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# What is the ratio of the sum of the odd positive integers b

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Founder
Joined: 18 Apr 2015
Posts: 6931
Followers: 114

Kudos [?]: 1344 [0], given: 6333

What is the ratio of the sum of the odd positive integers b [#permalink]  16 Sep 2017, 15:41
Expert's post
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Question Stats:

71% (01:34) correct 28% (02:09) wrong based on 7 sessions

What is the ratio of the sum of the odd positive integers between 1 and 100, inclusive, and the sum of the even positive integers between 100 and 150, inclusive?

(A) 2 to 3

(B) 5 to 7

(C) 10 to 13

(D) 53 to 60

(E) 202 to 251
[Reveal] Spoiler: OA

_________________
Director
Joined: 03 Sep 2017
Posts: 520
Followers: 1

Kudos [?]: 356 [2] , given: 66

Re: What is the ratio of the sum of the odd positive integers b [#permalink]  18 Sep 2017, 00:48
2
KUDOS
What we are asked is the ratio between the sums of two arithmetic progressions. Thus, using the formula for the sum of an arithmetic progression, $$S_n=\frac{n}{2}(f+l)$$ where $$f$$ is the first term of the progression and $$l$$ is the last one, I can compute the numerator as $$\frac{50}{2}(1+99)=2500$$ and the denominator as $$\frac{26}{2}(100+150)=3250$$. Dividing $$2500$$ by $$3250$$, I get $$\frac{10}{13}$$, thus the answer is C!
Re: What is the ratio of the sum of the odd positive integers b   [#permalink] 18 Sep 2017, 00:48
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