Use the difference of squares identity to simplify: Compute (69842 × 69842 − 30158 × 30158) ÷ (69842 − 30158) quickly.

Introduction / Context:Large-number arithmetic becomes trivial with algebraic identities. Here, recognizing the difference of squares lets us replace bulky computation with a one-line simplification, ideal for speed and accuracy in aptitude tests.

Given Data / Assumptions:

• Expression: (a^2 − b^2) ÷ (a − b) where a = 69842 and b = 30158.
• All arithmetic is exact integers.

Concept / Approach:Use the identity a^2 − b^2 = (a − b)(a + b). After cancellation with the denominator (a − b), the whole expression reduces to a + b. This avoids any need to compute squares explicitly.

Step-by-Step Solution:Recognize a^2 − b^2 = (a − b)(a + b).Divide by (a − b): ((a − b)(a + b))/(a − b) = a + b.Compute a + b: 69842 + 30158 = 100000.

Verification / Alternative check:Any direct computation of the squares will be huge but will still reduce to the same sum after cancellation. The identity guarantees correctness.

Why Other Options Are Wrong:69842 and 30158 are the original terms, not their sum; 39684 is their difference; 0 would require a = b, which is false.

Common Pitfalls:Attempting to square first; arithmetic overflow or time wastage; forgetting to apply the difference of squares identity.

Final Answer:100000