GMAT: Data sufficiency 6 | Data sufficiency | GMAT | Khan Academy

TL;DR

This video provides problem-solving strategies for three math problems related to integers, equations, and triangles.

Transcript

We're now on problem number 28. And the question is, is x an integer? Statement one tells us that x over 2 is an integer. So if you think about it, x has to be an integer, because x is divisible by 2. This tells us that x is divisible by 2, because when I divide by 2 it's not 5.5 or something. I get an even-- I get an integer. So x has to be an int... Read More

Key Insights

• ❓ Problem-solving often requires evaluating different statements independently to determine their relevance and sufficiency.
• 🖐️ Divisibility and integer properties play a crucial role in solving mathematical problems.
• ❓ Equations can be manipulated and simplified to find solutions efficiently.

Questions & Answers

Q: Why does Statement 1 in Problem 28 confirm that x is an integer?

Statement 1 indicates that x/2 is an integer, implying that x is divisible by 2, thus confirming that x is an integer.

Q: Why is Statement 2 irrelevant in determining if x is an integer in Problem 28?

Statement 2 states that 2x is an integer, which does not provide any specific information about the integer status of x. For example, if x = 1/2, 2x equals an integer, but x itself is not an integer.

Q: How do both statements in Problem 29 contribute to solving for x?

Statement 1 (2x + 1 = 0) and Statement 2 (x + 1 squared = x squared) are equivalent equations and independently sufficient to solve for x.

Q: Why are both statements in Problem 30 needed to find the value of 1/k + 1/r?

Statement 1 gives the numerator of 1/k + 1/r, while Statement 2 provides the denominator (kr = 64). Both statements are necessary to find the complete value of 1/k + 1/r.

Summary & Key Takeaways

• Problem 28: Statement 1 suggests that x is an integer because x/2 is an integer, while Statement 2 doesn't provide sufficient information.

• Problem 29: Both statements individually are enough to solve for x, as they lead to the same equation.

• Problem 30: Statement 1 alone is insufficient, but when combined with statement 2, it is enough to determine the value of 1/k + 1/r.