GMAT: Math 41 | Problem solving | GMAT | Khan Academy

TL;DR

Understanding the properties of consecutive integers and applying them to solve problems involving sums and averages.

Transcript

We're on problem 201 which I had continued in the last video, but, frankly, I had bad reading comprehension. I had read the first statement wrong, and I went down an incorrect path. So let me read it correctly. If the sum of n consecutive integers is 0, which of the following must be true? So I have n numbers in the row, and their sum has to be 0. ... Read More

Key Insights

• 🍹 Consecutive integers that sum to zero require both positive and negative numbers.
• #️⃣ The number of consecutive integers determines the range of numbers needed to achieve a sum of zero.
• 😫 The average of a set of integers is calculated by dividing the sum of the integers by the number of integers in the set.

Questions & Answers

Q: What is the key requirement for getting a sum of zero with consecutive integers?

For a sum of zero with consecutive integers, there must be both positive and negative numbers in the sequence.

Q: Can a sum of zero be achieved with an even number of consecutive integers?

No, a sum of zero cannot be achieved with an even number of consecutive integers; it requires an odd number of integers.

Q: What is the relationship between the sum of integers and the average?

The average of a set of integers is equal to the sum of the integers divided by the number of integers in the set.

Q: How can you determine the number of even integers between two given numbers?

Subtract the starting number from the ending number, then add 1 to account for both endpoints; this will give you the count of even integers within the range.

Summary & Key Takeaways

• Consecutive integers in a sum that equals zero require both positive and negative numbers.

• The number of consecutive integers in the sum affects the range of numbers needed (e.g. at least three integers for n=1, four for n=2).

• The average of a set of integers is equal to the sum divided by the number of integers.