Question

The number of whole numbers between the smallest whole number and the greatest 2-digit number is
(a) 101
(b) 100
(c) 99
(d) 98

Answer 1

Hint:For solving this problem, we first find out the smallest whole number as 0. Now we evaluate the greatest two-digit number as 99. By obtaining these numbers, we can easily find out the numbers lying between the smallest whole number and greatest two-digit number by using arithmetic progression.

Complete step-by-step answer:
According to the problem statement, we are required to find out the number of whole numbers lying between the smallest whole number and the greatest two-digit number.
Now, from the definition of whole number, the smallest possible whole number is 0. In the number system, the greatest possible two-digit number is 99.
Now, the series of numbers lying between 0 and 99 can be represented as: {1, 2, 3, 4………97, 98}.
The above series forms and A.P. whose first term is 1 and last term is 98 with the common difference of 1. By using the general expansion of A.P., we get $l=a+\left( n-1 \right)d$
On putting First term a = 1, last term l = 98, and common difference d = 1, we get
$\begin{align}
  & 98=1+\left( n-1 \right)1 \\
 & n-1=98-1 \\
 & n-1=97 \\
 & n=97+1 \\
 & n=98 \\
\end{align}$
Therefore, the number of numbers lying between the smallest whole number and greatest two-digit number is 98.
Hence, option (d) is correct.

Note: This problem can be alternatively solved by simple observation of a series of numbers lying between 0 and 99. Excluding 0 and 99, we have a total 98 whole numbers. Therefore, the answer is 98.