GMAT: Data sufficiency 33 | Data sufficiency | GMAT | Khan Academy | Summary and Q&A

TL;DR

The video discusses three different math problem scenarios, analyzing the sufficiency of various statements to reach a solution.

Key Insights

• #️⃣ Prime numbers are the only numbers with exactly two positive factors, but this alone does not confirm that a given integer is equal to 2.
• 🦕 Every prime number besides 2 is odd, as they cannot be divisible by 2.
• 💁 When solving for an unknown value, linear equations can be formed using given conditions to find the answer.
• 🥺 Sometimes, combining two statements can lead to a conclusive solution, even if each statement alone is insufficient.

Transcript

We're on problem 132. If the integer n is greater than 1, is n equal to 2? So they tell us that the integer n is greater than 1, and they ask us, is n equal to 2? Statement 1, n has exactly two positive factors. Well that's certainly true of the number 2. But it's also true of any prime number. I mean n could be 7. 7 only has two positive factors, ... Read More

Questions & Answers

Q: Why is Statement 1 in Problem 132 insufficient on its own?

Statement 1 only states that the given integer has exactly two positive factors, which is true for all prime numbers as well. While it suggests that the integer could be 2, it does not provide enough information to confirm this as it is also true for other prime numbers.

Q: What does Statement 2 in Problem 132 tell us about prime numbers?

Statement 2 implies that for prime numbers (other than 2), they are odd. This is because any prime number that is divisible by 2 would not be prime. Therefore, every other prime number has to be an odd number.

Q: How does Statement 2 in Problem 133 provide a solution?

Statement 2 states that if 5 club members fail to contribute, the share of each contributing member will increase by $2. By using this information along with the fact that the total contribution is $60, a linear equation can be formed to solve for the number of members, resulting in 15 members.

Q: Why is Statement 1 in Problem 134 insufficient to determine if the square root is an integer?

Statement 1 only provides that n is greater than m + 15, which implies n - m > 15. However, this does not guarantee that the square root of the difference is an integer, as it could be a non-integer value greater than 15.

Summary & Key Takeaways

• Problem 132: Two statements are given to determine if a given integer is equal to 2. Statement 1 (having exactly two positive factors) is insufficient, but Statement 2 (the difference between distinct positive factors is odd) combined with Statement 1 leads to a conclusive answer that it is indeed 2.

• Problem 133: Two statements are given to determine the number of members in a club based on their equal contributions to a gift certificate. Statement 1 (each member's contribution is $4) provides a straightforward solution, while Statement 2 (increase in contribution per remaining member if 5 fail to contribute) also leads to the same conclusion.

• Problem 134: Two statements are given to determine if the square root of the difference between two positive integers is an integer. Statement 1 (n is greater than m + 15) is insufficient, but Statement 2 (n is equal to m times m + 1) alone is enough to determine that the square root is an integer.