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What is the ratio of the sum of the odd positive integers between 1 an

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What is the ratio of the sum of the odd positive integers between 1 an  [#permalink]

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New post 15 May 2018, 02:49
00:00
A
B
C
D
E

Difficulty:

  55% (hard)

Question Stats:

60% (02:39) correct 40% (02:20) wrong based on 45 sessions

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BSchool Forum Moderator
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Joined: 05 Jul 2017
Posts: 503
Location: India
GMAT 1: 700 Q49 V36
GPA: 4
Re: What is the ratio of the sum of the odd positive integers between 1 an  [#permalink]

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New post 15 May 2018, 03:08
5
First, lets find out sum of all odd integers between 1 and 100

Total # of odd integers between 1 and 100

= \(\frac{99 - 1}{2}+1\)
= 50

Sum of all odd integers between 1 and 100
= total # of terms * average (First term + Last term /2)
\(=50 * \frac{1+99}{2}\)
\(=50 * 50\)

Now, lets find out sum of all even integers between 100 and 150

Total # of even integers between 100 and 150

= \(\frac{150 - 100}{2}+1\)
= 26

Sum of all even integers between 100 and 150
= total # of terms * average (First term + Last term /2)
\(= 26 * \frac{100+150}{2}\)
\(=26 * 125\)

There ratio
\(=\frac{50 * 50}{26 * 125}\)
\(= \frac{10}{13}\)

Answer is C
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Re: What is the ratio of the sum of the odd positive integers between 1 an  [#permalink]

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New post 15 May 2018, 03:12

Solution



To find:
• Ratio between 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

Approach and Working:

• From 1 to 100, inclusive, there are total 50 odd positive integers, which form an arithmetic progression
    o 1st term of the AP = 1
    o Common difference of the AP = 2
    o Number of terms of the AP = 50
    o Hence, sum of the AP = \(\frac{50}{2}\) (1 + 99) = \(25 * 100\) = 2500

• From 100 to 150, inclusive, there are 26 even positive integers, which form an arithmetic progression
    o 1st term of the AP = 100
    o Common difference of the AP = 2
    o Number of terms of the AP = 26
    o Hence, sum of the AP = \(\frac{26}{2}\) (100 + 150) = \(13 * 250\) = 3250

• Therefore, the required ratio = 2500 : 3250 = 250 : 325 = \(25 * 10 : 25 * 13\) = 10 : 13
Hence, the correct answer is option C.

Answer: C
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Re: What is the ratio of the sum of the odd positive integers between 1 an  [#permalink]

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New post 11 Aug 2019, 06:01
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Re: What is the ratio of the sum of the odd positive integers between 1 an   [#permalink] 11 Aug 2019, 06:01
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