The Sum of the First 50 Positive Even Integers is 2550 GMAT Problem Solving

Question: The sum of the first 50 positive even integers is 2550. What is the sum of even integers from 102 to 200 inclusive?

1. 5,100
2. 7,550
3. 10,100
4. 15,500
5. 20,100

Correct Answer: C

Solution and Explanation:

Approach Solution 1:

As stated in the question, the sum of the first 50 positive integers is 2550. It has asked to find out the sum of even numbers from 102 to 200.
number of even terms (multiples of 2) in the range from 102 to 200, inclusive, which is (last−first) / 2+1=(200−102) / 2+1 = 50.
Mean = (last+first)/2
The sum=(mean) ∗ (number of terms) = (200+102) / 2 ∗ 50 = 7,550
sum =(mean) ∗ (number of terms) = 7,550.
B is the correct choice.

Approach Solution 2:

As stated in the question, the sum of the first 50 positive integers is 2550. It has asked to find out the sum of even numbers from 102 to 200.
The first 50 even positive numbers added together equal 2550.
In other words, 2 + 4 + 6 + 8 + ...+ 98 + 100 = 2550

We want the sum: 102 + 104 + 106 + . . . 198 + 200
Important: Keep in mind that every phrase in this total is 100 more than every term in the first sum.

In other words, 102 + 104 + 106 + . . . 198 + 200 is the SAME AS…
(100 + 2) + (100 + 4) + (100 + 6) + ... + (100 + 98) + (100 + 100)
We can rearrange these terms to get: (100 + 100 + ... + 100 + 100) + (2 + 4 + 6 + 8 + ...+ 98 + 100)

Important: The red amount contains 50 100s, and we are informed that the blue sum is 2550.
Our total is therefore 5000 + 2550 + 50(100) = 7550.
B is the right answer.

Approach Solution 3:

Number of phrases equals (200-102)/2 + 1 = 50 (+1 as both are present)

Here's an illustration of arithmetic progression: 102, 104, 106,......, 200
The AP Formula's total of all n terms is: Sum equals n/2[2a + (n-1)d]

where n = number of words, in this instance 50.
beginning number for an is 102.
d = difference of AP = 2
So, Sum = 50/2[2*102 + (50-1)2]
Solving this will give us the result of 7550.

This is one more solution for this kind of problem.

“The sum of the first 50 positive even integers is 2550. What is the sum of even integers from 102 to 200 inclusive" - is a topic of the GMAT Quantitative reasoning section of GMAT. This question has been borrowed from the book “GMAT Official Guide Quantitative Review”.To understand GMAT Problem Solving questions, applicants must possess fundamental qualitative skills. Quant tests a candidate's aptitude in reasoning and mathematics. The GMAT Quantitative test's problem-solving phase consists of a question and a list of possible responses. By using mathematics to answer the question, the candidate must select the appropriate response. The problem-solving section of the GMAT Quant topic is made up of very complicated math problems that must be solved by using the right math facts.

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