Question

What is the missing digit which makes the number 34_ exactly divisible by 2?
A. 0
B. 7
C. 5
D. 3

Answer 1

Hint: In this question we have to find out the missing digit such that if we find the missing digit and put it at the respective place, the number so formed is exactly divisible by 2. So here we have to know about the criteria of divisibility by 2. Any number which is divisible by two must have an even number.it means that that the number is in the form of $ 2n $ where n is any integer. In other words, even numbers are those numbers which have 0,2,4,6,8 at unit place.so put all the options one by one and look for the number which is in the form of $ 2n $ .

Complete step-by-step answer:
From the question we have to find out the digit which makes the number 34_ exactly divisible by 2.
Since the number is divisible by 2, it is an even number, so the unit place is either 0,2,4,6 or 8.
Now if we put the missing digit 0, we get the number 340. This number can be written as
 $ 340=170(2) $ , which is in the form of $ 2n $ . So the number is 340 which is exactly divisible by 2.
Let us now inspect the other options
If we put missing digit as 7 we get the number 347 which can be written as
 $ 347=173(2)+1 $ which is in the form of $ 2n+1 $ so the number 347 is not divisible by 2.
If we put missing digit as 5 we get the number 345 which can be written as
 $ 347=172(2)+1 $ which is in the form of $ 2n+1 $ so the number 345 is not divisible by 2.
If we put missing digit as 3 we get the number 343 which can be written as
 $ 347=171(2)+1 $ which is in the form of $ 2n+1 $ so the number 343 is not divisible by 2.
Hence, we see that option A is correct.

Note: Any number which is not divisible by 2, is an odd number. The odd number is $ 2n+1 $ .
Also, we see that between any two consecutive odd numbers there is one even number and between any two consecutives even numbers there is one odd number.