Question

Aju once visited his friend's place, Amit to show him a Maths trick that he has learned. He asked Amit to multiply 10101 × 10101. While Amit was struggling to multiply, Aju did it in seconds. Amit was really amazed by the trick.
Can you determine the trick from the given options which left Amit totally puzzled?

• A. 102040201
• B. 10101 × (1000 + 100 + 1)
• C. 10101 × (10000 + 1000 + 1)
• D. 10101 × (10000 + 100 + 1)

Answer 1

The correct option is D 10101 × (10000 + 100 + 1)

If you try to multiply 10101 × 10101 by a conventional method, it might take you a long time.
It would go as:
10101
×10101
10101
00000
10101
00000
10101____
102030201

But if you use brackets instead, the work becomes so easy.
In 10101, the highest place is ten thousand.
So, 10101 - 10000 = 101
So, 10101 = (10000 + 101) ---------------------------------- Equation (1)
Now, in 101 highest place is hundreds.
So, 101 - 100 = 1
So, 101 = (100 + 1) -------------------------------------------- Equation (2)

Using equations (1) and (2), we can write 10101 as (10000 + 100 + 1)
So, 10101 × 10101 = 10101 × (10000 + 100 + 1)
= 101010000 + 1010100 + 10101
= 102030201

That's why Aju was able to do it so fast.