GMAT: Math 43 | Problem solving | GMAT | Khan Academy

TL;DR

The video explains how to find positive even divisors of a number and calculate the number of different positive integers that are factors of another number.

Transcript

We're on problem 207. If n is equal to 4p, where p is a prime number greater than 2, how many different positive, even divisors does n have including n? So how many integers go into n, or go into 4p? Well, definitely 4 goes into it, because this is going to be a multiple of 4. Then anything that goes into 4 will also go into it. So 2 goes into it. ... Read More

Key Insights

• #️⃣ Prime numbers cannot have any even divisors other than 2 and themselves.
• 😫 When comparing sets, the means and medians can be equal if one set is a subset of the other.
• 😘 The range of a set is the difference between the highest and lowest numbers.

Questions & Answers

Q: How many different positive even divisors does a number with the form 4p have, where p is a prime number greater than 2?

The only positive even divisors of 4p are 2 and 4 since p is prime and greater than 2. Thus, there are two even divisors.

Q: Can the mean of set S be equal to the mean of set T if T is a subset of S?

Yes, it is possible for the means of sets S and T to be equal if all the numbers in T are also in S. In this case, S contains T plus an additional number, so the means will be equal.

Q: What is the range of a set and can the range of set S be equal to the range of T?

The range of a set is the difference between the highest and lowest numbers. If T is a subset of S, the range of S must be greater than or equal to the range of T because all the numbers in T are also in S.

Q: How do you find the factors of a given number?

To find the factors, you need to prime factorize the number. Write the number as a product of prime numbers, then list all possible combinations of the prime factors, including duplicates, to find the factors.

Summary & Key Takeaways

• The first problem discusses finding positive even divisors of a number and determines that only the numbers 2 and 4 are even divisors of 4p, where p is a prime number greater than 2.

• The second problem involves sets containing different numbers and discusses statements that can or cannot be true about their means, medians, and ranges.

• The third problem focuses on finding different positive integers that are factors of a given number, using prime factorization.