How to Solve GMAT Data Sufficiency 33 (Problems 132–134) | Khan Academy

TL;DR

GMAT Data Sufficiency 33 evaluates which statements are sufficient to solve Problems 132–134. Problem 132 requires both statements to conclude that n is 2; Problem 133 can be solved from either statement, giving 15 club members; and Problem 134 is resolved by Statement 2 alone. Read on for the reasoning and equations behind each sufficiency decision.

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

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.

Questions & Answers

Q: How do you solve GMAT Data Sufficiency 33 from Khan Academy?

Test each statement separately before considering them together. Problem 132 requires both statements, Problem 133 can be answered by either statement alone, and Problem 134 can be answered by Statement 2 alone.

Q: Why is Statement 1 insufficient for Problem 132?

Statement 1 says that n has exactly two positive factors, which establishes that n is prime. It does not prove that n equals 2 because other primes, such as 7, also have exactly two positive factors.

Q: Why do both statements establish that n equals 2 in Problem 132?

Statement 1 restricts n to prime numbers, while Statement 2 requires the difference between its distinct positive factors to be odd. For 2, the factors are 1 and 2, and their difference is 1; every other prime is odd, so subtracting 1 from it produces an even difference.

Q: How does Statement 1 solve Problem 133?

Each club member contributes $4 toward a $60 gift certificate. Writing 4m = 60 and solving gives m = 15 members, so Statement 1 is sufficient by itself.

Q: What equations come from Statement 2 in Problem 133?

Let m be the number of members and c be each member’s original contribution. The conditions give mc = 60 and 5c divided by m minus 5 equals $2, because the remaining members must cover the amount that 5 members would have paid.

Q: Is Statement 2 alone sufficient for Problem 133?

Yes, because the purchase price supplies mc = 60 and Statement 2 supplies a second equation relating m and c. Substituting c = 60/m allows the number of members to be determined as 15.

Q: Why is Statement 1 insufficient for Problem 134?

Statement 1 says that n is greater than m + 15, so n minus m is greater than 15. That condition does not establish that the square root of the difference between the two positive integers is an integer.

Q: Why is Statement 2 sufficient for Problem 134?

Statement 2 gives n = m(m + 1). According to the problem analysis, that relationship alone is enough to determine that the square root in question is an integer, so Statement 1 is unnecessary.

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.