Question

State whether the given statement is true or false.
If n, p ,q, and r are consecutive integers, their sum is odd.
\[{\text{A}}{\text{. }}\]true
${\text{B}}{\text{.}}$ false

Answer 1

Hint: Here we have given n,p,q,r are consecutive integers that means we can write p = n+1, q= n+2, r=n+3
Now when we add them we have only one variable that is n so now further solution will be little bit easy because previously we have four variables that will be tough to solve.

Complete step-by-step answer:
We have given n,p,q,r four consecutive integers and we have to comment on whether their sum either sum is odd or something else.
It is given that these are consecutive integers that mean we can write p=n+1, q=n+2, r= n+3
We have to find
N+p+q+r= n+n+1+n+2+n+3
Sum is equal to 4n+6
Here n is a variable that means it can be even or odd but when we multiply by 4 it becomes even because we know that when we multiply any number by an even number we always get an even number.
And hence 4n is an even number and when we add 6 in it it will be even because we know that the sum of two even numbers is always an even number.
Hence option B is the correct option.

Note:Whenever we get this type of question the key concept of solving is we can solve as solved above but in this type of question we can solve by taking example then it will take much less time like assume 1,2,3,4 as four consecutive number and their sum is 10 that is even number that sum of four consecutive number is even number not odd.