Answer: Option C

Explanation:
7 × 100 = 700

Answer: Option C

Explanation:
Place value = Local value
Face value = Absolute value
The place value of 4 in 564823 is 4 x 1000 = 4000
The face value of 4 in 564823 is nothing but 4.
=> 4000 x 4 = 16000

Answer: Option A

Explanation:
Place value = Local value
Face value = Absolute value
The place value of 3 in 5769354 is 3 x 100 = 300
The face value of 3 in 5769354 is nothing but 3.
=> 300 x 3 = 900

Answer: Option C

Explanation:
23257 is not divisible by 3
23057 is not divisible by 3
23157 is divisible by 3
23357 is not divisible by 3
2+3+1+5+7 = 18
18/3 = 6.
x = 1

Answer: Option B

Explanation:
123p578
1 + 3 + 5 + 8 = 17
2 + p + 7 = 17
=> 9 + p = 17
=> p = 17 - 9 
=> p = 8

Answer: Option B

Explanation:
Local value of 4 = 4 x 100 = 400
Place value of 4 = 4
There fore = 4 x 400 = 1600

Answer: Option C

Explanation:
The sum of the digits of the number is divisible by 3, then the number is divisible by3.
2 + 3 + x + 5 + 7 = 17 + x
Least value of x may be 1
Therefore 17 + 1 = 18 is divisible by 3.

Answer: Option A

Explanation:
The sum of the digits of the number is divisible by 9.
Then the number is divisible by 9.
2 + x + 5 + 4 + 7 + 2 = 20 + x
Least value of x may be '7',
So that the total 20 + 7 = 27
is divisible by 9.
 

Answer: Option A

Explanation:
The Difference of the sum of the digits at odd place and the sum of the digits at even place of the number, is either 0 or a number divisible by 11.
(1 + 3 + 5 + 8) - (2 + k + 7) = 17 - 9 - k = 8 - k 
Therefore if k = 8, then the value become zero.
k = 8 is the least value 
so that 123k578 is divisible by 11.

Answer: Option D

Explanation:
Sum of first 'n' natural numbers = n(n + 1)/2
Sum of first 9 natural numbers = 9(9 + 1)//2 = 9 x 5 = 45
Sum of first 99 natural numbers = 99(99 + 1)//2 = 99 x 50 = 4950
4950 - 45 = 4905