Question

Write a pair of integers whose sum gives an integer smaller than only one of the integers.

Answer 1

Hint: We are asked to write a pair of integers in such a way that the sum of the integers is smaller than only one of the integers. So, you have to think a pair of integers say (a, b) then sum of a and b i.e. $a+b$ should be less than either only “a” or only “b” not both “a” and “b”.

Complete step-by-step answer:
In the above problem, we are asked to find a pair of integers in such a way that the sum of these pair integers is less than only one of them.
To select a pair of integers, let us take any two integers say $\left( 1,2 \right)$ adding these integers we get,
$\begin{align}
  & 1+2 \\
 & =3 \\
\end{align}$
Now, the summation of these integers is 3 which is greater than 1 or 2 which is not the requirement of the question.
So, the summation of two numbers is less than any of them is possible when we subtract two numbers but we have to add the two numbers so we will take one positive integer and one negative integer.
Let us take a pair of integers in which one integer is positive and other in negative integer say $\left( -2,1 \right)$ adding these two integers we get,
$\begin{align}
  & -2+1 \\
 & =-1 \\
\end{align}$
As you can see that summation of these integers is -1 which is less than 1 but greater than -2 so this pair of integers is satisfying the condition of the question that the sum of a pair of integers is less than only one of them.
We can also write a pair of integers as $\left( -3,0 \right)$ adding these two integers we get,
$\begin{align}
  & -3+0 \\
 & =-3 \\
\end{align}$
The summation of the above integers is -3 and the summation is less than only one of the integers is (i.e. 0) so this pair of integers is also acceptable.
Similarly, you can find the other pair of integers too.
In the above, we have found the pair of integers $\left( -2,1 \right)\And \left( -3,0 \right)$ as the pair of integers whose sum is less than only one of the pair of integers.

Note: The plausible mistake that could happen is that you miss the line “sum gives an integer smaller than only one of the integers” here “only” is the catch because if you miss that then you might think that the result of addition can be smaller than one of the integers or both the integers. And you can give this pair of integers $\left( -3,-1 \right)$ also because addition of these integers will give -4 which is less than both these integers which is wrong so be careful while reading the problem.