The difference between any two natural numbers is 10. What can be said about the natural numbers which are…
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?
There is only one such number.
There are only two such numbers.
There can be more than one such number.
No such number exists.
Solution
If two natural numbers differ by 10, the interval strictly between them contains 9 consecutive integers. Multiples of 5 occur every 5th integer, so within a span of difference 10 exactly two multiples of 5 will lie strictly between the two numbers (e.g. between 3 and 13: 5 and 10). Hence there are only two such numbers - answer (b).