Question

y > 4
Quantity A: \( \frac{3y+2}{5} \)
Quantity B: y

• A. Quantity A is greater.
• B. Quantity B is greater.
• C. The two quantities are equal.
• D. The relationship cannot be determined from the information given.
• E.

Hint:

In quantitative comparison questions with variables, try to simplify the comparison algebraically as if it were an inequality. This often reveals a simpler comparison that can be resolved using the given conditions. Always check if multiplying or dividing by a term could change the inequality's direction (it only happens with negative numbers).

Answer 1

The Correct Option is B

Step 1: Understanding the Concept:
We need to compare two algebraic expressions, Quantity A and Quantity B, given a condition on the variable y (that y is greater than 4). The best approach is to simplify the comparison algebraically.
Step 2: Key Approach:
We can set up a comparison between the two quantities and use standard algebraic manipulations (like multiplying or subtracting terms on both sides) to simplify it. The goal is to isolate the variable y and see what the relationship implies.
Step 3: Detailed Explanation:
Let's compare Quantity A and Quantity B. We can place a placeholder symbol ($\Box$) between them that stands for the relationship we want to find (e.g., <, >, =).
\[ \frac{3y+2}{5} \quad \Box \quad y \]
To eliminate the fraction, we can multiply both sides of the comparison by 5. Since 5 is a positive number, the direction of the inequality will not change.
\[ 3y + 2 \quad \Box \quad 5y \]
Next, to gather the terms with y on one side, we can subtract 3y from both sides.
\[ 2 \quad \Box \quad 5y - 3y \]
\[ 2 \quad \Box \quad 2y \]
Finally, we can divide both sides by 2 to isolate y. Since 2 is a positive number, the direction of the inequality remains unchanged.
\[ 1 \quad \Box \quad y \]
The comparison has been simplified to comparing 1 and y. Now, we use the given information from the question, which is \(y > 4\).
Since y is greater than 4, it must also be greater than 1. So, we can replace the box with a "less than" symbol:
\[ 1 < y \]
Since all our simplification steps are reversible and did not change the direction of the inequality, the original relationship must be the same.
Therefore, Quantity A is less than Quantity B.
Step 4: Final Answer:
Quantity A is less than Quantity B, which means Quantity B is greater. The correct answer is (B).