What is the primary function of comparisons in quantitative reasoning?

The primary function of comparisons is to evaluate and relate two or more quantities, determining their relative sizes or values, which is essential for problem-solving in GMAT quantitative questions.

What is the formula to express a relationship between two quantities when one is a multiple of the other?

If Quantity A is a multiple of Quantity B, it can be expressed as A = kB, where k is a constant multiplier. For example, if Quantity A is twice Quantity B, then A = 2B.

How can you recognize when two quantities are equal in comparison problems?

You can recognize equality by setting the two quantities equal to each other, e.g., A = B. If additional conditions or expressions are given, ensure all terms are properly simplified to see if they equate.

If Quantity A is 60 and Quantity B is 80, what is the comparison statement?

The comparison statement is A < B, since 60 is less than 80.

If Quantity A is represented by 4x + 8 and Quantity B is represented by 3x + 12, how can you determine which quantity is greater?

You can determine which quantity is greater by setting up the inequality 4x + 8 > 3x + 12 and solving for x. This will provide the values of x for which Quantity A exceeds Quantity B.

If Quantity A is 25% of Quantity B, and Quantity B is 120, what is the value of Quantity A?

To find Quantity A, calculate 25% of Quantity B: A = 0.25 * 120 = 30. Thus, Quantity A is 30.

When comparing two expressions involving variables, what is a useful technique to simplify the comparison?

A useful technique is to substitute a specific value for the variable(s) in both expressions to evaluate their sizes directly. This can often clarify which expression is greater.

In a comparison problem, what does the term 'net difference' refer to?

The 'net difference' refers to the absolute difference between two quantities, calculated as |Quantity A - Quantity B|. This is useful for understanding the magnitude of difference regardless of direction.

If Quantity A is defined as 2x - 4 and Quantity B as x + 6, when will Quantity A be greater than Quantity B?

Set up the inequality: 2x - 4 > x + 6. Solving gives x > 10. Thus, Quantity A is greater than Quantity B when x is greater than 10.

In comparison questions, how important is it to consider units of measurement, and why?

It is crucial to consider units of measurement, as comparing quantities with different units (e.g., meters to kilometers) can lead to incorrect conclusions. Always ensure quantities are in the same unit before comparison.

If Quantity A is 3 times Quantity B and Quantity B is represented as 10, what is the value of Quantity A?

To find Quantity A, calculate A = 3 * 10 = 30. Thus, Quantity A is 30.

When comparing fractions, what is a reliable method to determine which is larger?

A reliable method is to find a common denominator for the fractions before making the comparison. Alternatively, cross-multiplying can also help to determine which fraction is larger without finding the actual values.

What is the primary function of comparisons in GMAT questions?

The primary function of comparisons is to evaluate the relative sizes or values of two or more quantities, allowing test-takers to determine which quantity is greater, smaller, or equal.

State the key formula for expressing a comparison between two quantities.

The key formula is A > B, A < B, or A = B, where A and B represent the two quantities being compared. For example: If A = 2B, then A is twice the value of B.

What is a useful tip for solving comparison problems involving percentages?

Convert all quantities to the same base for easier comparison. For instance, if one quantity is given as a percentage, convert it to an actual number using the base quantity before comparing.