The difference between any two natural numbers is 10. What can be said about the natural numbers which are divisible by 5 and lie between these two numbers?
Correct Answer :
There can be more than one such number.
Solution :
The correct option is: There can be more than one such number.
Let us analyze the problem step-by-step to understand why this statement is true.
Step 1: Understand the Given Information
We are given two natural numbers. Let these two natural numbers be and , where .
The difference between the two numbers is 10, which means:
or .
We need to determine how many natural numbers divisible by 5 lie strictly between and (i.e., in the range ).
Step 2: Test Different Cases with Examples
Case 1: Suppose and (difference is ).
The natural numbers lying between 4 and 14 are: 5, 6, 7, 8, 9, 10, 11, 12, 13.
Among these numbers, the numbers divisible by 5 are 5 and 10.
In this case, there are two such numbers.
Case 2: Suppose and (difference is ).
The natural numbers lying strictly between 5 and 15 are: 6, 7, 8, 9, 10, 11, 12, 13, 14.
Among these numbers, the only number divisible by 5 is 10.
In this case, there is one such number.
Case 3: Suppose and (difference is ).
The numbers lying between 1 and 11 are: 2, 3, 4, 5, 6, 7, 8, 9, 10.
The numbers divisible by 5 are 5 and 10.
In this case, there are two such numbers.
Step 3: Conclusion
Depending on the choice of the initial natural numbers, the count of multiples of 5 lying strictly between them can be either 1 or 2.
Therefore, it is correct to say that there can be more than one such number (since having 2 such numbers is possible depending on the pair of numbers chosen).
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