Question

How many whole numbers are there between 45 and 54?

• A. 11
• B. 10
• C. 9
• D. 8

Hint:

- Whole numbers: \{0, 1, 2, 3, ...\}. - "Between a and b" typically means strictly greater than a and strictly less than b (i.e., a and b are excluded). - To count integers from \(x\) to \(y\) inclusive: \(y - x + 1\). - To count integers strictly between \(a\) and \(b\): count integers from \(a+1\) to \(b-1\) inclusive. Number = \( (b-1) - (a+1) + 1 = b-a-1 \).

Answer 1

The Correct Option is D

Step 1: Understand the term "whole numbers".
Whole numbers are non-negative integers: 0, 1, 2, 3, .
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.

Step 2: Understand the phrase "between 45 and 54".
This means we are looking for whole numbers \(N\) such that \( 45<N<54 \).
The numbers 45 and 54 themselves are not included.

Step 3: List the whole numbers that satisfy this condition.
The whole numbers greater than 45 are 46, 47, 48, .
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.
The whole numbers less than 54 are .
.
.
, 51, 52, 53.
So, the list of whole numbers between 45 and 54 is: 46, 47, 48, 49, 50, 51, 52, 53.

Step 4: Count the numbers in the list.
There are 8 numbers in the list.

Step 5: Alternatively, use a formula.
The number of integers (or whole numbers) strictly between two integers \(a\) and \(b\) (where \(a<b\)) is \( (b-1) - (a+1) + 1 = b-a-1 \).
Here \(a=45, b=54\).
Number of whole numbers = \( 54 - 45 - 1 = 9 - 1 = 8 \).
Or, the numbers are from \(a+1\) to \(b-1\).
Number of terms = \( (b-1) - (a+1) + 1 \).
The numbers are \(45+1 = 46\) to \(54-1 = 53\).
Number of terms = \(53 - 46 + 1 = 7 + 1 = 8\).
This matches option (4).