Question

If x is the sum of the following 3000 numbers: 3000 digits 2,22,222,......,222....222  , then the last four digits (thousands, hundreds tens, units) of x are................

Answer 1

Answer:

So, the last four digits of x are 9580.

Step-by-step explanation:

As the question is given, X=2+22+222+2222+...+ 222... up to 3000 digits.

Step 1

Adding the digits at the units place, we get

2 + 2 + 2 +... 3000 times. We can say 3000*2=6000

∴Last digit of X is 0.

Step 2  

Adding the digits at the tens place, we get

2 + 2 + 2+ ... 2999 times+600. We can say 2*2999+600 = 6598

Tens digit of x is 8.

Step 3

Adding the digits at the hundreds place and the carry, we get

2 + 2 + 2 + ... 2998 times+659 = 2 × 2998 + 659 = 6655

Hundreds digit of X is 5.

Step 4

Adding the digits at the thousands place, we get

2 + 2 + 2 + ...2997 times + 665 = 2 × 2997 + 665 = 6659

Thousands digit of X is 9.

So, the last four digits of x are 9580.