Question

Column A: (109)(87-14)
Column B: (109)(87)-(109)(14)

• 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

Hint:

Recognizing fundamental algebraic properties like the distributive, commutative, and associative laws can save you from performing tedious calculations. These properties are frequently tested in quantitative comparison questions.

Answer 1

The Correct Option is C

Step 1: Understanding the Concept:
This question tests the understanding of the distributive property of multiplication over subtraction.
Step 2: Key Formula or Approach:
The distributive property states that for any numbers a, b, and c:
\[ a(b - c) = ab - ac \] Step 3: Detailed Explanation:
Let's analyze the two columns in terms of the distributive property.
Let \(a = 109\), \(b = 87\), and \(c = 14\).
Column A is in the form \(a(b - c)\).
Column B is in the form \(ab - ac\).
According to the distributive property, these two expressions are algebraically identical. Therefore, the quantities must be equal.
Step 4: Verification by Calculation (Optional):
We can also calculate the value in Column A.
\[ (109)(87 - 14) = (109)(73) \] For Column B, we can factor out the common term 109:
\[ (109)(87) - (109)(14) = 109 \times (87 - 14) = (109)(73) \] Both columns simplify to the same expression.