Question

Which of the following is the digit for the sum of all of the distinct prime integers less than 20 ? A. $$4$$ B. $$5$$ C. $$6$$ D. $$7$$ E. $$8$$

Short answer

The answer is D, which represents $7$.

Step-by-step solution

Identify Prime Numbers

The prime numbers less than 20 are $2,3,5,7,11,13,17,19$.

Add Prime Numbers

Add all the identified prime numbers together: $2+3+5+7+11+13+17+19=77$.

Compare the Sum

The sum we got is 77, therefore, the digit we are looking for is the second digit of the sum, which is $7$. Compare the sum with the given options and choose the correct answer which matches the digit.

Key concepts

Integer Operations

Understanding integer operations is crucial in math because it serves as the foundation for more complex topics. Integers include whole numbers and their negative counterparts, but do not include fractions or decimals. There are four basic operations you can perform on integers: addition, subtraction, multiplication, and division. When adding integers, especially for prime numbers as shown in the original step-by-step solution, it's important to line them up properly to ensure accuracy.

• Always start from the smallest number and work your way up.
• Check your work as you go to make sure each addition is correct.
• For large sums, break them down into small manageable parts if necessary.

Adding prime numbers, as in our exercise, requires care in keeping track of each number to determine the correct sum. This helps prevent simple arithmetic errors that could lead to incorrect conclusions.

Math Problem Solving

Problem solving in math requires patience and a strategy. First, understand what the problem is asking. For our exercise, the goal is to sum the list of prime numbers less than 20 and find a particular digit. Here’s a step-by-step approach to tackle such problems:

• Identify the elements: Recognize the numbers upon which you need to perform operations, like the prime numbers in the exercise.
• Apply operations: Use integer operations such as addition, as done here, to progress towards the solution.
• Cross-check steps: Ensure each step is logically sound and re-evaluate if necessary to avoid any mistakes.
• Compare results: After obtaining the final sum, use it to find the needed result based on question requirements, such as identifying a digit or comparing it to other options.

Taking this structured method allows you to confidently approach math problems and ensure each calculation brings you closer to the answer.

GRE Test Preparation

In preparing for tests like the GRE, understanding prime numbers and integer operations is essential. The GRE often includes questions that test your fundamental knowledge of number properties and arithmetic. To ace such questions:

• Memorize key number properties: Knowing the first few prime numbers by heart can save you time during the test.
• Practice integer operations regularly: Quick and accurate addition or subtraction skills can make or break your performance.
• Work on time management: Balance speed with accuracy. Practice timed quizzes to improve efficiency.
• Familiarize with GRE question formats: Although the math concepts are essential, understanding how they are applied in test scenarios is crucial.

By focusing on these areas, you can improve not only your math skills but also your confidence and speed on test day, leading to better overall performance.