Is \(\mathrm{n}\) divisible by 6 with remainder 1 ? (1) \(n-7\) is divisible by 6 with integer result (2) \(\mathrm{n}-1\) is divisible by 6 with integer result A. 1 alone, not 2 alone B. 2 alone, not 1 alone C. 1 and 2 together (need both) D. 1 alone or 2 alone E. 1 and 2 together are not sufficient

Divisibility rules are shortcuts that help us determine if one number can be divided by another without leaving a remainder. For this problem, we're interested in the divisibility rule for 6. A number is divisible by 6 if it is divisible by both 2 and 3.
For example, consider the number 18. It's divisible by 2 (since it's even) and divisible by 3 (since 1 + 8 = 9, and 9 is divisible by 3). Therefore, 18 is divisible by 6.
In our exercise, we need to check if a number is divisible by 6 with a remainder of 1. Divisibility rules can help us simplify the problem by breaking it into smaller, more manageable parts.
By understanding these rules, you can quickly determine critical properties of numbers, saving time and effort on test day.

Integer operations involve basic arithmetic (addition, subtraction, multiplication, division) performed on integers (whole numbers).
In our exercise, we see integer operations in the transformation of the statements.
Statement 1: - 7 is divisible by 6 implying - 7 = 6k for some integer k. This then transforms to = 6k + 7.
Statement 2: - 1 is divisible by 6 implying - 1 = 6l for some integer l. This then transforms to = 6l + 1.
Using integer operations helps us transform problem statements into mathematical equations. This helps us to solve them more easily.
These transformations allow us to see patterns and relationships between numbers that might not be immediately obvious.

Effective test-taking strategies can significantly improve your performance on any exam, including the GMAT.
Read the questions carefully: Ensure you fully understand what is being asked before you begin analyzing the statements. Misreading can lead to errors.
Break down the information: As shown in the solution steps, subtle transformations and logical deductions simplify complex problems.
Eliminate incorrect choices: Use the process of elimination to narrow down the possible correct answers. In our exercise, knowing that statement 2 alone is sufficient helped eliminate other options quickly.
Practice timing: Allocate your time wisely during the test. Spending too much time on one problem may leave you without enough time to complete others.

Critical reasoning involves analyzing and evaluating information to reach a logical conclusion. It is crucial for solving GMAT problems effectively.
Evaluate statements individually: Determine the sufficiency of each given statement on its own. In our exercise, we first checked Statement 1's sufficiency. Once it was deemed insufficient, we moved to Statement 2.
Understand the implications: Each statement adds a piece to the puzzle. Knowing that - 1 = 6l for some integer l directly helped us derive = 6l + 1.
Check for sufficiency together: Even if one statement seems sufficient on its own, it's important to understand how combining them might affect the solution. In this case, combining statements didn't add new information.
Through critical reasoning, we develop a systematic approach to solving problems, ensuring we don't overlook key details.