A637362
B637400
C637962
D638638
Answer:
A. 637362
Read Explanation:
Efficient Multiplication Technique
For competitive exams, understanding and applying efficient calculation methods is essential for saving time. The multiplication problem involving 999 is a classic example where a simple trick can significantly speed up the calculation.
The core principle for multiplying numbers by a sequence of nines (like 9, 99, 999, etc.) is to recognize that these numbers can be expressed as (10n - 1).
In this specific case, 999 can be conveniently written as (1000 - 1).
Substitute this expanded form into the original expression: 638 × 999 becomes 638 × (1000 - 1).
Apply the distributive property of multiplication over subtraction, which states that a × (b - c) = (a × b) - (a × c).
Following this property, the expression transforms into: (638 × 1000) - (638 × 1).
Perform the individual multiplications:
638 × 1000 is easily calculated by appending three zeros to 638, resulting in 638000.
638 × 1 simply equals 638.
The final step involves a straightforward subtraction: 638000 - 638.