
Joined: 01 Jul 2017
Posts: 7

Kudos [?]: 0 [0], given: 167

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07 Aug 2017, 21:53

Kudos [?]: 0 [0], given: 167

Intern
Joined: 20 Sep 2016
Posts: 20

Kudos [?]: [0], given: 112

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17 Sep 2017, 05:10
Hi Bunuel,
Please help me understand this question. As per my reasoning goes, there are total (39-13)/2+ 1 odd terms. i.e. N= 14. thus according to the question sum of n is n2 which is 14*14.
What is the link am missing here ?

Kudos [?]: [0], given: 112

Math Expert
Joined: 02 Sep 2009
Posts: 41884

Kudos [?]: 128710 [0], given: 12182

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17 Sep 2017, 05:18
jyotipes21@gmail.com wrote:
Hi Bunuel,
Please help me understand this question. As per my reasoning goes, there are total (39-13)/2+ 1 odd terms. i.e. N= 14. thus according to the question sum of n is n2 which is 14*14.
What is the link am missing here ?

The question says that: The sum of first N consecutive consecutive odd integers is N^2, not that the sum of any N consecutive integers is N^2.
_________________

Kudos [?]: 128710 [0], given: 12182

Intern
Joined: 09 Aug 2017
Posts: 3

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

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17 Sep 2017, 09:05
How do we know the sum of all the integers 1 to 39 is 400? Is that derived a formula, trick or just something that a person should know. What about other numbers or evens?

Thanks.

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Math Expert
Joined: 02 Sep 2009
Posts: 41884

Kudos [?]: 128710 [0], given: 12182

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17 Sep 2017, 09:27
Plunkster82 wrote:
How do we know the sum of all the integers 1 to 39 is 400? Is that derived a formula, trick or just something that a person should know. What about other numbers or evens?

Thanks.

The sum of 20 odd integers from 1 to 39 (20 integers) is 20^2 = 400. You can derive it from arithmetic progression formula: https://gmatclub.com/forum/math-sequenc ... 01891.html
_________________

Kudos [?]: 128710 [0], given: 12182

Re: M20-31   [#permalink] 17 Sep 2017, 09:27
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# M20-31

Moderators: Bunuel, Vyshak

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