The question stem appears to be missing. Based on the options provided, this may be a numerical calculation pr

Question

The question stem appears to be missing. Based on the options provided, this may be a numerical calculation problem.

Examoogle · Accepted Answer

The correct answer is Option B: 6.98. Use the algebraic identity $a^2 - b^2 = (a-b)(a+b)$ in the numerator where $a = 4.33$ and $b = 2.65$. Notice that $a - b = 4.33 - 2.65 = 1.68$, which directly cancels the denominator.

Step-by-Step Solution & Concepts:
Shortcut Trick: Use the algebraic identity $a^2 - b^2 = (a-b)(a+b)$ in the numerator where $a = 4.33$ and $b = 2.65$. Notice that $a - b = 4.33 - 2.65 = 1.68$, which directly cancels the denominator.

Formula Used: $$a^2 - b^2 = (a - b)(a + b)$$

Given: Expression: \frac{4.33 	imes 4.33 - 2.65 	imes 2.65}{1.68}

Steps: Step 1: Identify the algebraic identity: The numerator has the form $a^2 - b^2$ where $a = 4.33$ and $b = 2.65$. We apply the difference of squares identity: $$a^2 - b^2 = (a - b)(a + b)$$. Step 2: Substitute and simplify the expression: Substitute the factored form into the given expression: $$\frac{(4.33 - 2.65)(4.33 + 2.65)}{1.68}$$. Step 3: Cancel common terms: Since $4.33 - 2.65 = 1.68$, the term $1.68$ in the numerator cancels out with the denominator $1.68$.. Step 4: Perform final addition: Add the remaining numbers: $$4.33 + 2.65 = 6.98$$

Answer: B is correct because simplifying the expression using the identity $a^2 - b^2 = (a-b)(a+b)$ yields $4.33 + 2.65 = 6.98$.

Exam Tip: Recognizing standard algebraic identities ($a^2-b^2$, $(a+b)^2$) in numerical calculations saves valuable time in quantitative aptitude tests.

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