Question

If N divided by 5 leaves a remainder of 4, and N divided by 2 leaves a remainder of 1 , then the one’s digit of N is?

Answer 1

Hint: Focus on the point that the number is an odd number as it is given that it leaves the remainder 1 when divided by 2. Also, as it is a number which leaves a remainder 4 when divided by 5, so the nearest multiple which is less than or equal to N is having the last digit as 5.

Complete step-by-step answer:
First let us start by using the statement that N divided by 2 leaves a remainder of 1. Using the statement we can say that the number N is an odd number as it is not divisible by 2. Now the other statement given in the question states that, if the number N is divided by 5 leaves a remainder 4. We also know that a number is divisible by 5 if its unit digit is either 5 or zero. So, let us analyse the case one by one by taking the unit digit of the largest number which is divisible by 5 and less than N.
First case is when the unit digit of the largest number which is divisible by 5 and less than N be 0. So, the unit digit of N will be 0+4=4. But unit digit 4 implies N is even, so this case is not possible.
Now we will consider the unit digit of the largest number which is divisible by 5 and less than N be 5. So, the unit digit of N will be 5+4=9, which is a possible case.
Therefore, we can conclude that the one’s digit of N is 9.

Note: It is very important that you interpret the statements given in the question according to your need. Also, you need to be very clear about the properties of the numbers which are divisible by 2, 5, 10 and other important numbers. For example: the number which is divisible by 5 has either 0 or 5 as its unit digit.