GMAT: Data sufficiency 39 | Data sufficiency | GMAT | Khan Academy

TL;DR

Problem solving with finding tens digit, determining if a difference of two numbers is odd or even, and analyzing discount amounts in a sale.

Transcript

We're on problem 148. What is the tens digit of positive integer x. We want to know the tens digit. Statement one tells us x divided by 100 has a remainder of 30. Well, then we know the tens digit is 3, right? Because, let's say 30 divided by 100 has remainder of 30 and its tens digit is 3. 130 divided by 100 has a remainder of 30 and its remainder... Read More

Key Insights

• 👂 Remainders of 30 when dividing by 100 indicate a tens digit of 3.
• 🦕 For the difference of two numbers to be odd, one must be odd and the other even.
• 🈹 Statement one is sufficient to determine the total discounts in a sale.
• ⚾ The third most expensive item must be less than the second most expensive item, based on statement one.
• ⁉️ The simplification of the question in the third problem facilitates analysis and understanding.
• 💁 Statement two in the third problem does not provide enough information to determine the answer.
• 💯 The concept of perfect squares helps determine the oddness of two numbers.

Questions & Answers

Q: How can we find the tens digit of a positive integer based on remainders?

The first statement indicates that when a positive integer is divided by 100 and has a remainder of 30, the tens digit is always 3. This pattern applies to any number that has a remainder of 30 when divided by 100.

Q: How can we determine if the difference between two numbers is odd or even?

For the difference to be odd, one of the numbers must be odd and the other even. In the second problem, statement one provides no information, but statement two reveals that if one number is a perfect square, the other will be its complement regarding oddness.

Q: Can we conclude whether the total discounts exceed 15% of the sum of regular prices in the third problem?

Yes, statement one alone is sufficient to answer this question. If the regular price of the most expensive item is $50 and the next most expensive item costs $20, then the third item must be less than $20. Therefore, the total discounts will be less than $40, and it is concluded that the discounts do not exceed 15%.

Summary & Key Takeaways

• The first problem involves finding the tens digit of a positive integer based on given statements.

• The second problem focuses on determining if the difference between two numbers is odd or even using two statements.

• The third problem analyzes the total amount of discounts in a sale, comparing it to 15% of the sum of regular prices.