Question

\(x<y<20\)
Column A: \(x + y\)
Column B: 35

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

Hint:

For quantitative comparison questions involving variables and inequalities, the "plug in numbers" strategy is very effective. Always try to test different types of numbers that fit the constraints: large numbers, small numbers, positive, negative, and zero. If you get different comparison results, the answer is always (D).

Answer 1

The Correct Option is A

Step 1: Understanding the Concept:
We are asked to compare the sum of two numbers, \(x\) and \(y\), with the value 35. We are given a set of inequalities that constrain the values of \(x\) and \(y\), but the numbers are not specified. We should test different possible values for \(x\) and \(y\) that satisfy the condition \(x<y<20\).
Step 2: Detailed Explanation:
The problem does not state that \(x\) and \(y\) must be integers, so we should consider real numbers. Let's try to find a case where Column A is greater than Column B, and another case where it is smaller.
Case 1: Try to maximize \(x + y\).
To make the sum large, we should choose \(x\) and \(y\) to be as close to 20 as possible, while still satisfying \(x<y<20\).
Let's pick \(y = 19\). Since \(x<y\), we can pick \(x = 18\).
In this case, \(x + y = 18 + 19 = 37\).
Here, Column A (37) is greater than Column B (35).
Case 2: Try to minimize \(x + y\).
To make the sum small, we can choose small positive values.
Let's pick \(y = 2\). Since \(x<y\), we can pick \(x = 1\).
In this case, \(x + y = 1 + 2 = 3\).
Here, Column A (3) is less than Column B (35).
The problem does not forbid negative numbers. Let's pick \(y = -5\). Since \(x<y\), we can pick \(x = -6\). Both satisfy \(x<y<20\).
In this case, \(x + y = -6 + (-5) = -11\).
Here, Column A (-11) is also less than Column B (35).
Step 3: Final Answer:
Since we found one scenario where Column A is greater than Column B (37 vs 35) and another scenario where Column A is less than Column B (3 vs 35), we cannot determine a fixed relationship between the two quantities.