Question Details

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?

Options

A

There is only one such number.

B

There are only two such numbers.

C

There can be more than one such number.

D

No such number exists.

Show Answer

Correct Answer :

Option C

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 a and b, where b>a.
The difference between the two numbers is 10, which means:
b-a=10 or b=a+10.

We need to determine how many natural numbers divisible by 5 lie strictly between a and b (i.e., in the range (a,b)).

Step 2: Test Different Cases with Examples

Case 1: Suppose a=4 and b=14 (difference is 14-4=10).
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 a=5 and b=15 (difference is 15-5=10).
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 a=1 and b=11 (difference is 11-1=10).
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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