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

Question

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

pikolo2510 · Accepted Answer

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

EgmatQuantExpert · Answer

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

Regor60 · Answer

There are  /2 + 1 = 26 even numbers.

They can be ordered 100 to 124, 13 numbers, and added to the other 13 numbers, 126 to 150, for 26 times 250.

Looking at the odd numbers, there are 34 of them. And 13 doesn't enter into the numerator to be factored out by the denominator, so 13 must remain in the denominator, leaving C as the only choice.

Posted from my mobile device

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

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